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THOMAS BRADWARDINE’S VIEW OF TIME:
A STUDY OF THE INTERRELATIONSHIP OF NATURAL
PHILOSOPHY AND THEOLOGY IN THE FOURTEENTH CENTURY

By

Edith Wilks Dolnikowski

A DISSERTATION

Submitted to
Michi an State University
in partial ful llrnent of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of History

1989

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ABSTRACT
THOMAS BRADWARDINE’S VIEW OF TIME:
A STUDY OF THE INTERRELATIONSHIP OF NATURAL
PHILOSOPHY AND THEOLOGY IN THE FOURTEENTH CENTURY
By

Edith Wilks Dolnikowski

Thomas Bradwardine is widely regarded as one of the most inﬂuential
thinkers of the early fourteenth century, both in natural philosophy and theology.
Most studies of Bradwardine’s work focus on his contributions either to
mathematics and physics or to theology, with little attempt at integration. This
dissertation seeks to take a broader approach by assessing the extent to which
Bradwardine’s expertise in natural philosophy inﬂuenced his theological outlook, as
he expressed in the De causa Dei, by examining his view of time as a mathematical,
philosophical and theological concept.

The investigation begins with two introductory chapters tracing discussions
about time from the classical period through the late thirteenth century. The next
three chapters concentrate on Bradwardine’s references to time in four
philosophical works, De propoﬂionibus, De continua, De incipit et destinit, and De
ﬁuuris contingentibus, in which he defines time as a successive, inﬁnitely divisible
continuum which encompasses all other continua. These chapters conﬁrm not only
Bradwardine’s indebtedness to traditional Euclidian mathematics and Aristotelian
natural philosophy in his treatment of time, but also his imaginative responses to the
challenges to these traditions which arose in the late thirteenth and early fourteenth
centuries. An additional chapter explores Bradwardine’s method for reconciling in
the De causa Dei his essentially Aristotelian definition of time with his Augustinian

notions of eternity and divine causality. The concluding chapter examines the

inﬂuence of Bradwardine’s ideas about time and related issues by comparing his
views with two younger contemporaries, Thomas Buckingham and Robert Holcot.
This study reveals that Bradwardine employed the conventional Augustinian-
Boethian distinction between the temporal existence of created being and the
eternal timelessness of God to justify those controversial positions on
predestination, grace and free will which have led to a major historiographical
debate about the true direction of his theology. By examining Bradwardine’s
theological positions from the perspective of late medieval approaches to time and
by comparing these views with those of his contemporaries, however, one arrives at
a more complete understanding of Bradwardine’s thought as a whole than studies of

either his natural philosophy or his theology alone permit.

ACKNOWLEDGMENTS

I would like to acknowledge the guidance and support of my entire graduate
committee, Dr. Stanley Chojnacki, Dr. Alan Fisher and Dr. Eleanor Huzar and
particularly Dr. Emily Z. Tabuteau and Dr. Richard E. Sullivan who prepared me
for the work of writing this dissertation.

I also wish to acknowledge the assistance given to me by Dr. Maurice Keen
and Dr. Jeremy I. Catto, who served as my supervisors during my year of research at
Oxford University, and Dr. William J. Courtenay of the University of Wisconsin,
who has made many useful suggestions in the course of my research. In addition, I
wish to thank the Fulbright Commission for providing the means for me to conduct
my research abroad.

I am both very grateful and deeply indebted to my parents and parents-in-law
for their encouragement and practical help which they have given to me throughout
my graduate career. My greatest gratitude, however, goes to my husband, Greg,
whose unfailing kindness and sense of humor have made my years as a graduate

student both a happy and a productive time.

iv

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

List of Abbreviations ....... - - vi
Introduction.-.- - - ....... -1
Chapter Two: Classical and Early Medieval Views of Time -- - _ - - 14
Chapter Three: Thirteenth-Century Approaches to Time - - - 46
Chapter Four: Mathematics, Proportionality and Time - _ -73
Chapter Five: Time and Continuity _ 101
Chapter Six: Time and Contingency _ --131
Chapter Seven: Time in the De causa Dei ...... - 162
Conclusion _- . 203
Notes
Introduction - -_ _- - - _____ -231
Chapter Two -- - _ - - - ..... -- -- -225
Chapter Three- -- - - 243
Chapter Four - - 252
Chapter Five -- .......... - - ..... - 258
Chapter Six - - -- - -269
Chapter Seven--- - _ 279
Conclusion - -_ -- - -- -- -- _ - ----- 298
Bibliography
Primary Sources- -- - -_ ..... - 302
Secondary Sources _ -- _ - ..... 308

AHDL

Barnes

CHLMP

De causa Dei

De continua

Deﬁuw'is

De incipit

De prapartianibus

MTSM

LIST OF ABBREVIATIONS

Archives d ’histaire dactrinaire et littéraire du mayen age.

The Complete Works afAn'statle: The Revised Oxford
Translation, Volume 1. Ed. Jonathan Barnes.
Princeton: Princeton University Press, 1984.

Cambridge History of Later Medieval Philosophy. Eds.
Norman Kretzmann, Anthony Ken and Jan
ngbzorg. Cambridge: Cambridge niversity Press,
1 .

Thomas Bradwardine. De causa Dei contra Pelagium, et
de virtute causarum ad suos Mertonenses, libn' tres.
Ed. Henry Saville. London: Ex Officina
Nortoniana apud Ioannem Billium, 1618.

Thomas Bradwardine. Tractatus de continua. Ed. John
Emery Murdoch. In "Geome and the Continuum
in the Fourteenth Century: A hilosophical
Analysis of Thomas Bradwardine’s ‘Tractatus de
Contmuo."‘ Diss. University of Toronto, 1957.

Thomas Bradwardine. Tractatus de ﬁttun's
cantingentibus. Ed. M. Jean-Francois Genest.
Recherches augustiniennes, 14 (1979), pp. 249-336.

Thomas Bradwardine. Tractatus de incipit et destinit.
Ed. Lauge Olaf Nielsen. In "Thomas Bradwardine’s
Treatise on ‘inci it’ and ‘destinit’: Edition and
Introduction." ahiers de l’Institute du mayen age
grec et latin, 42 (1982), pp. 1-83.

Thomas Bradwardine. Tractatus de prapartianibus. Ed.
H. Lamar Crosby. In Thomas afBradwardine, His
Tractatus de Prapartianibus: Its S ignificance far the
Development of Mathematical Physics. Madlson,
Wisconsin: University of Wisconsin Press, 1955.

Motion and Time, Space and Matter: Interrelatians in the
History of Philosophy and Science. Eds. Peter K.
Machamer and Robert G. Tumbull. Columbus,
Ohio: Ohio State University Press, 1976.

vi

SMPSL Moody, Ernest A. Studies in Medieval Philosophy,
Science and Logic: Collected Papers, 1933-1969.
London: University of Califorma Press, 1975.

RTAM Recherches de théalagie ancienne et médiévale.

vii

INTRODUCTION

Thomas Bradwardine is generally regarded as one of the most inﬂuential
English philosophers and theologians in the early fourteenth century. His
accomplishments in the fields of logic, mathematics, physics and theology,
outstanding in their own right, account for only part of his fame. His abilities
attracted the attention of a powerful patron, Bishop Richard of Bury, who helped
him to attain high public ofﬁce. As chancellor of St. Paul’s and confessor to Edward
111, Bradwardine demonstrated great skill in mastering the demands of ecclesiastical
and civil service and was rewarded with the see of Canterbury in 1349. Yet in spite
of his importance in fourteenth-century England and the survival of a relatively
large portion of his writings, many important aspects of Bradwardine’s thought
remain unstudied.

Historical research on Bradwardine in its present state does not successfully
integrate his philosophical and scientiﬁc ideas with his theological convictions.
Because of their highly technical nature and wide range of topics, Bradwardine’s
treatises present serious challenges to even the most skillful researchers. It is not
surprising, therefore, that most studies of his work consist of critical editions and of
commentaries on single texts rather than investigations of concepts which emerge in
various contexts throughout his writings. Taken together, however, existing studies
constitute a fairly complete record of Bradwardine’s academic work and provide
essential resources for a more synthetic approach to his thought. The recent growth
of interest in some of Bradwardine’s less well-known contemporaries, the men to

and for whom he wrote, has created a large body of supplemental material which

1

can be applied with good effect to an analysis of Bradwardine’s theological and
philosophical views.

This dissertation investigates the mathematical and philosophical
foundations of Bradwardine’s theology by considering his view of time, an issue
which interested almost all natural philosophers and theologians in the late Middle
Ages and which emerged in various contexts in all of Bradwardine’s major treatises.
Although some aspects of the problem of time, such as inﬁnity, continuity and
contingency, seem to be primarily philosophical, fourteenth-century thinkers
regularly considered these subjects in conjunction with more recognizably
theological topics such as eternity, divine foreknowledge and free will.1 In many
cases, in fact, it is impossible to separate philosophical concerns from purely
theological ones in late medieval discussions of time. Like many of his colleagues
and his thirteenth-century predecessors, Bradwardine tried to accommodate both
Aristotelian physics and Augustinian theology in his view of time. The
distinctiveness of Bradwardine’s approach to time resulted from his habit of treating
almost all intellectual inquiries, both physical and theological, from the perspective
of Euclidean mathematics. Bradwardine’s view of time therefore provides an
exceptionally clear example of the tendency among fourteenth-century thinkers to
explore theological truth through mathematical and philosophical means.

The speciﬁc aims of this dissertation are to describe the classical and
medieval corpus of speculation on time which Bradwardine inherited, to examine
his response to the problems of time in his early academic writing and to assess the
relative inﬂuences of Euclid, Aristotle and Augustine in his ﬁnal statements about
time in his monumental theological work, the De causa Dei, ﬁrst published in 1344.2
The purpose of this study is not just to show how one prominent fourteenth-century
thinker coped with a long—standing philosophical problem; it also seeks to examine

Bradwardine’s interaction with predecessors and contemporaries by focusing on a

topic which incorporates the methods and principles of several disciplines including
natural philosophy, logic and theology. This assessment of Bradwardine’s view of
time will help not only to establish the main issues in fourteenth-century academic
debates about time but also to assess Bradwardine’s particular role in those debates.

In spite of his many accomplishments, Bradwardine, like most fourteenth-
century personalities, remains a mysterious ﬁgure. What little is known about his
life comes primarily from his own writings and scattered references to his activities
at Oxford or in the service of Edward 111. Unfortunately, a purely textual approach
to the biography of such an obscure figure as Bradwardine can give a distorted
image of his character. One observer, Gordon Leff, has even suggested that an
uncritical reading of Bradwardine’s treatises might make him appear to be "an
inhumane genius" who "can hardly be called lovable."3 Although he enjoyed
prominence as a mathematician and theologian at Oxford in the 13205 and 13305
and eventually rose to the highest ecclesiastical ofﬁce in England, no historian has
yet been able to construct a biography for him which is as full, for example, as the
one which Katherine Walsh has been able to produce for his slightly younger
contemporary, Richard FitzRalph.4 Historians have estimated that Bradwardine
was born some time during the last two decades of the thirteenth century, probably
in the early 12905. There is no evidence of his birthplace but an oblique reference
in the De causa Dei to his father as living in Chicester suggests that he might have
come from Hertﬁeld or Heathﬁeld in Sussex.5 According to Oxford University
records Bradwardine resided at Balliol College, where he was a fellow from 1321 to
1323. In 1323 he accepted another fellowship at Merton and spent the next three
years completing his regency in the arts. Sometime during this period he becar‘m
the proctor of Merton; afterwards he served as Chancellor of the University.6

While at Merton Bradwardine was introduced to the brilliant circle of

nathematicians, logicians, physicists and astronomers whose work contributed to

the outstanding reputation for natural philosophy which Oxford University enjoyed
in the first half of the fourteenth century. Bradwardine’s early academic work
clearly indicates that he ﬂourished in this stimulating academic setting. Within a
decade of his arrival at Merton he had composed several important treatises on a
wide range of scientiﬁc and logical topics, including velocity, proportionality,
continuity, contingency, memory and signiﬁcation. His achievements in these ﬁelds

"7 and to compare his

alone have led historians to call him a "mathematical genius
works in physics favorably to those of Galileo.8 As a consequence of this
remarkable productivity, Bradwardine attracted the patronage of Richard of Bury,
Bishop of Durham, who was instrumental in encouraging scientiﬁc inquiry of all
kinds during the second quarter of the fourteenth century and was a particular
patron of the fellows of Merton College.9 When he was invited to join Bishop
Bury’s household in 1335, Bradwardine entered a group of some of the most
talented natural philosophers of the mid-fourteenth century. The dedication of the
De causa Dei to his colleagues at Merton conﬁrms his recognition of the prestige
associated with his former college as well as his sincere affection for it.
Bradwardine’s ecclesiastical career was equally distinguished, thanks again,
in part, to ‘Bury’s inﬂuence. Within two years of entering into Bury’s service,
Bradwardine became Chancellor of St. Paul’s in London. In 1339 he took on the
additional responsibility of serving as Edward III’s chaplain and confessor. In
fulﬁlling this ofﬁce, Bradwardine was called upon to travel extensively with the king
both at home and on campaigns and missions abroad. According to J. A. Weisheipl
and Heiko A. Oberman, who have analyzed the text of the Serma Epinicius ascribed
to Bradwardine, he almost certainly accompanied Edward 111 on his French
campaign of 1346 and witnessed the battle at Crécy on August 26.10 They have also
suggested that he participated in the negotiations for peace with France, having

been appointed an envoy on October 22, 1346.11 Moreover, during the late 1330s

and 13405 Bradwardine came to be regarded through his preaching, lecturing and
writing as one of England’s most gifted academic theologians. The culmination of
his ecclesiastical career occurred in July of 1349, when he was consecrated as
Archbishop of Canterbury at Avignon.12 Originally elected to this ofﬁce by the
monks of Canterbury in 1348, Bradwardine had been unable to take up the ofﬁce
earlier, owing to the king’s resentment that the monks had acted without ﬁrst
consulting him. Edward III’s candidate, John Ufford, ﬁlled the ofﬁce instead; but,
when he died from the plague, the king acknowledged Bradwardine’s election.
Unfortunately, Bradwardine himself soon fell victim to the plague and died on
August 26, only one month after his consecration.

In spite of his remarkable achievements as a natural philosopher and public
servant Bradwardine’s reputation in the twentieth century is based on his theological
works, the interpretation of which has generated considerable controversy. The
source of this controversy is the long-established strain in historical literature which
connects Bradwardine’s predestinarian thought with Wyclif’s. Whatever the true
nature of his inﬂuence on Wyclif’s theology, however, it is clear that Bradwardine
arrived at his conclusions about God in a way which was altogether different from
Wyclit’s: whereas Wyclif’s theology developed out of his philosophical studies,
Bradwardine’s was the product of a deeply spiritual conversion which occurred while
he was still studying in the arts faculty.13

The often-quoted autobiographical account of this conversion experience in
the De causa Dei tells of Bradwardine’s sudden disillusionment with the discussions
of grace and free will which he sometimes heard as a student of philosophy. He
laments his early attraction to the "Pelagian" notion, which pervaded philosophical
speculation at Oxford, "that we are the masters of our own free acts, and that it

stands in our power to do either good or evil, to be either virtuous or vicious."14 It

was not sophisticated arguments or even faithful contemplation which transformed
his opinion. Rather, he says:
. . . before I had become a student of theology, the truth before
mentioned struck u on me like a beam of grace, and it seemed
to me as if I behel in the distance, under a transparent image
of truth, the grace of God as it is prevenient both in time and
nature to all good deeds - that is to say, the gracious will of
God which precedently wills, that he who merits salvation shall
be saved, and precedently works this merit of it lip him, God in
truth being in all movement the primary Mover.

This revelation subsequently inspired Bradwardine to devote his
considerable energy and talent to refuting the arguments of his opponents, whom he
labelled the "modern Pelagians." His Opinions about grace and free will matured
throughout his academic career and he apparently reﬁned his views both by
engaging in debates with his peers and by incorporating his ideas into his sermons
after 1335. The De causa Dei itself presented a scathing attack on the views of
Bradwardine’s adversaries. Far from being an open-ended speculative treatise of
the type which abounded generally in the 13205 and 13305, this work was consciously
polemical. In it Bradwardine applied the full vigor of his exceptionally analytical
mind to the vindication of the absolute necessity of God’s will as ﬁrst cause in every
human act. Bradwardine so forcefully defended his conclusions that readers of the
De causa Dei, from the fourteenth century to the twentieth century, have objected to
his apparently rigid determinism. Fourteenth-century critics simply complained that
his conception of God’s relationship to humanity unnecessarily restricted human
free choice. They tried to refute his claims by attacking Bradwardine’s deﬁnitions of
time, eternity and contingency and so emphasized, as Bradwardine himself had
done, the interconnection of natural philosophy and theology.

After the Reformation, however, the fourteenth-century approach to

Bradwardine’s theology was all but abandoned in favor of one which stressed his

advocacy of an Augustinian form of predestination. Thus Bradwardine came to be

regarded as precursor to the Reformation. In the nineteenth and early twentieth
centuries, historians saw Bradwardine primarily as a theologian and made almost no
attempt to investigate the phi1050phical principles which inﬂuenced his religious
thought. Even now, studies of Bradwardine’s theology have not been entirely freed
from such concepts as nominalism, Ockhamism and determinism, themes which
have dominated treatments of fourteenth-century theology since the late nineteenth
century. Moreover, no treatment of Bradwardine has tried to incorporate both his
theological and his scientific texts into a single study of his life and thought.
Bradwardine has emerged, therefore, as a fascinating but enigmatic ﬁgure whose
interests pulled in many different directions. Some historians, in studies of
Bradwardine’s contemporaries, have recently begun to challenge the assumptions of
the traditional interpretation of fourteenth-century intellectual life by closely
examining the philosophical foundations of late medieval theology.16
Bradwardine’s provocative ideas about the relationship of natural philosophy to
theology also deserve to be reconsidered in this way.

Since the late nineteenth century, Bradwardine’s reputation as a scholar has
rested on his supposed contributions to two distinct intellectual movements: early
modern science (through Galileo to Newton) and Protestant Reformation theology
(through Wyclif to Luther). Bradwardine’s treatments of geometry and physics are
well-known to specialists in the history of science. His theological works have
received even broader recognition because of his supposed inﬂuence on Wyclif.
Historians such as Sebastian Hahn, Gotthardt Lechler, Herbert Workman and J. F.
Laun, who pioneered the study of Bradwardine’s writings at the turn of the century,
stressed the connection between Bradwardine’s and Wyclif’s approaches to
predestination.17 Aside from Wyclif’s role in exposing some of Bradwardine’s
theological views, however, this association with Wyclif has actively harmed his

reputation, not so much by implicating him in the Wyclifﬁte heresy as by distorting

his views in order to force them into forms which are recognizable components of
Wyclif’s thought.

Some of the problems of this traditional approach have been corrected in
two major studies of the De causa Dei: Gordon Leff’s Bradwardine and the Pelagians
(1957) and Heiko A. Oberman’s Archbishop Thomas Bradwardine, A Fourteenth-
Century Augustinian (1958).18 Because of their emphasis on theology and their
tendency to concentrate only on' the De causa Dei, neither historian does full justice
to Bradwardine’s contributions to fourteenth-century thought. Nevertheless, their
profound disagreement over Bradwardine’s determinism still dominates discussions
of his theology. Their differences of opinion arise less from variations in their
reading of Bradwardine than from their assessments of his position in fourteenth-
and ﬁfteenth-century scholarly debate. Leff presents Bradwardine as a theological
radical whose determinism struck at the heart of the prevailing philosophical
attitude of the early fourteenth century. Oberman, by contrast, portrays
Bradwardine as a conservative Augustinian who was merely trying to defend a
moderate, orthodox view concerning God’s prescience and will against nominalist or
Ockhamist attacks. These variations in interpretation arise fundamentally from
divergent views of the intellectual climate of the early fourteenth century. The
differences between Left’s and Oberman’s approaches to Bradwardine suggest,
therefore, that there is still room for discussion of such topics as Bradwardine’s
purpose in writing the De causa Dei, the composition of his audience, his sources
and the impact of his work on his contemporaries and successors. One of the
central aims of this dissertation, therefore, is to resolve some of the questions
suggested by the debate between Leff and Oberman by considering those questions
from the perspective of Bradwardine’s view of time.

Bradwardine’s work in natural philosophy had also begun to receive

attention by mid-century. If the commentators on the De causa Dei rarely mention

his scientiﬁc achievements, however, the historians who have examined his writings
on physics and mathematics have been just as disinclined to discuss his theology.
Apart from some critical editions, moreover, there have been no full-length studies
of Bradwardine’s scientiﬁc work comparable to the monographs of Leff and
Oberman. Anneliese Maier, Marshall Clagett, James Weisheipl and John Emery
Murdoch have made the greatest contributions to our knowledge of Bradwardine’s
scientiﬁc work through their specialized studies of his writings. None of these,
however, has explored either the full range of his scientiﬁc thought or the
relationship between his conception of natural phi1050phy and his theology.
Fortunately, interest in Bradwardine has remained strong in the last three
decades, and, despite the absence of fresh attempts to examine his thought as a
whole, he still attracts the attention of historians of late medieval intellectual and
religious life. The major thrust of current research is to determine as accurately as
possible what Bradwardine said and did between 1325 and 1349. To achieve
precision in dating Bradwardine’s career, historians have tried to examine the entire
corpus of his writings as well as the works of contemporaries with whom he
conversed. Lauge Olaf Nielsen, Hiiner Gillmeister, Niels-Jorgen Green-Pedersen
and Jean-Francios Genest have enlarged the body of printed material on
Bradwardine with their editions of some of his less known texts.19 Historians like
Zenon Kaluza and Katherine Walsh have made good use of this fundamental
research and have succeeded in correcting errors about Bradwardine’s position in
the schools at the beginning of the fourteenth century.20 Since they are most
interested in Bradwardine’s relationship with men such as William Ockham, Adam
Wodeham, Thomas Buckingham and Nicholas Aston, these historians have
concentrated on the common philosophical and theological concerns in their
thought, although there is ample opportunity for comparisons of their natural

philosophy as well.

10

This dissertation contributes to the current phase of research by presenting a
synthetic study of one aspect of Bradwardine’s thought. Though many historians
have remarked in passing on the mathematical structure and geometric precision of
his arguments in the De causa Dei, none has yet examined this text from the
perspective of his previous writings on mathematics and philosophy. A fundamental
concept in many of Bradwardine’s works is his deﬁnition of time, both in theological
and in natural terms. By exploring the approach to time in a series of his texts and
by comparing his opinions with those of his contemporaries, I hope to establish the
context for the assertions about time, contingency, divine foreknowledge and
predestination which he presented formally in the De causa Dei. The questions
which I shall address are: 1) To what extent does Bradwardine’s view of time make
him a determinist? 2) How did his conception of time as a physical entity inﬂuence
his theology, and how did he reconcile his Aristotelian physics with his Augustinian
theology? 3) Is there any correspondence between Bradwardine’s approach to time
and the approaches of his "Pelagian" adversaries, particularly William Ockham, and,
if so, what is the signiﬁcance of that correspondence? 4) How does Bradwardine’s
view of time ﬁt into his theological and scientiﬁc thought as a whole? Through a
systematic analysis of Bradwardine’s writing about time, I shall describe the close
relationship between natural philosophy and theology in fourteenth-century
academic discussions using a wider spectrum of Bradwardine’s responses to these
discussions than any historian has yet considered for this purpose.

This dissertation will consist, therefore, of three parts. In two introductory
chapters, I shall try to provide the historiographical context for studying
Bradwardine’s view of time by reviewing the antecedents of late medieval
discussions about time. Chapters Two and Three will summarize the medieval
debate about time and issues related to time from Peripatetic discussions in the ﬁfth

century B. C. to Bradwardine’s immediate thirteenth-century predecessors. These

11

chapters will emphasize the importance of the legacy of classical approaches to
medieval discussions of time. Although long-standing tension between Plato’s
metaphysical and Aristotle’s more physical approaches to time lay at the heart of
the medieval debate, many other thinkers were drawn to the problem of time and
made signiﬁcant original contributions. By the fourteenth century, a rich and varied
literature on time and subjects relating to time had become the foundation of the
arts curriculum, and no trained philosopher or theologian could escape its inﬂuence.
Time was one of the many concepts which emerged in philosophical and theological
debates in the schools. Discussions of such topics as contingency, continuity, inﬁnity
and motion all depended on explicit or implicit deﬁnitions of time and thus assured
frequent. reference to the various aspects of time. To understand Bradwardine’s
positions on these issues it is necessary to establish the character of academic
debates about time at Oxford on the eve of his arrival.

Chapters Four, Five and Six present a systematic examination of four of
Bradwardine’s treatises written in the 13205 which reveal the major elements of his
approach to time. The tracts De prapartianibus and De continua, both dating from
the late 13205, are examples of Bradwardine’s contribution to Oxford’s
achievements in the physical sciences in the late Middle Ages. Bradwardine’s
reputation as a mathematician rests on his innovative solutions to problems in
classical physics involving motion, velocity and inﬁnity. Since these topics all
demand speciﬁc reference to time, the De prapartianibus and the De continua deﬁne
Bradwardine’s view of time as a physical concept. Both treatises set out to endorse
Aristotle’s natural philosophy, but Bradwardine’s penetrating mathematical analysis
of velocity and continuity completely transformed Aristotle’s original positions. In
the former text, Bradwardine appeared to accept Aristotle’s definition of time but

reshaped the physical description of motion which underlay it. In the latter text,

12

Bradwardine used time to illustrate how one might apply the characteristics of
purely mathematical continua to physical continua, both permanent and successive.

Bradwardine’s De incipit et destinit and his De futuris cantingentibus are
primarily philosophical works which address two different aspects of the question of
foreknowledge. In the De incipit et destinit, Bradwardine argued that the future must
be considered contingent because the human mind cannot predict with certainty any
future event. In the De ﬁltllfiS cantingentibus, however, he maintained that the
future is not really contingent, since God, being outside time, knows all of his
creation in a single eternal present. These texts represent Bradwardine’s earliest
attempts to work out the contradictions between human and divine perspectives on
time, eternity and knowledge, which he later explored at greater length in the De
causa Dei.

Chapter Seven will concentrate on Bradwardine’s mathematical and
philosophical approach to time as he deﬁned it in the De causa Dei. This analysis
will reveal that he did not see a conﬂict between his modified Aristotelian
conception of the physical universe and his passionate Augustinian theology. A
close examination of his conception of the role of time in creation, sin and grace will
demonstrate that it is impossible to evaluate Bradwardine’s theology without
reference to his natural philosophy and will consider why many previous studies of
the De causa Dei have not approached the treatise in this way. Bradwardine’s
unique method for synthesizing the two rather distinct views of time which came out
of these traditions reﬂects an intellectual outlook which links him at once with such
predecessors as Thomas Aquinas, Anselm and Grosseteste and contemporaries such
as William Ockham, Thomas Buckingham and Robert Holcot. To look at the De
causa Dei from the perspective of the single issue of time and in light of

Bradwardine’s earlier considerations of the same problem is a novel and fruitful

13

method for studying not only this signiﬁcant text but also Bradwardine’s thought as a
whole.

Throughout my investigation of Bradwardine’s view of time, I shall try,
wherever possible, to point out the connections between Bradwardine and Ockham,
who, though they are often portrayed as antagonists, actually shared many attitudes
toward science and theology and together helped to give the early fourteenth
century its distinctive intellectual character. In a concluding chapter, I shall attempt
brieﬂy to trace this legacy in their younger contemporaries, especially Thomas
Buckingham and Robert Holcot, in order to show how ideas were disseminated in
the mid-fourteenth century, a period of unusually vigorous philosophical and
theological speculation. The burden of this chapter will be to show that these
younger scholars, usually described as Ockhamists on account of their nominalism
and hence as Bradwardine’s enemies, actually had a much more complicated
relationship with their masters: they sometimes rejected aspects of Ockham’s
metaphysical approach to time in favor of Bradwardine’s views and they were
equally engaged in the attempt which dominated fourteenth-century academic life
to reconcile theology with new discoveries in natural philosophy. The discussions
about time between the younger and the more established scholars reﬂect,
therefore, the wide range of debate in the ﬁrst half of the fourteenth century over
the most effective way to relate natural philosophy and logic to theology in an age of
expanding scientiﬁc knowledge. More important, however, the ideas of these
younger scholars provide the best possible context for evaluating Bradwardine’s
attempt to promote his geometrical synthesis of Aristotle and Augustine at a time of

substantial reevaluation of all ancient authorities.

CHAPTER TWO

CLASSICAL AND EARLY MEDIEVAL VIEWS OF TIME

Bradwardine’s views about time, like those of most other medieval thinkers,
were inﬂuenced by classical discussions of the subject. We shall see that
Bradwardine and his contemporaries were very familiar with the full range of
classical treatments of time and were aware that most medieval approaches to time
relied on deﬁnitions or concepts derived from Plato and Aristotle. Indeed Plato’s
and Aristotle’s discussions of time encompass even earlier discussions which
signiﬁcantly inﬂuenced medieval views. Classical philosophers not only tried to
solve the difﬁculties of measuring, describing and deﬁning time, but they also
struggled to explain time’s cosmological signiﬁcance. Their debates produced a
vocabulary for analyzing time which has been used extensively even into recent
times, but was especially important in late medieval discussions.

Before attempting to assess late medieval approaches to time in general and
Bradwardine’s view in particular, it is necessary to establish the characteristics of the
classical and early medieval discussions of time. This chapter begins, therefore, with
a short assessment of thought about time among the pre-Socratic philosophers,
followed by a more thorough analysis of the ideas of Plato, Aristotle and Plotinus,
each of whose concepts made tangible contributions to late medieval debates. Next
will come a synopsis of Augustine’s approach to time, which, because of its highly
original and compelling synthesis of classical and Christian traditions, became a

foundation for discussions of time throughout the Middle Ages. Finally, Boethius’

14

15

view of time will be surveyed brieﬂy. Boethius’ writings about eternity enriched
Augustine’s approach by broadening the range of questions which Christian thinkers
should consider in their speculations about time; they became a major source for
Bradwardine’s own position on eternity. This survey of approaches to time from the
pre-Socratic philosophers to Boethius will serve both to introduce the concepts
which shaped late medieval discussions of time and to provide a context for
evaluating Bradwardine’s conception of time.

The earliest attempts to understand time arose, quite naturally, out of
curiosity over astronomical phenomena. Long before philosophers had begun to
contemplate the signiﬁcance of time as a metaphysical entity, human societies had
become skilled in reckoning time through lunar, solar or planetary cycles. The
characteristic feature of the view of time in ancient Mediterranean cultures,
however, was the absence of a conception of time which was distinct from individual
events. In his analysis of views of time in the ancient world, P. E. Ariotti contrasts
the "multiple times" of the Egyptians, Babylonians and Hebrews, in which
chronologies were marked by changes in natural phenomena, with the notion of
some ancient Greeks of a single time representing a neutral frame of reference for
establishing sequences of events.1 The ﬁrst evidence of a trend towards the
singularization of time is found not among philosophers but among Greek, poets
who created a separate nature for time by embodying its characteristics in a god,
Chronos.2 Some Greek thinkers, however, rejected deiﬁed time and began to
explore alternative conceptions of time, as well as other features of the natural
world such as space and motion, as abstract cosmological principles. Although these
early natural philosophers had difﬁculty separating concepts of time from those of
motion and space, their more sophisticated understanding of the practical aspects of

time helped them to reﬁne their ideas with increasing success.3

16

The ﬁrst debates about the nature of time in the Western tradition emerged
from the teachings of two pre-Socratic philosophers, Heraclitus of Ephesus and
Parmenides of Elea. Heraclitus’ main contribution, aside from his insistence that
the natural order was not created or inﬂuenced by anthropomorphic gods, was his
idea that natural occurrences and processes are cyclical4 but that the changes which
take place in the course of these cycles are nevertheless real.5 The Pythagoreans
adopted this principle of cycles and, in their attempts to analyze every aspect of
nature in terms of number, gave time a mathematical deﬁnition. The most concise
expression of the Pythagorean view of time is Archytas of Tarentum’s statement that
time is "the number of a certain movement, or also, in general, the proper interval of
the nature of the universe."6 Although some modern commentators confuse
Archytas’ understanding of "number" with Aristotle’s more precise use of the term
and therefore try to interpret Archytas’ statements from an Aristotelian point of
view, it is more accurate to see Archytas’ deﬁnition of time as representative of a
completely separate Pythagorean approach to time.7 Archytas’ signiﬁcance lies not
in his inﬂuence on Aristotle but in his introducing into the Western philosophical
tradition the concept of absolute and mathematical time.8

In contrast to Heraclitus, Parmenides and his followers doubted that time
and the changes which time seems to engender existed at all. Parmenides himself
argued that both motion and time are unreal because they lack permanence.9 The
cornerstone of his philosophy was the rejection of all multiplicity and change. His
student, Zeno, the best known adherent of the Eleatic system, tried to prove that
motion and time cannot exist with his four arguments against movement, or
"paradoxes." All four paradoxes hinge on the apparent contradiction that motion,
time and space can be conceived either as inﬁnitely divisible and continuous or as
indivisible and therefore discontinuous. Although his proofs of the unreality of

motion, time and space are contrary to the evidence of sensory observation, his

17

objections to contemporary definitions of time raised important philosophical
questions which subsequent thinkers had to address. It is ironic, of course, that
major advances in the philosophy of time should have been prompted by one who
denied time’s very existence,10 but the critical approach of the Eleatic school to
inﬁnity and continuity had an equally strong inﬂuence on the mathematization of
time in the late Middle Ages and beyond.11

A more direct inﬂuence still on medieval views about time was made by
Zeno’s contemporary Plato, who synthesized elements of both Parmenides and
Heraclitus in his own philosophical system. Like Parmenides, Plato believed that
reality could be found only in what was eternal and unchanging. Along with
Heraclitus, however, Plato acknowledged that the changes which human beings
constantly experience are signiﬁcant and have an aspect of reality about them which
must be accounted for in any study of nature. Plato tried to resolve this dilemma by
distinguishing the ﬂux, succession and sensibility of changing human experience
from certain eternal forms, ideas and values which give shape to ever-changing
human perception.12 In Plato’s cosmology, there is a creator and the reality of
creation depends on the existence of eternal being. Since creatures obviously are
not eternal, both because they pass in and out of existence and because they change
continually throughout their lives, they lack both being and eternity. Still, the
"becoming" of creatures is analogous to the "being" of the creator, just as the time in
which creatures experience this "becoming" resembles the creator’s eternity. If
creatures could share directly in the perfect being of the creator, there would be no
time.13

Although Plato thought that time is essentially unreal, he wrote extensively
about the characteristics of time and the relationship between time and eternity.
These treatments proved to be highly inﬂuential both in the classical period and

throughout the Middle Ages. His most concise statements about the nature of time

18

appear in his early dialogue, the Timaeus, an allegorical poem about creation. In it,
the protagonist, Timaeus, asserts that time was created along with the rest of the
universe and its existence depends on the existence of the universe: "Time, in fact,
came to be with heaven, that, as they were born together, they might also be
destroyed together, if they ever should be destroyed, and was fashioned on the
model of the everlasting, that heaven might be as like to it as might be."14 When
asked why the creator (God) had made the universe in the ﬁrst place, Timaeus
answers that God had wanted to bring order and harmony out of the primordial
chaos. Because God is good and desires only the good for his creation, ". . . he put
mind in soul and soul in body in fashioning the universe, so that he might be the
creator of a work that was fairest and best."15 The mind and soul of the universe
are discerned in the regularity of its motion: whatever order and harmony exist in
the universe are due to the intelligence which God has imparted to it. Because it
possesses the characteristics of mind and soul, the universe is an animal, a complete
animal in which all other intelligible animals and visible creatures are contained.16
Pleased at his creation of a living, moving universe, God wished to perfect it
further by making it even more like the divine model of an animal. Because the
model animal is eternal, however, and something created can never be eternal, God
made "a moving image of eternity, and in the very act of ordering the universe he
made an image of eternity abiding in it as unity, an eternal image proceeding
according to number."17 This image of eternity is time. The things which we use to
measure time, such as days, seasons and years, did not exist before the universe was
created but came into existence when and because the earth was made. The parts of
time which we call past and future are therefore created forms of time which are not
eternal. Eternal being simply is and does not become younger or older because of
time, just as the cycles and processes of change which we observe in sensible objects

do not occur in eternal being. Time imitates eternity, however; and, consequently,

19

we can understand at least something of the nature of eternity by studying its image
in time.18

As "an image proceeding according to number," time depends for its
existence on the orderly, measurable motions of created bodies. In the Timaeus,
Plato suggests that the regular movements of the sun, moon, stars and planets
determine and preserve the "numbers of time." These orderly celestial motions
allow us to measure time with mathematical precision. In contrast to the ancient
Greek religious tradition, which, for example, conceived of a year as a progression
of seasons, Plato deﬁnes the year much more precisely as the amount of time it
takes for the sun to leave and return to its position at the winter solstice. Similarly,
a month is deﬁned by the time it takes for the moon to complete its phases.19 Thus
time and motion are completely interrelated and are measures of each other. Like
a clock, the heavenly bodies moving through space provide an absolute standard of
time which is independent of human perception.20

The conception of time which Plato presents in the Timaeus is precise,
thoughtful and appealing. It gracefully reconciles the Eleatic demand for attributing
reality only to changeless being with Pythagorean observations about the
connections among motion, time and space. By making time coterminous with the
universe, it gives time, theoretically at least, a definite beginning and end. It
establishes the characteristics of time in such a way that one can observe and
comprehend them. Unfortunately, the Timaeus does not resolve all of the problems
which Plato’s predecessors had raised regarding time and, in fact, presents entirely
new ones. Certain difﬁculties arise simply from the metaphysical language which
Plato uses in the Timaeus. Such words as "God," "creation" and "goodness," which
function perfectly well in Timaeus’ allegorical explanations for the natural order,

also have explicit religious connotations which Plato almost certainly does not

intend. Moreover, he consciously chooses his metaphors not to render a

20

scientiﬁcally accurate account of creation but "to awaken in the soul of the reader
an insight into the nature of the universe and its motions that could be produced . . .
in no other way"?!1 Literal interpretations of Plato’s speciﬁc remarks about motion
. and time can lead to serious misunderstanding of his real intentions, as the
subsequent discussion of Aristotle’s criticism of Plato will illustrate.

The problem of misinterpreting Plato’s view of time is not conﬁned, however,
to his contemporaries or to those who take his metaphors too literally. Sometimes
confusion arises from the reader’s unwillingness to admit that inconsistencies in
Plato’s account of creation could be the result of Plato’s own mistakes, especially
when those readers have been trained to use a philosophical vocabulary which
insists on precise deﬁnitions for every term. D. Corish notes, for example, that
many readers refuse "to believe that when Plato speaks in the Timaeus of a situation
before time existed he is merely contradicting himself. Plato must be deliberately
using the fanciful language of the myth here . . . because ‘no sane man’ could believe
that there was anything before time."22 Corish suggests that it is more likely in this
case that Plato simply contradicted himself because he was "not quite used to the
full logical demands of temporal theory."23 Whether or not the contradiction was
deliberate, however, it is still true that many commentaries on Plato’s view of time
from the classical period to the present involve the sorting out of Plato’s seemingly
ambiguous position on "time before time" and eternity.

The most signiﬁcant source of confusion over Plato’s ideas about time is his
failure to consider all of the ramiﬁcations of his cosmological system. Although he
discussed various aspects of continuity and divisibility in the Timaeus and other
works, he offered no consistent treatment of these concepts, which were at the heart
of the conﬂict between the Eleatics and the Pythagoreans. Moreover, his cosmology
of time neglected completely the role of the human observer and thus sidestepped

many important questions concerning the objectivity or subjectivity of time. More

21

important still, Plato never resolved the paradox that time depends on the uniform
and continuous motion of the heavenly bodies, when, in fact, these bodies, being
themselves created, can never attain perfect continuity and uniformity. He openly
admitted in the Republic that the heavenly bodies are incapable of providing a
perfect order for time when he stated: "The genuine astronomer . . . will think it
absurd to believe that these visible material things go on forever without change or
the slightest deviation . . . ."24 Plato’s failure or unwillingness to account fully for
the discrepancies which existed in his description of creation stimulated subsequent
studies of time, motion and space. In spite of all its deﬁciencies, however, Plato’s
conception of time stands as a remarkable intellectual achievement which suggested
for the ﬁrst time a precise relationship between eternal being and the created,
sensible world.

Advances on Plato’s conception of time followed quickly through the
speculations of his student Aristotle. Although he neglected to acknowledge his
indebtedness to his teacher, Aristotle’s philosophy reveals his great dependence on
Plato. Aristotle cannot be credited with the full measure of originality which he
claimed for himself, but his systematic reevaluation of Plato’s work and his powerful
insights into the problems of time which Plato had posed without resolving make his
comments on time extremely important in their own right.” More signiﬁcant still
was his profound inﬂuence on almost all areas of medieval thought, including
natural philosophy, logic and theology. Through Aristotle’s imaginative synthesis of
classical natural philosophy, medieval thinkers were introduced not only to a large
body of information about the natural world but also to a sophisticated theoretical
framework for analyzing it. Any study of medieval conceptions of time requires,
therefore, some knowledge of Aristotle’s contributions to the subject.

Aristotle’s principal discussion of time is found in Book IV of his Physics. In

chapters 10 to 14 of this book, Aristotle addressed such problems as the nature of

22

the present, the reality of time and the relations among time, space and motion.26

Like Plato, Aristotle afﬁrmed the inseparability of time and change and deﬁned
time as the number (or measure) of motion.27 Aristotle demonstrated in the
development of these themes, however, that his understanding of motion and other
physical concepts was much more sophisticated than those of Plato as developed in
the Timaeus. Aristotle was prepared to accept Plato’s assertion that time depends
on the regular movement of the heavenly bodies and so is coterminous with the
universe, but he was troubled by Plato’s apparent willingness to deﬁne time solely in
terms of celestial motion. Moreover, because Aristotle saw time as an integral part
of nature and the reality of nature was paramount in his philosophy, he could not
conceive of time as unreal, as Plato had done.

Since his purpose in the Physics was to examine natural phenomena as
sensible objects, not to provide a cosmological explanation for them, Aristotle was
concerned with space, motion and time as features of observable reality. He did not
begin his analysis of time with the kind of creation myth which appears in the
Timaeus; his arguments move in the other direction, from precise deﬁnitions of
sensible phenomena to more general principles concerning natural processes.
Throughout his analysis of time there is the implication that Plato’s account of time
lacked scientiﬁc foundation. So while Aristotle frequently ended up reafﬁrming his
teacher’s conclusions, his different interpretation of fundamental concepts and his
more analytical outlook produced a conception of time which was quite distinct
from Plato’s.28

Aristotle’s fascination with the physical world led him to study change and
consequently time, the medium in which change occurs. Aristotle thought that,
although time is real in itself, it cannot be observed without observing some change,

because we can only perceive time in conjunction with change or motion: . . . when

the state of our minds does not change, or we have not noticed its changing, we do

23

not think that time has elapsed."29 The paradox of time is that, while it requires
change for its existence, it cannot be deﬁned solely in terms of movement: change
or movement happens within things, often at irregular rates, but time is always
uniform, distinct from objects and universal.30 Aristotle tried to resolve this
dilemma by deﬁning time as a kind of number, but not the discrete arithmetic
numbers which the Pythagoreans and Plato had applied to celestial measurement.
Unlike ordinary mathematical units, units of time do not have a minimum value. In
other words, time is not a number in the sense that it is composed of distinct,
indivisible units which we can count as if we were counting objects. Instead, a unit
of time is a measurable segment of the continuum of time in which a motion occurs.
As such, a unit of time can vary in duration according to the motion being measured,
unlike arithmetic units which all must have identical value.

Therefore, Aristotle concludes that "time is not a movement, but only a

movement in so far as it admits of enumeration." Furthermore, because 'we
discriminate the more or the less [of things] by number, but more or less movement
by time," time is a kind of number.31 Thus Aristotle conceives of time as a
magnitude consisting of a succession of connected parts. Because it has no
minimum it can be divided inﬁnitely and proceed, through addition, without end.
As a continuous entity, it cannot have a beginning or an end; and, because the world
is eternal, time must be also: . . these was never a time when there was not
motion, and there will never be a time where there will not be motion."32

After attempting to deﬁne time as an aspect of motion, Aristotle goes on to
consider its attributes, making use of an analogy between time and a line. The now
of time can be seen to represent a point on a line; the inﬁnite distances on either
side of the point represents past and future respectively. Like a point on a line, the

now of time both connects past and future and also serves as a limit to each.

Although Aristotle contends that the now functions simultaneously in these two

24

ways, he is careful to note that these functions are essentially different. The major
problem with the line analogy is that a point on a line is stationary, whereas the now
is continually moving from past to future.33 According to Aristotle, alluding again
to the complementarity of time and motion, the now is more like a point moving
along a line. Aristotle is careful, however, not to pursue this analogy too far. The
motion of a moving point is absolutely dependent on sequential movement in any
direction. Time, however, is continuous and must always move forward from past to
future. Thus Robert Cushman observes: "Aristotle insists that the ‘before-and-
aftemess’ of time is conceptually separable from motion, but in the actuality of
physical change it is not so separable."34

In addition to his more careful evaluation of the physics of time, Aristotle’s
greater awareness of the role of human perception in deﬁning time represents an
advance over Plato’s conception of time. Aristotle never went so far as to say that
time is in any way subjective or that its existence depends on human observation of
motion. Still, Aristotle’s dissatisfaction with Plato’s remote, objectified, celestial
time led him to consider the relationship between absolute time and the human
perception of it. In his analysis of the now, for example, Aristotle took the trouble
to examine the morphology of time. He was interested in how such expressions as
"suddenly," "presently," "long ago" and "lately" help to illustrate the function of time
in the process of change.35 On other occasions, as we have seen, he considered
whether time could exist without consciousness; and, although he failed to explore
this question in any great detail, be identiﬁed an important teleological problem
about time which others, most notably Augustine, would later develop more fully.36
Unfortunately, Aristotle, preferring to concentrate on the physical characteristics of
time, never reached a ﬁrm position on this confusing issue. His contribution was

mainly to point out that the issue of consciousness was a valid consideration in any

philosophical treatment of time.

25

It is easy to see how Plato’s conception of time might be misunderstood if
one were to approach it from the perspective of Aristotle’s deﬁnitions of motion,
number and measurement. The vocabularies of the two philosophers are similar
enough to cause confusion, and commentators have struggled with ambiguities of
terminology from classical times to the present. Despite this confusion, indeed to
some extent because of it, Plato’s and Aristotle’s views about time have exerted
tremendous inﬂuence on almost all subsequent approaches. This brief summary of
their ideas about time does not include analysis of all the speciﬁc points in the
Platonic and Aristotelian discussions about time which are relevant to this
dissertation: their opinions about continuity, inﬁnity and contingency are more
appropriately placed later in this dissertation. The purpose of this summary is
simply to introduce the fundamental concept of time’s relationship to motion and
change which persisted in deﬁnitions of time from the classical period until the late
Middle Ages.

The discussion about time entered a new phase in the third century A. D.
when the philosopher Plotinus tried to rehabilitate Plato’s cosmological system. In
his treatise "On Eternity and Time," Plotinus enlarged his predecessors’ conceptions
of time by giving time a moral dimension. Plotinus’ cosmology, while largely
dependent on Plato’s, nevertheless reﬂects the inﬂuence of Aristotle’s methods of
systematic analysis. His investigation of the problem of time proceeded according
to a well-organized critical review of all previous efforts to describe the distinction
between time and eternity. This analysis clearly reveals his unwillingness to accept
without question what Plato and Aristotle had said about time. After refuting both
non-Aristotelian and Aristotelian theories, Plotinus went on to develop his own
approach which integrated many of his predecessors’ views into a substantially new
perspective on the problem of time.37 His purpose was to demonstrate that time is

not merely a created and therefore imperfect measure of the universe, as Plato had

26

claimed. Plotinus thought instead that time belongs to a higher order than that of
the created universe and has a special relationship to eternity. His philosophical
system, in which time and eternity played a major part, attracted a wide audience.
His followers, often called the Neoplatonists because of their adherence to many of
Plato’s fundamental deﬁnitions and assumptions, produced a variety of
interpretations of Plotinus’ view of time. Because Plotinus and his followers had an
undisputed inﬂuence through Augustine on early Christian and medieval views of
time, some understanding of their philosophy of time is essential for this study.38
As the title of his treatise suggests, Plotinus considered it necessary to focus
on the interdependence of time and eternity. His initial descriptions of these two
concepts varied little from Plato’s: time relates to the "sphere of becoming and the
sensible universe," while eternity relates to the "everlasting nature."3’9 According to
Plotinus, we can arrive at a superﬁcial understanding of both becoming and the
sensible universe through intuition but it breaks down when we try to probe more
deeply. Although he felt assured that the "ancients of happy memory" had found
answers to the paradoxes of eternity and time, Plotinus wanted to make his own
inquiry so that he could discover the truth for himself. He thought this inquiry
should begin with eternity rather than time, "for if we know what the unchanging
model is, perhaps we can thereby arrive at a knowledge of its image, which we call
time."40
After considering various deﬁnitions of eternity, Plotinus concludes that
eternity encompasses every feature of the intelligible world, including motion and
rest, difference and identity. Eternity, says Plotinus, is
the life that is forever unchanging and possesses all its reality
in the present. There is no succession involved in this life,
since nothing has passed and nothing is to come, but whatever
it is it is always . . . . Since there is nothing that it can come to
assess that it does not already possess and nothing that it

oses of what it possesses, we cannot say of it that it was, or will
be, but only that it 18. Thus we ﬁnd that eternity is the life of

27

being in its very bailng, at once whole, complete and entirely
Without successron.

Plotinus later attributes to Plato the notion that the eternal nature is bound up with
unchanging being: Plotinus calls the unity of the eternal nature with unchanging
being the "One." Then he enlarges Plato’s cosmology by inserting another level
between the One and the sensible world. He makes the One the source of all unity
and goodness but without being or real knowledge. Eternity rests in the
intermediate stage of "intelligible essence . . . which may be thought of as an
unmoving circle which has the One or the Good as its center, and it is this proximity
to the very source of all unity that gives to the intelligible essence the kind of life we
call eternity."42

Turning now to time itself, Plotinus claims that time exists on the next step
below eternity in a series of states which link the sensible world with the One. He
begins his analysis of time with a review of three categories of theories about time’s
relationship to motion. First, he challenges the thesis that time is identical with
motion on the grounds that motion is in time and must therefore be distinct from it.
Motion, moreover, can be sporadic and cease, while time remains continuous.43
His arguments against this thesis rest heavily on Aristotle’s assertion that all things
moving or at rest are in time; and, in spite of a few minor discrepancies, Plotinus
largely accepts Aristotle’s deﬁnition as far as it goes. The chief difference between
their approaches centers on Aristotle’s apparent lack of interest in investigating the
relationship between the sensible world and the One."’4

Plotinus then criticizes a second theory of time which denies time any
existence apart from that of the moving sphere. Like Aristotle, Plotinus dismisses
this theory as untenable, though his method of refuting it is different from

Aristotle’s."5 Finally, Plotinus refutes the theory that time is an extension of motion

on the grounds that the extensions of all the many kinds of motion are too irregular

28

to account for the uniformity of time.46 Nor can Plotinus wholly accept Aristotle’s
argument that time is the number or measure of motion. Time certainly cannot be
the measure of particular motions, since "if we are to make time a measure of
motion and at the same time preserve the unity and continuity that we realize it
possesses, we cannot think of it as the measure of all motion, but only of a single,
uniform motion, speciﬁcally that of the universe."47

On the surface, this position simply qualiﬁes Aristotle’s own view without
opposing it. Another of Plotinus’ criticisms of Aristotle is more serious, however,
because it calls into question the validity of Aristotle’s technique for deﬁning time.
To describe time in terms of motion is acceptable on a superﬁcial level, he says, but
this approach cannot tell anyone what time actually is.48 Plotinus therefore looks to
Plato for a cosmological explanation of time which takes into account the
relationship between time and eternity.

Nonetheless, Plotinus’ cosmology is more complex than Plato’s for it is based
on a hierarchy of levels of existence instead of Plato’s two-fold division between
perfect eternal being and the "becoming" of the sensible world. Within this
hierarchy Plotinus places the intermediary of "soul" between eternity and time:
"Soul must precede time because we understand time to be related somehow to the
motion of the universe that is the product of soul; and time must precede motion, in
the order of nature, because we say that motion is in time."49 Plotinus’ view of time,
clearly echoing Plato’s, can be summarized as follows:

Time is an image of eternity, therefore, as life on a lower
level of perfection. ts striving to be as like eternity as possible
is the reason for its constant progress, in order that it may be a
whole in succession .as eternity is a perfect whole without
successron. ThlS strlvmg explains why time Will never end, for
its complete fulﬁllment is always beyond it. Time does not
proceed according to number because ideal number is ﬁxed at

a higher level, and to think that the soul producessb in
accordance with number conﬂicts with the inﬁnity of time.

 

29

Plotinus’ conclusions about time, then, though undeniably inﬂuenced by Aristotelian
physics, came out of a cosmological system which depended in large measure on
Platonic philosophy.

Plotinus did not follow Plato in every respect, however, particularly in
metaphysical matters. The essence of Plotinus’ theory of hierarchy of being is the
succession from lower to higher orders of existence. Whereas Plato regarded time
as a true image of eternity and a source of order and harmony on which one could
model one’s moral life, Plotinus perceived time as only one stage in a long series of
states of being which link the individual to eternity.51 Plotinus attracted many
disciples who embraced both the moral tone and the emphasis on levels which
characterize Plotinus’ philosophy. In fact, the Neoplatonists after Plotinus increased
the number of spheres in the hierarchy, even to the point of dividing time itself into
spheres, which resulted in many subtle variations in Neoplatonic approaches to
time.52 Modern philosophers have dismissed these approaches to time as too
complicated and untenable. Historians, theologians and philologists, on the other
hand, have made considerable efforts to understand the N eoplatonists because of
their tremendous inﬂuence on Christian and Islamic thought in the early Middle
Ages.53 Neaplatonic ideas are particularly important in any discussion of medieval
views of time because early Christian thinkers drew heavily on N eoplatonism when
they wished to provide a philosophical basis for their theological insights into time
and eternity. The moral outlook of the Neoplatonists as well as their unique
rendering of the relationship of time and eternity had an especially strong effect on
two of Bradwardine’s most important sources, Augustine and Boethius.

While the ancient Greeks and the Neoplatonists gave the problem of time a
special philosophical signiﬁcance, Augustine transformed it into a theological
problem as well. His most thorough and concise treatment of time appears in Book

XI of his Confessions, in which he presents time as a quality which arose out of

 

30

creation. Although he based his arguments ﬁrmly on the words of Genesis, and in
addressing the problem of time, desired only to arouse in himself and others greater
love of God,54 his analysis of time reﬂects the inﬂuence of his classical education.
Augustine’s contribution to the study of time is important not just because he
invested time with theological signiﬁcance: his attempt to solve the problem of time
was also highly original. Indeed, his "psychological" solution to the problem of time
has inﬂuenced discussions of time from the fourth century to the present.

1 Augustine’s view of time has received, therefore, a great deal of attention
from modern theologians, historians and philosophers. Their chief concerns have
been to explain what Augustine had to say about time and such related issues as
eternity, memory, creation, free will and contingency, but they also regard the
question of Augustine’s indebtedness to his predecessors as a crucial one. Those
who emphasize the continuity between classical views of time and Augustine’s view
focus on his special reliance on Neoplatonism, which he had followed before his
conversion to Christianity. Others, who wish to stress Augustine’s originality, argue
that many accounts of Augustine’s dependence on the Neoplatonists are
exaggerated.55

It is undeniable that Augustine’s conception of time depended on certain
concepts which he borrowed, consciously or unconsciously, from the Greek
philosophical tradition which formed the basis of his education. Like Plato’s
Timaeus, Augustine’s essays on time in the Confessions and the City of God have a
strikingly poetic quality: they both rely on symbolism and imagery rather than on
logical deduction to convey the mystery of creation. Nevertheless, Augustine’s
conclusions about time also echo Aristotelian themes. Augustine says that time is
the measure of motion and that nothing exists of time except the present, which is
indivisible. 'Augustine shared with classical philosophers the tendency to analyze

time according to its parts, past, present and future. He agreed with them that time

31

came into existence only with creation and had a counterpart in eternity.
Augustine’s main divergence from Plato and Aristotle was that, while they were
content to describe or explain time (a characteristic feature of Greek philosophy),
he wanted to discover the meaning of time in both its human and divine contexts.56
His fascination with the mysterious elusiveness of time and its effect on the sensible
world led him to ask a broader range of questions than Plato and Aristotle had
done. Augustine’s originality stemmed from his insight: "Few men," observes
Herman Hausheer, "have been as intensely sensitive to the pathos of mutability, of
the rapidity, tran5itoriness, and irreversibility of time."57
Augustine’s conception of time, moreover, was greatly enhanced by his
reading of the Neoplatonists. Richard Sorabji remarks that many of Augustine’s
mystical impulses towards time and eternity were derived from or reinforced by his
reading of Plotinus. Sorabji cites Augustine’s discussion with his mother about the
eternal life of the saints as an example of Augustine’s dependence on Plotinus’
concept of "the life which is wisdom." Augustine writes:
Life is that Wisdom by which all these things that we know are
made, all things that ever have been and all that are yet to be.
But that Wisdom is not made: it is as it has always been and as
it will be for ever - or rather, I should not say that it has been or
will be, for it simply is, because eternity is not in the past or in
the future. And while we spoke of the eternal Wisdom, longing
for it and straining for it With all the strength of our hearts, for
one ﬂeeting instant we reached out and touched it. Then with
a sigh, leaving our spiritual harvest [Rom. 8:23] bound to it, we
returned to the sound of our own speech, in which each word
has a beginning and an ending — far, far different from your
Word, our Lord, who abides in himsey8 for ever, yet never
grows old and gives new life to all things.
Augustine’s image of the soul striving beyond simple understanding to attain a
higher spiritual state and his association of that experience with feelings of passion
and shock are strikingly reminiscent of Plotinus’ writings about striving towards the

One.59

32

Sorabji warns, however, of the danger of reading too much of Neoplatonic
philosophy into Augustine’s conception of time and eternity. Just because
Augustine was familiar with Neoplatonism and often seemed to express his ideas in
Neoplatonic form does not mean that he accepted N eoplatonism uncritically. More
often than not in his direct references to the Neoplatonists, Augustine portrayed
their ideas as uninformed, imperfect versions of Christian truths: their assertion
that God’s mind contains the ideal forms was an implicit acknowledgement of God
as creator of all being; their recognition of three levels of reality, the One, the
World Intellect and the World Soul, reﬂected their acceptance of the Trinity.60
Thus Sorabji concludes that Augustine’s relationship to the Neoplatonists was a
complex one of "initial acceptance and of subsequent borrowing, adapting,
distancing himself and urging them to follow."61

Augustine begins his discussion of time in the Confessions with an
exclamation of frustration, which sets the tone for his own uniquely psychological
approach to time: "if no one asks me [what time is], I know; if I try to explain it to
someone, I do not know."62 His investigations into the nature of time start with an
account of creation, which, like Plato’s creation story in the Timaeus, emphasizes the
non-existence of time before creation and posits a divine goodness as the motive for
creation. Augustine departs from Plato in insisting that God created the universe
not out of pre-existing chaos but out of nothing. Paying particular attention to the
text from Genesis "In the beginning God created heaven and earth," Augustine
argues that Scripture attributes a beginning to every creature. Because time
involves change, it also is a creature, and so has a deﬁnite beginning. Therefore
neither time nor the world is eternal. Augustine has no patience with people like
the Manicheans, who impertinently ask what God was doing before the moment of
creation.63 In his view, Scripture clearly tells us that there was nothing before

creation: one cannot even say that God was before creation because, perfect and

33

immutable, God has no before and after. God simply is in a motionless eternity.64
Augustine is not speaking here, however, of any kind of eternity that human beings,
bound in time, can comprehend or experience. In fact, Augustine sharply opposes
Plato’s and Aristotle’s arguments in favor of the eternity of the world. Because the
world, and thus time, had a deﬁnite beginning in the event of creation and will
continue according to principles established by God, it is neither eternal, nor does it
share in any way in God’s capacity for everlasting being.65

Augustine was not satisﬁed simply with refuting the opinions of his
predecessors or with determining the characteristics which time does not have. His
real goal was to discover what time really is like, to the extent that a human being
can actually recognize its features. His treatment of time in the Confessions
involves, therefore, a transition from an ontological discussion of the origins of time
to a psychological analysis of the effects of time on the soul.66 In fact, from
Augustine’s point of view, human experience, subjective as it is, must be paramount
in any discussion of time because, although time could still exist in a created world
without people, in the world which God actually created, it is people who measure
time in their minds. Like all other creatures, humans live and change in time; but,
because they have souls, they can transcend, in certain respects, the limitations of
creation. Their souls make them more like God and make God’s eternity more
accessible to them. Thus humanity stands between time and eternity and the soul is
the tool for measuring and interpreting time.67

Augustine’s ultimate conception of time is based on his observation that time
seems to have three parts, past, present and future; that it proceeds in a single,
irreversible direction; and that it consists of a succession of segments which are
easily perceived but are extremely difficult to analyze in any rigorous way. These
observations raise serious problems about the nature of time because they seem to

present contradictory evidence. Of the three "parts" of time, only the present seems

34

actually to exist, because the past is "no more" and the future is "not yet"; but if the
present is always moving forward, how can we determine exactly where the present
is? Moreover, we can think of past times as having long or short duration, but can
one really measure something that no longer exists? Indeed, we cannot even
measure the present, for every duration of time has its own sequence of past,
present and future.68 Augustine points out that even the hour

is made of ﬂeeing moments; so much of the hour as has ﬂed

away is past, what still remains is future. If we conceive of

some point of time which cannot be divided into. even the

minutest parts of moments, that is the only point whieh can be

called the present; and that point ﬂees at such lightemng speed

from being future to being past, that it has no extent. of

duration at all. For if it were so extended, 1t wgbrld be d1v151ble

into past and future; the present has no length.

Nevertheless, says Augustine, we cannot deny that we think of the world in
terms of the concepts of past, present and future, even though we can develop no
standard for determining when the present actually is. The present remains a
crucial concept because it distinguishes past and future. Its function in making this
distinction depends, however, not on some objective continuum such as the motion
of heavenly bodies but on the mind itself. Augustine concludes his speculations on
the relationship of the present to past and future with the suggestion that

perhaps it would be more correct to say: there are three times,
a resent of things past, a present of things present, a resent
0 things future. For these three exist in the mind, an I ﬁnd
them nowhere else: the present of things past is memory, the
present of things present is immediate intuition (cantuitus), the
present of things future 15 expectation. . . . By all means
continue to say that there are three times, past7(present and
future; for though it is incorrect, custom allows it.
Augustine’s approach to time, then, is consciously subjective, at least to the degree
that he believes that the parts of time are realized and measured within the mind.

This emphasis on the mind emerges from Augustine’s acceptance of an Aristotelian

35

description of time as successive, continuous and inﬁnitely divisible. Augustine

71

wanted to protect the eternity of God from anything changeable without

sacrificing his belief that the human mind is capable of understanding God’s activity
in the world. Therefore he had to place the human capacity to understand time in

the soul.

If the present has no extension, and past and future do not exist, how then do
we measure time? Augustine answers that we measure time in the memory.
Through the power of our minds we can create and measure segments of time which
bear no resemblance to the actual succession of individual moments. The memory
is a spiritual power which allows images in the soul to be measured: as such, it can
stop the course of time and stabilize it.72 Using the example of the recitation of a
poem, Augustine describes how the memory not only makes the various aspects of
time accessible to human experience but also represents the unity of parts and

whole in every aspect of human life:

Sup ose that I am about to recite a psalm that I know.
Before be 'n, my expectation is directed to the whole of it;
but when I ave begun, so much of it as I pluck off and drop
away into the ast becomes the matter for my memory; and the
whole life of t e action is stretched out between my memory, in
regard to what I have said, and my expectation, in regard to
what I am still to say. But there is a present act of attention, by
which what was future passes on its way to becoming past. The
further I o in my recitation, the more my expectation is
dirninishe and my memory lengthened, until the whole of my
expectation is used up, when the action is completed and has
passed wholly into my memory. And what happens in the case
of the whole psalm happens for each part oft e whole, and for
each syllable; and likewise for any longer action, of which the
canticle may be only a art: indeed, it is the same for the
whole life of man, of w 'ch all man’s actions are arts; and
likewise for the whole history of the human race, a which all
the lives of all men are parts. 3

Augustine recognizes previous deﬁnitions which associate time with motion
as valid insofar as motion occurs in time: we might even use the motion of an object

to measure time; but the act of measurement takes place entirely within the soul.

36

Observations of individual motions become images which the mind uses to
determine intervals. Augustine’s emphasis on the mind as an active agent in
deﬁning time had bearing on many of his other theological positions which involved
the soul’s activity, particularly in regard to the Trinity.74 By stressing the
connection between time and the soul Augustine offers a psychological answer to a
metaphysical problem, or, as many commentators would argue, he transforms the
metaphysical problem of time into a psychological one.

This transformation had consequences in all areas of Augustine’s theological
system, but it was especially important in those discussions which involved some
explanation of God’s understanding of human activities. Here Augustine had to
address the paradox that God, omniscient and outside of time, allows his creatures
to act freely within time. Augustine readily admitted that he had trouble in
resolving this problem but he ultimately concluded along Platonic lines that God
created time so that his creatures, in all of their limitation and imperfection, could
exercise their wills under his divine guidance. It was the spiritual contrast between
the ﬁniteness of human experience and the inﬁnity of God, not the physical contrast
between time and eternity which most fascinated Augustine. According to Robert
Jordan, "Augustine’s investigation of time is a study in contingency, ﬁniteness,
creatureliness, dependency, incompleteness, imperfection - a study of the limitations
of being that characterize any ﬁnite entity, that entity which is, but which is not He
Who Is. Time exists because there are existent things in the universe which are just
so much reality, but no more. The existence of only one of these things is of
genuinely intimate concern to man - himself."75 Time thus becomes more than a
cosmological problem: it is a problem of moral philosophy, bound up with the
religious life of humanity.76

The fundamental problems of time arose, therefore, not only in Augustine’s

formal discussions of time in Book XI of the Confessions but also explicitly or

37

implicitly in many other contexts. Most notably, he approached the whole problem
of God’s foreknowledge and human free will from the perspective that God’s
knowledge in his timeless present that a person will sin does not compel that person,
living in earthly time, to sin. In Augustine’s opinion, God’s eternal foreknowledge
actually safeguards the freedom of the human will since will is a divinely created
gift. Indeed, he remarked in the City of God:

Our wills are ours and it is our wills that affect all that we do by

willin and which would not have happened if we had not

wille . But when antyone has something done to him against

his will, here, again, e effective power IS will, not his own but

another’s. But the power of achievement comes from God. . . .

Therefore, let us never dream of denying‘ his foreknowledge in

the interests of my freedom, for it is wit his help that we are,

or shall be, free.
Although in this case, divine knowledge, not time, was the main issue, Augustine’s
deﬁnition of the relationship between time and eternity provided the basis of his
solution to a difﬁcult cosmological and theological dilemma.

Because Augustine’s theology had such a lasting impact on medieval
theological discussions of all sorts, it is not surprising that his ideas about time
appear repeatedly in the works of his successors. Comparisons between Augustinian
and Greek philosophies of time reﬂect both his dependence on an established
vocabulary and list of concerns and also his remarkable originality. Augustine’s
analysis of time is important because through it later thinkers were introduced to
principles of classical philosophy which retained many of their original features in
spite of Augustine’s reinterpretation of them. Moreover, since Augustine’s writings
soon came to be considered theologically central, his philosophical treatment of
problems such as time legitimized not only a philosophical approach to theology but

also an acceptance of ideas whose origins were in a non-Hebraic pre-Christian

tradition.

38

Augustine’s psychological view of time and eternity is closely related to that
of Boethius, whose speculations on the nature of eternity greatly inﬂuenced
discussions about time throughout the Middle Ages. Although Boethius was not
interested in time as such, his deﬁnition of eternity hinges on the contrast between
human temporal existence and the non-temporal existence of God. Boethius was a
scholar of considerable skill, who not only composed several original works on logic,
theology and natural philosophy but also embarked on the ambitious task of
translating all the writings of Plato and Aristotle into Latin. Although he completed
only a fraction of this work, he was successful in introducing many classical concepts
into medieval scholarship in their original form. Unlike Augustine, whose
philosophical impulses were always directed towards theological ends and whose
assimilation of classical ideas was almost subconscious, Boethius openly advocated
the study of philosophy, particularly ancient Greek philosophy, for its own sake. In
addition to his contribution to the debate about time and eternity, Boethius added
to the medieval literary tradition Aristotle’s logical system of categories and
suggested a method for organizing disciplines of learning which formed the basis of
the medieval academic curriculum. His best known work, the Consolation of
Philosophy, is an allegorical account of his conversion to the belief that philosophy,
deﬁned as the love of wisdom, the pursuit of wisdom or the quest for God, is the
highest human aspiration.78

It is not surprising, therefore, that Boethius’ conception of time bears the
mark of his study of the ancient Greeks, the Neoplatonists and Augustine. Boethius
shares with Augustine a psychological view of time and eternity: both saw the
problem of the relationship of time and eternity as a matter of interaction between
God and the human soul, rather than simply an explanation of a phenomenon of
nature. Some modern commentators judge Boethius’ treatment of these problems

superior to Augustine’s because of Boethius’ special philosophical training.79 His

39

approach to eternity in the Consolation of Philosophy involves an attempt to prove a
theological assumption about the eternity of God using philosophical means without

reference to Scripture. To this end Boethius states:

That God is eternal, then, is the common judgement of all who
live by reason. Let us therefore consider what eternity is, for
this makes plain to us both the divine nature and knowledge.
Eterni , then, is the complete possession all at once of
illimita le life. This becomes clearer by comparison with
temporal things. For whatever lives in time proceeds as
somethin present from the past into the future, and there is
nothing p aced in time that can embrace the whole extent of its
life equall . Indeed, on the contrary, it does not yet gras
tomorrow ut esterday it has already lost; and even in the li e
of today you 've no more fully than in a mobile, transitory
moment. . . . Therefore, whatever includes and possesses the
whole fullness of illimitable life at once and is such that
nothing future is absent from it and nothing past has ﬂowed
away, this is ri tl judged to be eternal and of this it is
necessary both t at eing in full possession of itself it be always
present to use“ and that it have the inﬁnity of mobile time
present [to it].

Boethius’ argument that eternity is completely distinct from the sequential character
of human time is entirely in keeping with Augustine’s view because it emphasizes
both the divine nature of eternity and the difﬁculty human beings have in grasping
either time or eternity.

Recognizing this difficulty, Boethius attempts in another passage to explain
what he means by "the complete possession all at once of illimitable life." He
agreed with his predecessors that eternity is neither simply a limitless duration of
time nor a state of static atemporality.81 His analysis of the misunderstanding of
eternity in his treatise 0n the Trinity offers a remarkably clear rendering of the
classical conception of eternity. Boethius thus contends:

What is said of God, [namely, that] he is always, indeed

signiﬁes a unity, as if he had been in all the past, is in all the

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and of the imperishable bodies; but it cannot be said of God in
the same way. For he is always in that for him always has to do

40

with the present time. And there is this great difference
between t e present of our affairs, which is now, and that of
the divine: our now makes time and sempiternity, as if it were
running along; but the divine now, remaining and not moving,
and standing still, makes eternity. If you add ‘semper’ to
‘eternity’ you get sempiternityBéhe perpetual running resulting
from the owing, tireless now.

For Boethius, then, eternity is not a sterile condition which removes God from the
temporal reality of his creation, however hard it might be for us to understand how
this can be so. Boethius’ God transcends time: indeed, as Anthony Kenny observes,
he might be pictured "as surveying the battle-ground of human existence from a high

tower above, with past, present, and future as different parts of the ﬁeld open to

divine vision."83

Boethius also, like Augustine, tries to consider how his conception of divine
eternity relates to human experience. In the ﬁrst place, he addresses the question of
whether the world is eternal. Preferring not to rely, as Augustine had done, on the
authority of Scripture, Boethius looked to Plato and Aristotle for inspiration. It was

Plato’s view which had the greatest sway in Boethius’ conclusions:

So what is subject to the condition of time is not yet such as
rightl to be jud ed eternal, even if, as Aristotle believed of the
worl , it never egan to exist, and does not cease, but has its
life stretched out with the eternity of time. For even if its life is
inﬁnite, it does not include and embrace the whole extent of
that life all together, since it does not yet possess the future
and alread lacks the ast. . . . Hence those are not right who
hear that lato thou t this world had no beginning in time
and will have no end, and who conclude that the created world
is in this way made co-eternal with the creator. For it is one
thin to be drawn through an endless life, which is what Plato
attri uted to the world, and another to have embraced e ually
the whole presence of a life which cannot end, which is c early
the special characteristic of the divine mind. Nor should God
be thought older than created things by some amount of time,
but rather by the peculiarity of his nature which is simple. . . .
Thus if we want to apply names appropriate to thin 5, let us
say, folloug'pg Plato, t at God indeed is eternal, but t e world

perpetu .

41

Boethius’ argument that the world is not eternal because it was created and exists
under the inﬂuence of time corresponds to Augustine’s assertion that time had its
origin in creation. While Boethius does not deny creation, however, he is not
prepared to go so far as Augustine in claiming that creation has a deﬁnite beginning
and end. He prefers Plato’s designation of the world as perpetual, which suggests
that worldly time, though not identical with eternity, bears some relation to it. This
Opinion, though hardly orthodox in the Augustinian sense, nevertheless came to be
considered theologically valid, thanks to the widespread inﬂuence of Boethius’
writings throughout the Middle Ages.85

Boethius’ ideas are more in keeping with Augustine’s on a second aspect of
the problem of time’s relation to eternity, that of God’s foreknowledge. We have
already seen that Augustine proposed the solution that God sees all human action at
once and that his knowledge that a person will act in a particular way does not
constitute coercion. Boethius takes a similar position, but his treatment, having
been derived from carefully argued philosophical premises, is clearer than
Augustine’s. Boethius declares in the Consolation of Philosophy that God can know
the future without manipulating it because God exists in a state of eternal
presentness: "Embracing the inﬁnite lengths of past and future, [he] considers
everything as if it were going on now in a simple mode of awareness."87

The appeal of Boethius’ argument lies in its comprehensibility and simplicity.
He deﬁnes God’s relationship to the temporal world in such a way as to free human
will from the necessity of God’s foreknowledge without denying that God indeed
knows every possible human act in his eternal present. The problem with Boethius’
conception of eternity, from the Augustinian perspective, is that it fails to take into
account evidence from Scripture of God’s intervention in the world. Boethius’
philosophical account of divine knowledge makes no provision for grace; and,

although Augustine had arrived at the same conclusion as Boethius about God’s

42

capacity to have knowledge while ensuring the freedom of his creation, Augustine,
as a theologian, could not avoid the elements of Christian revelation which
complicate the discussion. The persistence of both Augustinian and Boethian
traditions throughout the Middle Ages indicates the compelling nature of the
problems of time and eternity for medieval thinkers. Even Boethius, who did not
devote much attention to these issues, strongly inﬂuenced medieval discussions of
time and eternity, not the least because he consciously introduced classical
approaches to topics which fascinated medieval thinkers. Thus interest in time and
eternity ﬂourished in the West during the early Middle Ages, particularly in the late
eleventh and twelfth centuries, when such thinkers as Anselm, Peter Abelard and
Garlandus Compitista all made useful contributions to the debate.

In almost all of his major works, Ansehn referred to the themes of time and
eternity and to the philosophical and theological problems which arise from them.
Historians have long recognized that Anselm was inﬂuenced by Augustine, even
though he did not have access to the Confessions. It is not often considered,
however, that Anselm was also familiar with Boethius’ views on time as set forth in
his commentaries on Aristotle’s Categories.88 Although it is difﬁcult to ascertain the
exact source of inﬂuence, it is clear that Anselm’s treatment of time involves
geometrical deﬁnitions which bear greater resemblance to a classical tradition than
to an Augustinian one. Not only did Anselm, like Plato and Aristotle, use
mathematical terminology to describe the nature of time and eternity, but he also
held the Aristotelian opinion that eternity differs from time because of its incapacity
for measurement. Anselm argued that the distinction between time and eternity
rests on the fact that time is a sequence of parts, while eternity is whole, without
parts and dimensionless.89 In order to emphasize this point, he compared the unity
of eternity with the unity of the Trinity: "We do not think of God as having grades

of different standing, for He is one; nor, when we show how the Son is ‘ot’ the

43

Father, or the Holy Spirit of Father and Son, do we construct intervals in eternity
which is beyond all time."90

While Anselm’s view of time was mathematical, Abelard and Garlandus
treated time as a grammatical or dialectical problem. Drawing on both Greek
sources and Augustine’s discussions of the ambiguities of tensed language,
Garlandus showed that grammatical limitations can interfere with an adequate
metaphysical deﬁnition of time.91 Abelard also discussed the grammatical
problems associated with time, but he went beyond these to address some of the
.underlying phi1050phical and theological roots of these problems. He pointed out,
as Augustine had, that the simplest way to teach students about time is to direct
them to the revolutions of planets and stars; but Abelard agreed with Augustine that
this approach is theoretically incorrect because the existence of time "must be
independent of any one means of measuring it."92 Abelard also recognized the
difﬁculty in describing durations of time which consist of continuous series of points,
saying: "time is either indivisible, like the present moment which we call an instant,
or it is composite, like an hour, a day, a week, a month, a year, which is made up of
different instants following one another in succession, past, present and future."93

Anselm, Garlandus and Abelard, therefore, all focused on the practical
problems of measuring and describing time which were central features of ancient
Greek discussions of time. Although they obviously drew on classical treatments,
however, their own approaches reﬂect the logical and philosophical interests of their
own age. Augustine and Boethius helped to shape these later discussions not so
much by dictating the course that investigations about the nature of time should
take, as by providing access to the rich and varied history of the subject in an age of
scarce literary resources but keen and inquiring minds.

This brief survey of the origins of medieval discussions about time reveals

several important themes. First, the problem of time had been the subject of

44

rigorous philosophical speculation in the Western tradition from an early age.
Second, discussions of time are intimately bound up with, and must be viewed in
terms of, thinking about creation, God and eternity. Third, as the main contributors
to the discussion addressed the views of their predecessors, the debate about the
nature of time became increasingly complex and approaches to the problem more
varied. By the time of Boethius, philosophers and theologians could draw on
Pythagorean, Platonic, Aristotelian, Neoplatonic and Christian explanations of time;
they could conceive of time mathematically, astronomically, metaphysically or
psychologically; and they often used more than one approach to explain the
anomalies of time.

The legacy of this long discussion for the later Middle Ages rests not just on
the sources of ideas it provided, but also on the inspiration it gave to thinkers to
explore the complicated and frustrating problem of time in all of its manifestations.
Each generation to approach the subject of time brought to the discussion its own
concerns as well as the accumulated wisdom of the past. It is a testament to the
major innovators on this topic, Plato, Aristotle, Plotinus, Augustine and Boethius,
that no age has been able to dismiss completely their insights about time. In fact.
one can hardly begin to evaluate the emergence of time as a philosophical and
theological topic in the late Middle Ages without understanding these men’s ideas

about time.

CHAPTER THREE
THIRTEENTH-CENTU RY APPROACHES TO TIME

During the century and a half before Bradwardine, the problem of time arose
within the context of the general discussions of Aristotelian philosophy which had
become common among Western scholars by the late twelfth century. A major
stimulus to these discussions was the increased accessibility of Aristotle’s writings
through new translations from Arabic into Latin. Much of this work was
accomplished in Spain, where Muslim, Jewish and Christian thinkers had mingled
for centuries. By the mid-twelfth century, Muslim scholars not only had translated a
large number of Greek philosophical texts into Arabic but also had produced an
impressive array of commentaries, especially on Aristotle’s writing, which
reevaluated classical philosophy from the perspective of Islamic theology. Although
some scholars in Spain and Northern Europe rejected non-Christian natural
philosophy and tried to resist its inﬂuence, many more welcomed translations of
Aristotle’s writings on physics, astronomy, biology and cosmology which had not
been readily available for study in the early Middle Ages.1 The inﬂuence of these
translated texts on Western thought was considerable and had direct bearing on
subsequent discussions of time in the thirteenth and fourteenth centuries.

The appeal of this new body of literature was its comprehensive treatment of
natural philosophy. According to Etienne Gilson, Western medieval thinkers
embraced the Greco-Arabic tradition of natural philosophy with great enthusiasm
because Scripture did not provide them with an adequate cosmology, that is, a

"scientiﬁc and metaphysical description of the structure of the universe," for genuine

46

47

philosophical study.2 Certainly by the thirteenth century, Western thinkers had
become interested in many topics which belong more in the category of natural
philosophy than in theology. Classical works on physics, biology, astronomy and
mathematics, along with their Muslim commentaries, excited curiosity both by
suggesting new questions which one might ask about the natural world and by
conveying speciﬁc information or observations about natural phenomena.

Unfortunately, both Aristotle and the Muslim scholars who commented on
his writings usually failed to distinguish their opinions about the natural world from
their religious beliefs. Many conservative Christian thinkers in the thirteenth
century were alarmed, therefore, by the rapid spread of "pagan" philosophies which
appeared to obscure, when they did not actually contradict, accounts of creation
found in Scripture. In the ﬁrst half of the thirteenth century, some conservatives
tried unsuccessfully to abolish the teaching of Aristotle at the universities, or at least
restrict Aristotelian studies to his works on logic. More moderate thinkers
attempted in various ways to reconcile Aristotle with Christian thought, but few
accomplished this task convincingly. In spite of strong efforts to forestall it,
Aristotle’s scientiﬁc and metaphysical thought was ﬁrmly established in the
university curriculum by the end of the thirteenth century and young scholars turned
with vigor to classical problems of cosmology which they encountered in their
studies of that material.

The purpose of this chapter is to examine late twelfth- and thirteenth-century
discussions of time in light of this rediscovery of classical natural philosophy. The
signiﬁcance of this period for Bradwardine’s generation of scholarship arises from
the characteristic enthusiasm of thirteenth-century thinkers for combining
philosophical, scientiﬁc and theological evidence in their answers to metaphysical
questions. Time, as we have already seen, lends itself to a multi-disciplinary

investigation; indeed one could argue that a successful study of time is impossible

48

without such an approach. In the twelfth century the Muslim philosopher Averroes
and the Jewish philosopher Moses Maimonides reinterpreted Aristotelian views of
time and eternity both philosophically and in light of monotheistic theology. Their
work provided an important legacy for such inﬂuential Western scholars as Albertus
Magnus, Thomas Aquinas, Robert Grosseteste and John Duns Scotus, who tried in
various ways to reconcile theological truth with the concepts and methods of
Aristotelian natural philosophy. Although these thinkers did not exert equal
inﬂuence on Bradwardine, and their ultimate conclusions about time varied
considerably, their struggles to understand time offer valuable insights into the
unsettled intellectual climate into which Bradwardine entered early in the
fourteenth century.

Any discussion of the revival of Aristotelian natural philosophy in the
Christian West must consider the important contributions of Averroes. An active
participant in the vibrant, international academic community of twelfth-century
Spain, his studies included theology, jurisprudence, medicine, mathematics and
philosophy. In addition to his work as a judge, he composed several original
treatises on a variety of topics. His fame in northern Europe, however, rested
chieﬂy on his commentaries on Aristotle.3 In these commentaries, Averroes set
about the task of establishing the relationship between Aristotelian philosophy and
religious truth revealed through the Koran. Not wishing to stray too far from
orthodoxy, he openly acknowledged the miraculous nature of the Koran, which
brought truth to all people whatever their capacity to receive it. According to
Averroes, anyone could understand the Koran’s superﬁcial and symbolic meanings,
bUt only highly trained scholars could hope to penetrate its hidden messages. In
addition, he contended that the highest aim of human speculation must be
philosophy, because every other kind of speculation, including theology, is tainted

with the distracting elements of emotion and faith.4 Therefore, those who are

49

capable of ﬁnding truth should turn their attention to the philosophy of Aristotle,
who provides both an explanation for the natural order and a method for
investigating it. In fact, Averroes went so far as to proclaim: "The doctrine of
Aristotle is the supreme truth because his intellect was the zenith of human
intellect. It is therefore rightly said that he was created and given to us by divine
providence, so that we might know all that can be known."5 Although few Christian
thinkers were prepared to regard Aristotle as the zenith of the human intellect,
Averroes’ powerful portrayal of Aristotle had a positive inﬂuence on many Latin
scholars.

Averroes’ commentary on Aristotle’s view of time reﬂects both his profound
respect for his teacher and his own preoccupation with philosophical problems.
Averroes was troubled by Aristotle’s deﬁnition of time as the number of motion
because it did not adequately distinguish time from motion. Averroes felt
compelled, therefore, to exarrrine the source of Aristotle’s dilemma without openly
criticizing any of Aristotle’s statements. In his analysis of Aristotle’s view of time
Averroes included several insights on the nature of time which Avicenna had
advanced in his own commentary on Aristotle, although he did not acknowledge his
indebtedness.6 Averroes’ main complaint was that, by linking the concepts of time
and motion too closely, Aristotle seemed to imply that one had to observe motion to
experience time. This theory presents many difﬁculties, not the least of which is the
anomaly that the heavenly bodies continue to measure time even under conditions
which prevent human observation of their motion.7 To resolve this dilemma,
Averroes suggested that the experience of time is not related to the individual
perception of earthly or celestial motion: our capacity to sense change is inadequate
to the task of accounting for the regular and continuous passage of time.8 Although,
like Augustine, Averroes seemed at ﬁrst to stress the importance of perception in

assessing the nature of time, his approach was not a psychological one. While the

50

occasion of a motion might allow us to perceive time, Averroes argued, time itself
does not depend merely on our observation of motion. Because we are always both
in a state of change (in esse mata) or in a state which anticipates our essential
capacity for change, we perceive time subjectively. The objective, ordered passage
of time is assured, however, by the circular motion of the celestial sphere: all
movement and change depend on its motion, which continues in an orderly fashion
whether or not we can comprehend its course. Without departing from Aristotelian
principles, therefore, Averroes nevertheless reconsidered and reﬁned Aristotle’s
problem of explaining the interrelationship of time and motion.9

Averroes’ most original contribution to the medieval debate about time and
his chief advance over Aristotle arise from his insistence that time is a fundamental
feature of material being, which must possess the capacity to move and change.10
This theme is revealed in Averroes’ comment on possible interpretations of
Aristotle’s teaching on time. Here Averroes made a distinction between perception
of time based on our direct experience of local motion and our universal
acknowledgement of a uniform temporal order which applies whether or not we
observe change. According to Averroes, the latter position best expresses Aristotle’s
opinion because it is based on his teaching about the uniform motion of the
heavenly bodies.11 After examining the main principles of Aristotle’s temporal
theory Averroes concluded that when Aristotle deﬁned time as the number of
motion, he was talking not about any observable or measurable motion but about
the particular motion of the celestial sphere.12 Averroes thus clariﬁed Aristotle’s
position to the point of over-simpliﬁcation in order to protect Aristotle from the
criticism that his theory of time was ambiguous. Consequently, his reevaluation of
Aristotle helped to deﬁne in terms comprehensible to medieval scholars the

problem of time as both a philosophical and a physical problem. Because it made

no reference to theological truth, many Muslim and Christian thinkers refused

51

wholly to accept Averroes’ interpretation of Aristotle’s temporal theory, although
they hungrily read his commentaries for information about Aristotelian
metaphysics.13 This fascination with Aristotle accounts for the wide circulation and
inﬂuence of Averroes’ ideas in northern Europe in the thirteenth and fourteenth
centuries.

Averroes’ contemporary, Moses Maimonides, also relied heavily on Aristotle,
but he was interested as well in other ancient philosophical traditions, such.as
Neoplatonism. His writings demonstrate an impressive knowledge of contemporary
philosophical discussions, including Averroes’ work. Unlike Averroes, however,
Maimonides believed that faith was a prerequisite for seeking philosophical truth,
and his most widely read book, the Guide for the Perplexed, is primarily a work of
theology. In this book, Maimonides modiﬁed Averroes’ argument that the highest
form of intellectual activity involved the study of Aristotelian metaphysics. He
presented divine law and philosophy as two equally valid areas of inquiry, both of
which are necessary for establishing a rational conﬁrmation of faith.14 Maimonides
hoped to show that it was possible for an educated, perceptive person to reconcile
physical principles with the literal meaning of the Scriptures. Although he looked to
a variety of sources of scientiﬁc knowledge, he relied most heavily on Aristotle for
explanations of natural phenomena. Maimonides’ critical approach to both
Aristotelian physics and Muslim theology and his ﬁrm attachment to the Old
Testament made the Guide for the Perplexed a valuable resource for Christian
scholars, despite its largely unsystematic structure.15

In addition to his general inﬂuence on medieval Western theology,
Maimonides contributed speciﬁcally to the discussion of time through his comments
on the eternity of the world. Although he accepted much of Aristotle’s physical
theory, he could not accept Aristotle’s argument that the world had had no

beginning in creation. Since he could ﬁnd nothing in Aristotle’s writings to prove

52

that the world had not been created by God, Maimonides felt justiﬁed in rejecting
this element of Aristotelian physics in favor of the scriptural doctrine of creation in
time. On the other hand, Maimonides admitted that creation in time cannot be
proved. Therefore, acceptance of creation in time cannot serve as a philosophical
principle for proving theological truths such as the existence of God.

Maimonides based his proof of God’s existence on an entirely different kind
of argument: being is necessary and requires a primary mover or cause, which is
God. According to this argument, God exists as the primary agent of creation,
whether he made the world from nothing in time or whether the world existed from
all eternity.16 The importance of Maimonides’ discussion about eternity in the
medieval debate about time does not rest in any clarifying remarks that he made
about time itself. It was rather his attitude that biblical principles could be defended
without physical proof that caught the attention of Christian thinkers of the
thirteenth century. Both Averroes and Maimonides provided examples of how the
philosopher might try to solve cosmological problems by considering both
philosophical and theological evidence. More important still for this study, by
turning their attention to the problems of time and eternity they emphasized the
inadequacy of approaching time exclusively either from a theological or a
philosophical perspective.

The thirteenth-century scholar Boethius of Dacia offers an example of how
Averroes and Maimonides inﬂuenced Christian thinkers. In addition, his discussion
of eternity indicates the ambiguity of medieval studies of time which did not readily
separate the philosophical from the theological aspects of this problem. Boethius’
analysis of time and eternity is based on Averroes’ conviction that philosophy is the
best kind of intellectual activity and therefore completely avoids theological
considerations. Although he never went so far as to deny the value of faith,

Boethius ascribed to the philosopher the capacity to achieve the experience of

53

greatest human pleasure through the contemplation of the "prime principle," that is,
the eternal, the immutable and most perfect. In his treatise 0n the Sovereign Good
or On Philosophical Life Boethius echoes Averroes’ admiration for philosophical
inquiry, clairrring that
. . . each one ﬁnds his delight in what he loves, and his greatest
delight is what he loves most, and since the philosopher
supremely loves this Prime Principle . . . it follows that the
phrl'rll‘oso her ﬁnds his supreme delectation in this Prime
' cip e and. in the contemplation of its goodness, and that
this electation is the only right one. That is what a
philosopher’s life is, and whoever does not lead it does not live
right. Now I call ‘philosopher’ any man who, living according
to the right order pf nature, has attained the best and ultimate
end of human life.
Such views made Boethius an easy target for conservative theologians who wanted
to discredit the idea that philosophy, particularly Aristotelian philosophy, could
achieve good without being informed by faith. Modern scholars still disagree over
whether Boethius was really a "pagan" philosopher or truly wanted to protect the
role of faith in his philosophical system.18
In any event, even Boethius, with his enormous reverence for both Aristotle
and Averroes, could not accept all of their conclusions about time and eternity.
When he set about to write his own account of the eternity of the world, his main
source was neither Aristotle nor Averroes, but Maimonides.19 Boethius chose the
complex problem of eternity to illustrate his thesis that there is no conﬂict between
Christian faith and philosophy. His argument rests on his belief that natural
philosophy - the observation of the world as it actually is - has no connection with
speculation about the possibility of supernatural creation. Like Maimonides,
Boethius believed that neither the eternity of the world nor its creation in time
could be proven through demonstrable arguments, although he showed a greater
willingness than Maimonides to accept the possibility of an eternal world.20

Moreover, in an attempt to correct the misconceptions of his predecessors, Boethius

54

followed an argument proposed by Maimonides to demonstrate that Aristotle had
not successfully proven the eternity of the world.21 Preoccupied as he was with the
thirteenth-century debates concerning the relationship of faith to reason, Boethius
felt compelled to ﬁnd a way of balancing his own deep commitment to philosophy
with the religious concerns which dominated his age. His reading of Maimonides
helped him to envision the problem of eternity as a signiﬁcant but abstract problem
which the methods of neither theology nor natural philosophy could solve.22 His
conclusion that faith and reason should not be forced to compete in the search for
truth is an approach which was not regularly taken in the Middle Ages.
Nevertheless, his atypical approach focuses attention on the struggle between faith
and reason which inﬂuenced all medieval discussions of time. Indeed, those
fourteenth-century theologians who eventually did try tentatively to separate faith
from reason were disturbed by the implications their speculations had for both
theology and natural philosophy.

More common in the thirteenth century than Boethius’ separation of faith
and reason was the attempt to integrate natural philosophy and Scripture into a
consistent whole. Sometimes the integration involved the synthesis of Greco-Arabic
and Christian traditions into a single philosophy, but most Christian thinkers did not
go that far. In this context, it is useful to look at the view of time presented by the
Dominican scholar Albertus Magnus. Albertus is widely regarded as one of most
inﬂuential and gifted scholars in northern Europe in the mid-thirteenth century, not
the least because he was the teacher of Thomas Aquinas between 1245 and 1248.
Although Albertus was both a prominent churchman and an avid student of
philosophy, it is hard to classify him either as a theologian or as a philosopher. His
voluminous writings, consisting mainly of translations and commentaries on an
extremely wide range of topics, reﬂect both his broad interests and his

encyclopaedic knowledge. In order to enrich his theological studies, Albertus

55

wanted to have experience with every branch of learning, including, logic,
metaphysics and natural phi1050phy. Though he was aware that Greco-Arabic
learning sometimes conﬂicted with the Western Christian tradition, Albertus
nevertheless believed that the truths of one tradition could be applied usefully to
intellectual enquiries in the other. He therefore encouraged his contemporaries to
master as much scientiﬁc and philosophical material as possible, regardless of its
origin. Albertus was not primarily concerned, however, to build his own
philosophical or theological system out of the information which he accumulated in
his studies. For this reason, Albertus is often identified as a scholar in the general
sense rather than as a theologian or a philosopher.23

It is not surprising, then, that Albertus’ view of time is a composite of several
theories which were available for him to consider. His reading of classical works
and the commentaries of the Muslim philosophers gave him a good introduction to
Greco-Arabic approaches to time, while his knowledge of Augustine and the other
Church Fathers provided him with information concerning the biblical doctrines of
time and eternity. Albertus’ speciﬁc theory of time combines passages from
Scripture with classical descriptions of creation. According to Gilson, Albertus
accepted a classical interpretation of Scripture which held that God’s ﬁrst act of
creation was to make four coevals: "matter, time, the empyrean heaven and angelic
nature."24 Albertus followed Proclus in placing matter ﬁrst since "being" depends
logically on the existence of matter. After characterizing the various kinds of matter
which God created, Albertus discussed the distinctions between the philosophical
and the theological approaches to matter. For theologians, matter is the single
substance out of which God fashioned the universe in six days; for philosophers,
most notably Aristotle, matter is the subject of change, and, since there are many

kinds of change there must be many kinds of matter.

56

Albertus accepted both positions, claiming that it is not a contradiction to say
"that all matters are one and the same with respect to the work of creation, and that
matters are generically different with respect to the generically distinct sorts of
forms which they receive."25 Having established the nature of being, Albertus went
on to deﬁne time as the "duration that is proper to each different type of being." He
then recalled the well-established distinction between the human experience of time
and God’s experience of an ever-present now. Albertus deﬁned eternity as the
"limitless duration proper to the uncreated esse of God, which is the act of divine
essence."26 Time, by contrast, belongs to the realm of corruptible being and so is
deﬁned as the measure of motion or change. Like Augustine, Albertus conceived of
time as a series of ﬂeeting nows and contended that time could only be known by
the soul.

In another sense, however, time is an inherent quality in all existing things
"because the process of their passing from potency to act is a successive one, and,
consequently, of its own nature, it implies a before and after that are susceptible of
measurement."27 Just as with matter, time is described in completely different ways
by theologians and philosophers. Theologians see time as the measure of any
change, divisible or indivisible, spiritual or corporeal; and they apply it to all created
things, including angels, for whom time has neither a before nor an after.
Philosophers, on the other hand, think of time as a measure of continuous motion
which always includes a before and an after: it is the ﬂeeting now or "the mode of
duration proper to being that is becoming."28 Again, Albertus contends that the
two views do not contradict each other, for "just as every sort of substance has its
own kind of matter, every sort of duration has its own kind of time; mutations in
intellective faculties and wills are measured by their own time; mutations in

heavenly bodies are not in the same time as the mutations of sublunary beings."29

57

In his analysis of the philosophical deﬁnition of time, although he mentioned
other sources, such as Avicenna, Themistius, Alexander of Aphrodosias,
Theophrastus and Porphyry, Albertus most closely followed Averroes.30 He largely
accepted Averroes’ reevaluation of Aristotle and, in restating it in his own words,
succeeded in clarifying it further.31 Like Averroes, Albertus wanted to prove that
the various times which creatures experience really constitute a single uniﬁed time:
if they do not, it would be impossible to measure time at all. It is the uniform
motion of the heavens which provides a fundamental reference by which all other
motions and times are numbered}2 Albertus’ active role in the medieval discussion
of time, then, was not one of original insight, but instead one of informed
commentary. His conclusions that philosophical and theological approaches to
matter and time do not contradict each other cannot legitimately be called a
synthesis because he made no further effort to bring them together. On the other
hand, as an active proponent of both kinds of knowledge, Albertus would have
opposed any claim that there are certain questions which either faith or science
alone can answer. Both his speciﬁc views about time and his opinions about
knowledge in general had bearing on subsequent discussions of the problem of time.

Albertus’ student, Thomas Aquinas, is credited with the effort to achieve an
actual synthesis between Christian doctrine and Greco-Arabic learning. Although
Aquinas did not have Albertus’ encyclopaedic knowledge, his writing demonstrates
a much greater sensitivity to complex philosophical problems. Because one of the
main objectives of Albertus’ ministry was to encourage theologians, especially in the
Dominican Order, to have a thorough understanding of classical philosophy,
Aquinas, as Albertus’ student, was exposed to a wide range of philosophical
traditions. During three years of study under Albertus, Aquinas heard him lecture
on moral philosophy and on the Bible. Albertus’ published lectures on Psalms,

Jeremiah and Daniel date from the period of Aquinas’ study with him. At the same

58

time he was preparing a paraphrase of Aristotle, a commentary on Book IV of Peter
Lombard’s Sentences and lectures on the Apocalypse and Gospels.33

The young Aquinas took seriously his teacher’s devotion to classical learning
and soon became familiar both with Aristotle and with the Arabic commentaries,
particularly those of Averroes. Unlike Albertus, however, Aquinas was not satisﬁed
with acquiring and assimilating many sources of learning to support the broadly
based, almost cosmopolitan kind of theological speculation which is characteristic of
Albertus. Aquinas’ special gift was for philosophical analysis, and so his preference
was to produce a more conscious synthesis of Scripture, patristic writings and
classical philosophy than Albertus had ever attempted to achieve. For this reason,
Aquinas’ writings have almost as much signiﬁcance in the ﬁeld of philosophy as they
have in theology, which was in Aquinas’ eyes the more important discipline.

Considering the nature of his training and his interest in philosophy, it is not
surprising that Aquinas frequently mentioned aspects of time in his own writing. As
a synthesizer he found it necessary to examine time both as a spiritual and as a
physical phenomenon. On the one hand, he had to take into account the biblical
explanation of time as a part of creation as well as Augustine’s psychological
approach, which emphasized the function of the soul in deﬁning time. On the other
hand, he wanted to acknowledge the Aristotelian approach to time, which provided
a more objective explanation of time’s relationship to space and motion. When he
set out to discuss the nature of eternity, moreover, Aquinas was well aware of the
long debate over time’s relationship to eternity which dated from Plato’s treatment
of this issue.

Aquinas’ own views on time are scattered throughout several of his works,
including his commentaries on Lombard’s Sentences and on Aristotle’s Physics as
well as his own Summa thealagica. Hence, Aquinas’ references to time arise in

many different contexts. In every instance, however, he approached the problem of

59

time in a way which demonstrates both a good understanding of the Aristotelian
position and a respect for Christian authority. He carefully combined Platonic,
Aristotelian and patristic opinions to produce his own view, which, though not
unique, provided a reasonable guideline for reconciling contradictory traditions.
His work of synthesis, which his contemporaries and followers read avidly, helped to
transform old ideas into new subjects for debate. Aquinas’ writings about time are
important, therefore, not so much because of their originality, as because they
reintroduced the problem to scholars whose expertise in classical physics was
becoming increasingly mature.

A useful way of beginning a review of Aquinas’ view of time is to examine
what he had to say about eternity, for, like many of his predecessors, he thought that
the two concepts were interrelated. Aquinas accepted the standard distinction
between the eternity of God, who is perfect and unchanging, and the transitory
existence of created being. Like Augustine, Aquinas stressed not only God’s all-
encompassing nature but also his active participation in everything he creates. Thus
Aquinas states in the Summa thealagica that God "is inﬁnite and comprehends
within himself the plentitude of all perfection of all being," whereas every creature is
mutable.34

Aquinas then proposes the distinction between God’s complete perfection
and the mutability of creation as the principle for distinguishing time from eternity:

Some seize on this as the difference between time and eternity,
that time has a beginning and an end, but eternity not. This
difference, however, is quite incidental and not essential; for
even granting that time always was and always will be, there
remains this difference between them, that eternity is

simultaneously whole, whereas time is not. Eternity is the
measure of permanence; time the measure of change.

60

Aquinas’ view of time and eternity reﬂects the inﬂuence of both the Platonism of
Augustine, which emphasizes time as a function of creation, and the Aristotelian
position that time is a function of change.

Much of Aquinas’ discussion about time and eternity can also be seen as a
modiﬁcation of Augustine’s psychological view of time. In Aquinas’ opinion, the
distinction between time and eternity is important not just because it allows the
memory to separate past and future but because it facilitates the attainment of

diﬁerent kinds of knowledge:

The higher reason and the lower reason, of which
Augustine speaks, are in no wise distinct faculties. For he says
that by the former a man is intent on things eternal,
contemplating them in themselves and consulting them for his
rule of conduct, while by the latter he is intent on things
temporal. Now these two, namely eterni and time, are so
related that one is the medium in which t e other is known.
For in the order of discovery, we come to the knowledge of
things eternal through things temporal, according to the words
of St. Paul, the things of God are clearly seen, being understood
by the things that are made. On the other hand, in the order of
interpretation, we judge of temporal thin in light of eternity
and dis se of tern oral matters accor ing to eternal laws.
The big er and the ower reason, then, are one and the same
faculty, distinguished only by different habits and active
functions. Wisdom is agg'buted to the higher reason, scientiﬁc
knowledge to the lower.

Aquinas also observes that Augustine’s conception of memory underestimates the
complexity of the relationship between the intellect and time. Pastness, for
example, can be applied either to an object or to an act of knowing an object in the
past. In the case of an object, its being in the past, present or future is incidental;
but in the second case, "the pastness of an act can be essential to the intellect, for
our act of understanding is a particular activity at a certain time."37 In Aquinas’

more highly developed ideas about sense, intellect and knowledge, it is not accurate

to conﬁne the conception of past, present or future to the mind alone. Aquinas

61

therefore advocated a broader approach to time which also included Aristotelian
observations about motion and change.

How, then, does Aquinas deﬁne the human experience of time? First of all,
he emphasizes that time has both intellectual and physical dimensions and is a state
which affects only created beings:

Because our knowledge is enclosed in the order of time,
either directly or indirectly, the time-factor enters into our
calculations, and our knowledge reckons things as past,
present, or future. Past, in memory; present, in experience;
ture, by anticipation in present causes. Future events are
either certainties, when they are wholly determined in their
causes, or conjectures, when they can usually be forecast, or
unknown, when their causes are not yet comnutted to action.
God, however, is entirely above the order of time. He 15 at
the peak of eterni? surmounting everything all at oneg.
Thence the stream 0 time can be seen in one simple glance.
Aquinas shows here his agreement with Augustine and Boethius that God, being
above time, sees all creation as a totality, whereas his creatures must experience
existence as a continuous succession of nows; this notion has important implications
for subsequent discussions of human will and contingency.39 Moreover, although
God actively participates in his creation, he does so in a way that does not change
him: "Since God is outside the whole scheme of creatures, though all of them are
ordered to him, and not conversely, it is clear that while creatures are really related
to God, in God there is no real relation to creatures, but only a logical one."40 The
two main features of Aquinas’ view of time, therefore, are that God created time for
a speciﬁc purpose along with the rest of the universe, and, ultimately, that the
measure of time is the divine will, which is eternal. It is pointless to ask precisely
when God created time because such a question implies that there was time before
creation by which one could measure the event, and this is impossible."’1
Second, Aquinas acknowledges that our perception of time depends to some

extent on motion. In fact, much of his language about time reﬂects his dependence

62

on the Aristotelian tradition: time is aliquis matus, an aspect of motion; time is a
continuum; time is a number which arises from the division of motion; time is an
image of motion.42 Just as he refuses to accept Augustine’s view of time
uncritically, so Aquinas also draws out of Aristotle the themes which best support
his own view while dismissing what he thinks is incorrect. Although he discusses
time in terms of motion according to the Aristotelian tradition, for example,
Aquinas recognizes that the concept of motion itself poses serious difﬁculties for the
natural philosopher. In his commentary on Aristotle’s Physics he prefers to describe
the relationship between time and change, rather than time and motion, because
"any process is a kind of change and [even] what happens suddenly is temporal, for it
is what happens in a moment of time. Time itself is deﬁned in terms of change."43
Nor can Aquinas accept what he considers Aristotle’s rather primitive assertion that
time and motion are essentially different aspects of the same phenomenon. In his
commentary on Aristotle’s Metaphysics, therefore, Aquinas asserts that "Aristotle
was convinced that motion was everlasting, and time likewise. But his arguments [in
the eighth book of the Physics] are probable and not cogent, except perhaps as
disproofs of some early physical theories about the inception of motion."44

This criticism of Aristotle rests on the distinction which Aquinas liked to
'make between eternal and created being: "For time itself is contained in the
universe, and therefore when we speak about creation we should not inquire at what
time it happened."45 The only appropriate context for the question whether the
world existed before time is a purely logical one in which one can consider "an
instant before any other instant."46 So, although Aquinas was fascinated by the
philosophical implications of time and eternity for creation and made repeated
references to this topic in his commentaries on Aristotle, his theological impulse was

to accept Augustine’s conception of time and matter as created and not eternal.

Aquinas’ willingness to discuss the question of the etemity of the world and even to

63

suggest ways of treating it without contradicting scripture nevertheless reﬂects his
strong desire to reconcile Christian and Greco-Arabic traditions."7

Aquinas also demonstrated his capacity for synthesis in his analysis of time as
a continuum. Although we think of time as a succession of before and after, we
cannot grasp the now which is ﬂeeting and unsubstantial. Neither is it a simple
matter to measure time by observing change for change has the same characteristic
as time: both "have potentiality mingled with actuality."48 The now of time shares
certain features with a point on a line, in that it represents part of a continuous
sequence; but unlike points which make up a line, nows do not produce measurable
substance. The now is like a point mainly in its capacity to connect past to future.49
Because the now is dimensionless and has no substance, it cannot have number in
the conventional sense: number is impossible without substance, continuum or
quality.50 To the extent that time can be measured, therefore, it must be measured
in respect of the continuous succession of nows and not on the basis of the duration
of a single now. Aquinas thus was forced to consider the same sorts of problems
about time which his predecessors had faced, and his attempt at synthesis led him to
accept both a modiﬁed psychological view of time as far as perception is concerned
and a modiﬁed statement of Aristotelian physics regarding the measurement of
time.

Aquinas’ view of time, therefore, is a composite of several traditions.
Modern commentators generally concede that his views were mostly in keeping with
Aristotle and that Averroes’ reevaluation of Aristotle strongly inﬂuenced him.51 It
has been suggested, however, that, unlike Aristotle or his teacher Albertus, Aquinas
thought of time less as a factor in scientiﬁc inquiry than as a subject for
philosophical inquiry, because he did not consider time, space or motion to be

subsistent things.52 Although he did not contribute much to the solution of

problems involving the physical manifestations of time, he took the original step of

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isolating some aspects of the problem of time from physical, theological and
psychological considerations and so introduced a distinctly philosophical approach
to time.

The type of intellectual activity which Albertus had tried to instill in Aquinas
and other continental scholars had a counterpart in England. In some respects, the
study of natural phi1050phy as an adjunct of theology became by the end of the
thirteenth century an even stronger feature of the curriculum at Oxford than it was
at Paris. The importance of this trend was two-fold for Bradwardine, who like many
other students, beneﬁted enormously from the vibrant interactions of logicians,
natural philosophers and theologians who were active at Oxford at the turn of the
fourteenth century. First, as the reputation of Oxford became identiﬁed increasingly
with the physical and mathematical studies of such men as Roger Bacon and Robert
Grosseteste, the arts curriculum at Oxford began to favor subjects like astronomy,
mathematics and optics. Second, because Oxford continued to promote theology as
most worthy of advanced study, the best arts students were encouraged to suspend
their studies of natural philosophy in order to take higher degrees in theology, with
the result that many young scholars left their "scientiﬁc" pursuits just when they were
just beginning the most productive stages of their intellectual development.

Of the several thirteenth-century English thinkers who shaped intellectual
life at Oxford, Robert Grosseteste and John Duns Scotus most inﬂuenced
fourteenth-century approaches to time. While Duns’ work was fundamentally
philosophical and theological in nature and therefore speculative rather than
empirical, Grosseteste’s achievements are usually associated with his dedication to
experimental science. Like Albertus, Grosseteste is noted for the breadth of his
interests. Born in 1175, he studied at Paris and at Oxford, where he became a
master of theology, and later served as the chancellor of Oxford.53 The summit of

his ecclesiastical career was his service as bishop of Lincoln between 1235 and 1253.

65

During his lifetime, he was not only an active administrator but also a productive
writer. Before his election to the see at Lincoln he composed commentaries on the
Bible and on Aristotle. After 1235 he was engaged in translating Aristotle from
Greek to Latin. Throughout this entire period he regularly composed original
treatises on a variety of topics in natural philosophy, including logic, mathematics
and optics, for which he is best known.54

The source of the view that Grosseteste advocated a kind of experimental
science is his commentary on Aristotle’s Posterior Analytics. In this treatise
Grosseteste explored Aristotle’s claim that the purpose of natural philosophy is to
acquire demonstrable knowledge of observable phenomena. A. C. Crombie
develops the thesis that Grosseteste derived from Aristotle the notion that "scientiﬁc
knowledge, properly speaking, was the demonstrative knowledge of things through
their causes, and its instrument was the demonstrative syllogism, which established
the connexion between premisses and conclusions, or causes and their effects,
through the middle term."55 In his commentary on the Posterior Analytics
Grosseteste seemed to envision science as an intellectual activity which applied
observation and mathematical precision to the examination of matter. Indeed, he
claimed that real science is "the comprehension of the truth of those things which
always behave in a given manner, and in mathematics both the premisses and
conclusions are known in this way . . . . Therefore, to know simply and most
appropriately is to understand the unchanging cause of a thing in itself, . . . and this
knowledge is the most special goal of this [metaphysical] science and is acquired by
demonstration most properly so called."56 On the basis of this and other passages
from Grosseteste’s writings, Crombie argues that Grosseteste devised a theory of
scientiﬁc investigation which became the foundation of modern empirical science.

Grosseteste’s extensive commentaries on many tapics in natural philosophy and his

66

praise of mathematical applications to physics lend support to Crombie’s
interpretation.

More recently, however, this view has been questioned. Eileen F. Serene
suggests, for example, that Crombie has placed too much emphasis on Grosseteste’s
and Aristotle’s concern for demonstration, since they were primarily concerned not
with empirical but rather with logical veriﬁcation of natural phenomena.
Furthermore, Grosseteste’s philosophy was so heavily inﬂuenced by Augustinian
Neoplatonism that it is misleading to overemphasize the connections between
Aristotelian physics, Grosseteste’s methods of inquiry and modern science.57
Nevertheless, Grosseteste’s belief that certainty comes as a result of divine
illumination which only clariﬁes what already exists in the mind, encouraged natural
philosophers to make careful observations and to interpret them in reasonable
ways.58 The most intriguing aspect of his philosophy, therefore, was not his
experimental method but his conviction that questions about God and about the
human capacity to understand the physical universe are fundamentally related. To
the extent that Bradwardine shared the same conviction, he was undeniably one of
Grosseteste’s most successful followers.

James McEvoy develops at length Serene’s thesis that Grosseteste’s
philosophy displays a subtle blend of Aristotelian and Augustinian elements.
According to McEvoy, Grosseteste’s cosmology was essentially Aristotelian. By
carefully comparing Grosseteste’s views to Aristotle’s, however, McEvoy exposes
signiﬁcant deviations. While be readily accepted Aristotle’s treatment of the
physical aspects of time, for example, Grosseteste, like many of his contemporaries,
rejected Aristotle’s belief in the eternity of the world. Instead, Grosseteste
advocated a cosmology which acknowledged the world’s creation in time.
Moreover, Grosseteste’s enthusiasm for describing nature mathematically has no

counterpart in Aristotle.59 In his treatise Concerning Lines, Angles and Figures,

67

Grosseteste claims that there is a recognizable mathematical component in all
natural phenomena: "all causes of natural effects can be discovered by lines, angles
and ﬁgures, and in no other way can the reason of their action possibly be known."60
According to McEvoy, this notion emerges with even greater force from his Notes on
Physics, in which Grosseteste "describes God as a mathematician who established
the basic indivisible units of space and time from which the whole extension of the
material world is effected."61

Grosseteste also considered the validity of Aristotle’s deﬁnition of time as a
measure of motion, concluding that he had failed to demonstrate concretely the
reality of time. In his own explanation of time, Grosseteste, like many before him,
compared time to a line, arguing that, because both the line and time have a single
inﬁnite dimension, exact numerical measurement of either puts one "in an area of
such difﬁculty that it lies almost beyond the scope of the human mind."62
Nevertheless, although Grosseteste admitted that time deﬁes accurate
measurement, he believed, according to McEvoy, that there is "an ultimate
foundation of the extension of space and time, a ﬁnal unit and measure which
determines their nature."63 The human mind is incapable of comprehending the
inﬁnity of time and space, which consists of an extension of inﬁnite points. Only
God, who possesses wisdom "without number," can perceive and measure time and
space accurately: for God an inﬁnite number is as ﬁnite as the number two is for
us.64 Although Grosseteste did not go on to develop possibilities for coping with
the difﬁculty of measuring time, his conception of time as the creation of a
mathematical God helped to transform the problem of time into a geometrical one,
a change which had an obvious impact on Bradwardine’s thinking about time, space
and motion.

The contribution of Duns Scotus to the medieval discussion of time is more

philosophical than scientiﬁc. Duns was born in Scotland in 1266, a little more. than

68

a decade after Grosseteste’s death. He was a Franciscan who studied and taught in
Paris, Oxford and Cambridge. Before his death in 1308 he composed an extensive
array of philosophical works, including commentaries on Aristotle’s metaphysical
works, commentaries on the Sentences and several original treatises. His most
important work, the Opus Oxaniense, appears to be a written compilation of the
course which he gave at Oxford, but it contains his most mature reﬂections on many
philosophical and theological problems and so has been called his "deﬁnitive work
and masterpiece."65 Even as a young student Duns showed a remarkable talent for
metaphysical speculation which his teachers recognized and helped him to develop.
Later as a teacher he earned the title of Subtle Doctor, which attests to the respect
which he received from his students and peers.66 Duns’ thought deserves to be
considered, therefore, not only because he proposed original solutions to a wide
range of philosophical problems but also because he attracted a large following,
particularly at Oxford.

Duns’ philosophy must be seen in the context of the debate which raged in
his day over the relative merits of Augustinian and Aristotelian metaphysics. Both
sides accepted "the strict metaphysical transcendence of God over creatures." They
disagreed when it came to deﬁning the precise relationship of God to his creation.67
In response to the burst of interest in Aristotelian philosophy in the second half of
the thirteenth century, many conservatives complained that Christian interpreters of
Aristotle, particularly Aquinas, stressed too much God’s transcendence and urged
instead a more Augustinian approach which did not depend on such a rigid
separation of God and creation. Threatened by the radical Aristotelianism
espoused by certain followers of Averroes, theologians from many schools, including
some Dominican masters, raised opposition to even the moderate Aristotelianism of
Albertus and Aquinas. The most vocal opponents of Aristotelian philosophy,

however, were the Franciscans.68 As a Franciscan, Duns responded to the dispute

69

not by taking a side but by trying to synthesize a new philosophical system which
preserved the best features of both approaches. To achieve such a synthesis, he
criticized both traditions with great skill and insight.69 His comments on time and
space in particular reﬂect his subtle reconsideration of both Aristotelian and
Augustinian metaphysical theory.

In his analysis of time as a phenomenon of nature, Duns readily accepted
Aristotle’s deﬁnition of time as the measure of motion. In the De rerum principia
Duns conﬁrmed Aristotle’s assertion that motion and time are different aspects of
the same thing.70 Duns also maintained, however, the validity of Augustine’s view
that the human experience of time is subjective because time consists of a
continuum of unanalyzable nows. To support his synthesis of the two positions Duns
recounted Aristotle’s story of the sleepers of Sardis which illustrates how our sense
of time comes from the subjective experience of before and after rather from the
objective observation of motion. When the sleepers awoke they failed to realize
that any time had passed because the last now of their former consciousness was
linked to the ﬁrst now of their waking; thus the intervening time was essentially lost
to them. Duns then related Aristotle’s story to the common experience of falling
asleep and awakening in a dark place: usually we cannot tell what time it is without
referring to an external source of information.71

This is not to say that there is no objective basis for time, but merely that we
cannot easily recognize it. Our perception of time relies on our perception of the
sequence of past, present and future, which has nothing to do with motion itself,
though it does involve change.72 Duns warns us not to confuse his
acknowledgement of the difﬁculty of measuring time with an acceptance of
Augustine’s position. In Duns’ opinion Augustine erred by conceiving of time purely

subjectively and by failing to "consider it a property of real things."73 Nor does

70

Duns entirely accept Aquinas’ objective conception of time, which identiﬁes the
unity of time with "the unity of the ﬁrst heaven, by which all motion is measured."74

Because he wished to preserve some features of Augustinian subjectivity
while retaining the basic objectivity of Aquinas’ view, Duns attempted to reconcile
the two approaches. Thus he proposed that "time and motion are objectively (in re)
identical, but conceptually (farmali ratione) diverse. According to its esse materiale,
time exists in things; according to its esse farmale, in virtue of which it is to be called
time in the truest sense, it depends on the mind and exists in the mind."75 Duns
insisted that his view was in keeping with Aristotle and Averroes, both of whom
stressed that time has a universal nature as the number of motion and a subjective
nature, because the number of time is determined by the mind.76 Although time is
the objective measure of motion, we perceive time subjectively as a continuum of
past, present and future.

Duns next suggested that the real problem with previous efforts to
understand time lay in the tendency of some of his predecessors to identify time and
motion when, in fact, they are signiﬁcantly different:

Motion, therefore, taken in its strictest sense, does not include
in 1ts notron the concepts of before and after, except
otentially, in so far as these may be added to it by thou ht.
ut time 1ncludes them. formally in its concept and is there ore
partrally subjectrve, bemg a measure of motion. It is plain,
then, that from the standpornt of the objective world motron is
more real than time, for motion is in its essence the continuous
flux whose being is not derived from thought, but quite
1ndependent of it. Time, cppsequently, has a feebler being
than motion, and is less real.
The relationship between time and eternity rests on this concept of time’s weakness
compared to motion. Time is the measure of change in corruptible being; eternity,
because it is completely removed from time and is a feature of God’s perfect,

unchanging being, cannot be measured. Between time and eternity is the aevurn,

which governs such created beings as angels and heavenly bodies which have a

71

beginning in time, but only potentially an end, because they do not pass in and out
of existence as earthly creatures do.78

Duns’ synthetic view of time was essentially a reconsideration of his
predecessors’ distinction between time and motion from the perspective of their
distinction between time and eternity. In forging this synthesis, Duns was especially
indebted to Aquinas’ own efforts to reconcile Aristotelian and Augustinian views of
time. Like Aquinas, Duns ultimately failed to provide a solution to the problem of
measuring duration when time is deﬁned as having both objective and subjective
characteristics. Duns admitted that there must be some principle which explains
time, aevum and eternity in terms of each other, but he was unable to propose
either a mathematical or a philosophical principle which determined precisely how
they coexist.79 Thus he was caught up in the same dilemma over time which had
frustrated natural philosophers and theologians since the classical period.

In many respects, therefore, temporal theory itself seems to have developed
little in the late twelfth and thirteenth centuries although Christian thinkers learned
to approach the problems surrounding time with increasing sophistication. The
prevailing tendency of the age either to correct the Aristotelian position or to
integrate Aristotelian and Augustinian principles was not conﬁned to the problem of
time, which was only one of many philosophical and theological problems under
discussion in this period. The real achievement of thinkers like Albertus, Aquinas,
Grosseteste and Duns was not that they solved any of these problems but that they
embraced new ways of seeking the truth about the connection between natural
phenomena and God’s plan for creation. The foundation of these accomplishments
was the body of scientiﬁc and philosophical material which had become available at
the end of the twelfth century. By the end of the thirteenth century the energetic
interplay between advocates for Greco-Arabic learning and their conservative critics

had given way to a more serious debate about the possibility of reconciling the two

72

traditions. It was during this troubled phase of speculation that Bradwardine

entered Oxford as a young student in the early fourteenth century.

CHAPTER FOUR
MATHEMATICS, PROPORTIONALITY AND TIME

If the thirteenth century was the age of Aristotelian revival in the medieval
universities, the early fourteenth century was a period of great diversiﬁcation in the
application of classical philosophical methods to problems of contemporary interest.
The basic tools of propositional logic and Euclidean mathematics which
accompanied the Aristotelian revival allowed fourteenth-century thinkers to develop
a variety of new approaches to long-standing philosophical dilemmas about complex
issues such as time. The expansion of the curriculum in natural philosophy,
especially at Oxford, encouraged students to conceive of old problems, even
theological ones, in new ways.1 This movement has been called the
"mathematization" of theology because fourteenth-century theologians not only
discussed theological questions in physical and mathematical terms but in some
cases adopted the axiomatic model of Euclidean geometry to present their
theological arguments.2

Bradwardine’s academic work provides an excellent illustration of this
tendency towards "mathematical" theology. His mastery of Euclidean geometry and
Aristotelian physics is a central feature of all of his major treatises. Indeed,
Bradwardine achieved such a high standard of mathematical logic that he was able,
both in philosophical and theological texts, to launch devastating attacks against his
opponents. Unlike most of his contemporaries, who composed lengthy and
exhaustive refutations of their opponents’ views, Bradwardine took a much more

subtle approach: he criticized his opponents by isolating the principles which

73

74

underlay their primary assertions and then systematically exposed their weaknesses
them using the axiomatic methods of Euclidean geometry.3 The next three chapters
of this dissertation trace the development of Bradwardine’s critical method through
an examination of his treatments of time as a physical phenomenon and a
philosophical problem.

Because Bradwardine’s reputation rested, in his own age and for several
' centuries to follow, on his mathematical works, it is appropriate to begin to explore
his views about time by reﬂecting on one of his early scientiﬁc treatises. The De
prapartianibus4 clearly demonstrates the capacity for mathematical reasoning which
characterize all of Bradwardine’s works, including those devoted exclusively to
philosophical or theological topics. Written in 1328, when Bradwardine was just
embarking on his theological studies, the De prapartianibus proposed an unusually
precise mathematical language for describing various kinds of motion than had been
available previously. His colleagues at Merton not only received it enthusiastically
themselves but, by their frequent references to it in their own treatises, helped to
ensure its circulation among all the European universities. Indeed, by the end of the
fourteenth century, the De prapartianibus had become standard academic reading
and its principles profoundly inﬂuenced physical speculation of all sorts for at least
another century.5

The signiﬁcance of Bradwardine’s mathematical approach to natural
philosophy goes well beyond his attempt to discuss motion, space, time and other
physical phenomena in terms of a well-ordered geometrical system. Bradwardine
was certainly not original in his zeal for applying mathematics to physics nor were
many of his observations about motion entirely correct, at least if judged by modern
standards. In her study of late medieval physical theory, Anneliese Maier portrays
Bradwardine as a precocious thinker handicapped by the rudimentary level of

mathematical knowledge in the early fourteenth century. Referring to the depth of

75

his mathematical insight, Maier comments: "One might almost say that Bradwardine
would have wanted to write the Principia mathematica philasaphiae naturalis of his
century,"6 but she goes on to demonstrate why he was unable to do so.
Bradwardine’s generation lacked the knowledge of certain aspects of higher
mathematics such as logarithms and the calculus which are necessary for developing
a comprehensive mathematical description of the problems which interested them.
Moreover, when Bradwardine left Oxford a few years after writing the De
prapartianibus, his concentration on natural philosophy in an academic setting came
to an end. In spite of these obstacles, however, Bradwardine produced in the De
prapartianibus a mathematical approach to physics which stimulated interest in
natural philosophy for several generations. The De prapartianibus is also an
important historical text. Through it, the historian can discover how scientific
information passed from scholar to scholar and how thinkers like Bradwardine
responded to the views of their predecessors. The obvious sources for
Bradwardine’s speculations about motion are Aristotle’s Physics and Euclid’s works
on geometry, but medieval thinkers such as Robert Grosseteste and Roger Bacon
offered precedents for applying mathematics to physics which also inﬂuenced
Bradwardine’s scientiﬁc works.7

The purpose of this chapter is to analyze the De prapartianibus: ﬁrst, as a
text of general interest in the history of late medieval science; second, as an
extension of Bradwardine’s mathematical thought which originated in his short
treatise, the Geametn'a Speculativa; and third, as an illustration of his analytical
approach to time. Although the De prapartianibus is not speciﬁcally devoted to the
problem of time but only concerns time as an incidental feature of motion, it helps
to clarify Bradwardine’s conception of the relationship between time and motion.
This discussion of the De prapartianibus will suggest that Bradwardine’s scientiﬁc

thought was ﬁrmly rooted in an Aristotelian tradition and that, despite his

76

willingness occasionally to correct or modify Aristotelian deﬁnitions, he largely
adopted Aristotle’s description of the physical universe. The novelty of
Bradwardine’s work lay in his attempt to use geometry to reconcile contradictions in
traditional physics which previous Aristotelians such as Avicenna and Averroes had
been unable to resolve because they did not supplement their philosophical
approaches to physics with mathematical analysis.

A review of the main themes and structure of the De prapartianibus
emphasizes the signiﬁcance of this work in early fourteenth-century scientiﬁc
thought. In his introductory remarks Bradwardine set out both his intentiOns for the
treatise and also his general views about the applicability of mathematics to the
study of physics: -

Since each successive motion is roportionable to another
with respect to speed, natural p ilosophy, which studies
motion, ought not to ignore the proportron of motions and
their speeds, and, because an understanding of this is both
necessary and extremely difﬁcult, nor has as yet been treated
fully in any branch of philoso by, we have accordingly
com osed the following work on t e subject. Since, moreover
(as oethius points out in Book I of his Arithmetic), it is agreed
that whoever omits mathematical studies has destroyed the
whole of hilosophic knowledge, we have commenced by
setting fort the mathematics needed for the task in hand, in
order tq3 make the subject easier and more accessible to the
student.
Following this preface, Bradwardine spelled out in four chapters precisely how he
proposed to establish Aristotle’s thesis concerning the proportionality of motion,
proceeding from general deﬁnitions and properties of proportions to criticism of
four attempted revisions of Aristotle, to a discussion of the relationship between
force and resistance, and, ﬁnally, to an analysis of the principles of circular motion,
which was commonly held to be the most regular and perfect kind of motion.
Bradwardine’s insistence on deﬁning the problems surrounding motion

mathematically and according to Euclidian patterns of suppositions sets his analysis

77

apart his predecessors, who had not appreciated the advantages of approaching
studies of motion in this way.

Beyond the insights which this introduction provides into Bradwardine’s
purpose in the De prapartianibus, it reﬂects his commitment both to the Aristotelian
tradition, which identiﬁed the study of nature with the study of motion, and to the
Platonic tradition, which emphasized mathematics as the appropriate language for
philosophical and scientiﬁc discourse. The rest of the De prapartianibus reveals,
however, that Bradwardine did not wish to use mathematics in a purely Platonic
way, that is, as a description of a natural order which could be perceived through
philosophical speculation. Nor was he content with an Aristotelian approach to
motion, whose theories did not take into account sufﬁciently the axiomatic
principles of mathematics.

The De prapartianibus not only incorporated features of these ancient schools
of thought, both of which had been widely pursued in the thirteenth century, but it
also presented a novel approach to natural philosophy based on a mathematical
view of nature. Bradwardine’s work on the proportionality of motion helped to push
discussions of natural philosophy in new directions and to encourage speculation
among his peers, principally his colleagues at Merton, the Oxford "Calculators." It is
useful, therefore, to look at the antecedents of his mathematical thought, both in the
ancient sources of Plato, Aristotle, Euclid and Boethius and among his more
immediate predecessors. Only then can his views be seen in the appropriate context
and the themes which have particular signiﬁcance for his view of time be adequately
isolated and evaluated.

Bradwardine’s convictions about the applicability of mathematics to nature
stemmed from a long debate which dated from the classical period. Because the
classical philosophers had often approached the problem of time mathematically

and described time geometrically, the philosophical issues which shaped this debate

78

deserve attention.9 The disagreement between Plato and Aristotle over the role of
mathematics in natural philosophy was fundamentally cosmological. Plato’s view of
the material world rested on his belief that being is composed of four elements,
earth, air, ﬁre and water, each particle of which is a deﬁnite, regular geometrical
shape. The unity of the universe and the course it takes in its development come
from the mathematical rule of geometric proportion. Thus one cannot attain
complete knowledge of the sensible world without comprehending the mathematical
framework which determines its forms. According to Plato, therefore, the pursuit of
natural philosophy demands the contemplation and the analysis of mathematical
laws which govern the form of matter, not the observation of natural phenomena as
such.

Although Aristotle considered mathematics an extremely useful tool for
scientiﬁc investigation, he completely rejected the notion that all knowledge of the
world must be expressed in the abstract terminology of mathematics. Such an
approach would make it impossible to consider sensible qualities which are at the
heart of physical investigation. Thus he remarks in the Metaphysics:

. in his investigations [the mathematician] ﬁrst abstracts
eve ' g that is sensible, such as wei t and lightness,
har ness and its contrary, and also heat an cold and all other
sensible contrarieties, leaving only quantity and continuity -
sometimes in one, sometimes in two and sometimes in three
dimensions - and their affections qua quantitative and

continﬂpus, and does not study them with respect to any other
thing.

 

The mathematician, moreover, shares in the process of scientiﬁc investigation by
evaluating information, but he does not dominate it. In the discipline of astronomy,
for example, " . . . it is the business of the empirical observer to know the fact, of the
mathematician to know the reason for the fact."11 Without denying the validity of
mathematics as a scientiﬁc resource, Aristotle minimizes its position in natural

philosophy on account of its inability to express real, sensible features of the

79

universe. His conﬂict with Plato centers on their divergent views about the nature
of reality itself.

Both sides in this dispute found their way into early medieval philosophy.
Augustine and Boethius focused on the Platonic concept of the mathematical order
of nature and asserted that creation proceeds according to numerical principles in
the mind of God. It was Boethius, however, who also established the medieval
classiﬁcation of disciplines along Aristotelian lines.12 Throughout the earlier
Middle Ages, such thinkers as Hugh of St. Victor, Thierry of Chartres, Gilbert of
' Porrée, William of Couches and Clarembaud of Arras recognized the distinctions
between mathematics and physics although they were not entirely free from the
temptation to emphasize the transcendence of numbers in the natural order. In his
Didascalican, for example, Hugh of St. Victor accepted aspects of both Aristotelian
and Platonic approaches to mathematics. oh the one hand, his conception of
scientiﬁc disciplines was rooted in Aristotle’s notion of sensible entities. He
distinguished between mathematics, which treats abstract things such as lines and
surfaces, and physics, which concerns real things. Thus mathematics "has its
business in the consideration of things which, though actually fused, are rationally
separated by it. . . . The business of physics, however, is to analyze the compounded
actualities of things into their elements."13 In his treatment of the soul, however,
Hugh accorded to the study of numbers a metaphysical reality far greater than
Aristotle had ever acknowledged. In fact, for Hugh "number itself teaches us the
nature of the going out and the return of the soul."14

Bradwardine’s immediate predecessors in the thirteenth century wrestled
with the same ambiguity about the proper role of mathematics in natural
philosophy. This conﬂict is best illustrated by Grosseteste, who tried to integrate
physics and metaphysics along mathematical lines. Grosseteste is best known for his

development of the "metaphysics of light," a system which sought to deﬁne the ~

80

function of light in the creation of the universe. He did not conﬁne his speculations
to natural philosophy; theology, epistemology and metaphysics all contributed to his
synthesis. Although his use of light to explain the creative forces of the universe had
Platonic origins, many of his concrete statements about mathematics and physics
were more in keeping with Aristotelian principles of natural philosophy.
Grosseteste might have been attracted to N eoplatonic discussions of light because
of his interest in giving natural phenomena mathematical explanations. His
consideration of the Neoplatonists and the Muslim philosopher Alkindi led him to
develop a "light metaphysics" based on geometrical optics, which he hoped could be
veriﬁed experimentally.15 Basing his system both on the geometrical concepts of
Neoplatonism and on Aristotle’s scheme of four elementary spheres, Grosseteste
tried to accommodate the ideas of both traditions in a single physical system which
was also thoroughly in harmony with his Christian theology.

In his commentary on Aristotle’s Physics, Grosseteste expressed a view
concerning the proper relationship between mathematics and time which was later

echoed by Bradwardine. Grosseteste asserted that mathematics and physics

have much common ground and because of this a physicist can
easily make the mistake of thinking that mathematical being is
physrcal being and that ph sical being is mathematical being;
and so that he [Aristotle himself will not in this science
[physics] suppose something purel mathematical to be a
emonstration on the assumptron t at it is physical, or omit
something physical on the ground that it is mathematical, he
subtly shows the difference between ph sics and mathematics
so that it may be possible to distinguis what belongs to this
science and what not. And so I say that there are three things,
namely, physical bo , magnitudes which belong to physical
bodies, and acci ents of bodies purely s eaking.
Mathematicians abstract magnitudes from motion an matter
and have as subjects abstract magnitudes, and from these they
demonstrate accidents which are per se accidents of
magnitudes. But the physicist does not demonstrate per se
accrdents of magnitudes as belonging simply to magnitudes, but
he demonstrates the ﬁgured magnitudes of physical bodi as
belonging to physical bodies in so far as they are physical.

81

Thus Grosseteste afﬁrmed Aristotle’s distinction between the abstract analysis of
the mathematician and the observation of sensible qualities which is the proper task
of the natural philosopher.

In his geometrical treatise, Concerning Lines, Angles and Figures, Grosseteste
emphasized the essential place that mathematics holds in physical investigations.
According to Grosseteste, the mathematician helps the physicist to elucidate the
structure of things by providing a system for describing natural phenomena.17 In a
continuation of this treatise entitled De natura lacarum, Grosseteste stressed the
necessity of mathematical analysis in the study of light. As a conclusion to his
discussion of reﬂection and refraction of light, for example, he claimed:

These rules, foundations, and fundamentals having been given

by the power of geometry, the diligent investigator of natural

things can in thrs manner specify the causes of all natural

effects. And he can do this in no other way, as has already

been shown in general, since every natural action is varied in

strength and weakness according to the variation of lines,

angles and ﬁgures.
Through this study of light and his commentaries on Aristotle, Grosseteste achieved
a balance between Platonic and Aristotelian views which gave mathematics a
prominent place in natural philosophy while preserving the integrity of investigation
based on the observation of sensible qualities. In Grosseteste’s view, the world is
not composed of mathematical entities, but it exists in patterns which mathematics
can explain and describe once observations have been made.

Another thirteenth-century thinker who stressed the importance of
mathematics to scientiﬁc inquiry was Roger Bacon. In his Opus maius Bacon argues
that Aristotle himself placed the highest value on mathematics as a method for
determining the causes of things:

But only cause leads to true knowledge (scientia), or at least it

does so far better than effect, since_ Aristotle says in the
Posterior Analytics, book I, that we thll‘lk we know when we

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know the causes. Therefore, since demonstration, as he says in

the same place, is a syllogism causing us to know,

demonstration by cause is necessarily far more powerful than

demonstration by effect. . . . Therefore, since in natural things

demonstration by cause is obtained by means of mathematics,

and demonstration by effect is obtained through natural

philosophy, the mathematician is better able to obtain e

owledge of natural things than is the natural philosopher.

Mathematics maintains this advantage over natural philosophy because it can be
used to create an internally consistent and self-verifying argument. Bacon contrasts
science, which, "full of doubts and sprinkled with opinions and obscurities, cannot be
veriﬁed except through other sciences," with mathematics, which "remains certain
and veriﬁed to the limits of veriﬁcation."20 It is the philosophical rigor of
mathematics, whose principles can be mastered by any educated person, which
makes it indispensable for any advanced study of nature.

Bacon was certain, therefore, that mathematics could enrich the full range of
human inquiry, including theology, not by reducing all subjects to numerical or
geometrical forms, but by providing a precise vocabulary for describing those
subjects. Like Grosseteste, moreover, Bacon believed that knowledge of God and
the Scriptures depended on the scientiﬁc investigation, aided by mathematics, of all
natural phenomena: "the theologian must know the things of this world if he wishes
to understand the sacred text."21 This progression of mathematics from a simple
tool to a necessary language for natural philosophy and ﬁnally to a component in
theological speculation underlay all discussions of mathematics in the early
fourteenth century and must be taken into account in any investigation of
Bradwardine’s use of mathematics in his philosophical and theological studies.

Bradwardine’s position on the role of mathematics in philosophical inquiry,
as it emerges in the De prapartianibus and even more fully in the De continua,

developed out of his early studies in elementary geometry. Since geometrical

analysis is the hallmark of all of Bradwardine’s work, it is worthwhile to look brieﬂy

83

at one of his earliest treatises, the Geametria speculativa.22 Bradwardine’s purpose
in writing this work was to organize the material on geometry which had been
presented in lectures required for the master of arts degree. More a notebook than
a treatise, the Geametria speculativa did not display particular originality although
its clear and effective structure ensured its wide circulation among other students,
ﬁrst at Oxford but soon beyond England as well. The primary inﬂuences on this
work, naturally, were Aristotle and Euclid, on whose texts the lectures on geometry
were based. Bradwardine also drew on Boethius’ Arithmetica and perhaps his
Musica, as well as the Arabic commentaries on Aristotle.23 The contents of the
Geametria speculativa covered all the major topics of elementary geometry,
including the deﬁnitions of points, lines and angles; Euclidean theorems regarding
these deﬁnitions; an analysis of polygons and circles; an examination of ratios; and a
study of regular solids and spheres.24 Although Bradwardine occasionally took time
to explore a current controversy over a geometrical problem, his treatise was
essentially a systematic review of basic terms and concepts as they had been
presented in the lectures. His arrangement and treatment of standard topics
nevertheless reﬂect his own style of mathematical thinking and reveal many of his
philosophical assumptions.

The Geametria speculativa nevertheless reﬂects some of the theoretical
problems which mathematicians encountered in the thirteenth and early fourteenth
centuries. One controversy which has already been mentioned was, of course, the
question of how to use mathematics in the pursuit of natural philosophy. The
mathematicians themselves complicated the discussion by taking different positions
in the debate. Some mathematicians, following the Platonic tradition, argued that
mathematics was a fundamentally conceptual activity; that is, they stressed the
abstract qualities of mathematics and preferred to concentrate on abstract problems

which were removed from any reference to physical reality. Others, who were more

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sympathetic with the Aristotelian approach to physics, tried to make mathematics
conform to sensible qualities and so have been called realists.

In the discipline of geometry, each side could claim to hold the ideologically
stronger position. The conceptualists, being aware of the abstract nature of
geometrical deﬁnitions and manipulations and comforted by the traditions of
Platonism and Neoplatonism, argued quite convincingly that an understanding of
geometry could reveal the mathematical basis of nature without any reference to the
sensible world. The realists, on the other hand, claimed that geometry would be an
empty discipline if it were not used to explore the physical world which directed and
shaped human existence. Both sides encountered problems in deﬁning the proper
scope of geometrical studies. As A. G. Molland points out, "the realist may have
had difﬁculties in adapting his geometry to the physical world, but the conceptualist
could not easily ﬁnd grounding for a mathematical natural science."25 According to
Molland, who has studied the Geametria speculativa at considerable length,
Bradwardine’s early position in this debate placed him near the realists. Because his
analysis of geometrical subjects in this text routinely involved a statement of
relevant Aristotelian principles, an exposition of the problems to which these
principles generated and a brief consideration of possible solutions. In fact, the text
came to be seen not as a general work on geometry as such, but as an Aristotelian
manual, "gathering together all the geometrical conclusions which are most needed
by students of arts and the philosophy of Aristotle."26

It is in the Geametria speculativa, for example, that Bradwardine ﬁrst
addressed the dilemma of inﬁnity, a necessary concept in Euclidian geometry which
directly contradicts Aristotle’s assertion that the world is ﬁnite.27 We shall return
to this problem later in the discussion of the De continua, but it is interesting to note
here that, by referring to the problem at all, Bradwardine showed that he was

already thinking about the difﬁculties of applying mathematical principles to natural

85

phenomena. Bradwardine also showed awareness of the opinions of Aristotle’s
medieval commentators, as when he discussed Averroes’ interpretation of
Aristotle’s views concerning space. Indeed, Molland argues that, at least in the case
of the Geametn'a speculativa, Bradwardine revealed much greater concern for

theoretical questions than for technical issues such as geometrical exactness, though

he did pay careful attention to the special problem of measurement.28

In the context of the De prapartianibus, the most interesting section of the
Geametria speculativa is the one which deals with ratio theory. Bradwardine first
distinguishes between arithmetic ratios and the much wider range of geometric

ratios and then devises a deﬁnition which would apply to both types. Thus he states:

Because the intention of ‘ratio’ is extended and applied to
almost all things that are mutually comparable according to
greater and less, it can be deﬁned in accord with this eneral
concept: A ratio is a certain habitude of some things t at are
mutually comparable one to the other. For example, of a
number to a number, a magnitude to a magnitude, a sound to a
sound, a time to a time, a motion to a motion, a humour to a
humour, a heat to a heat, a taste to a taste. But geometry
ascribes the intention of ‘ratio’ to ma 'tude and has it to be
deﬁned thus: A ratio is a certain habrtude of two qualities of
the same genus, one to the other. I say ‘35 the same genus’
because only such are mutually comparable.

Bradwardine goes on to distinguish between rational and irrational ratios along the

lines of Book V of Euclid’s Elements:

Ratio is divided into two species which are received in
comparison with proportionally diverse quantities. For some
quantities are communicating or commensurable, some
incommunicatin and incommensurable. Commensurable
quantities are ose for which there is a common quantity
measuring them. One quantity is said to number another if
when taken according to a certain number [taken a certain
number of times] it produces it [the second quantitY], as a foo:
line [produces] a two-foot line and a three-foot line.
There ore, a two-foot line and a three-foot line are
communicatin quantities which a foot line numbers by Two
and Three. ut quantities for which there is no common
quantity numbering them are called incommensurable. Of this
kind are the diagonal and side of a square. According to this,

86

therefore, there are two species of ratios, namely rational and
irrational. A rational ratio is found (debetur in
commensurable quantities, and it is the only one that is ound
in numbers. But an irrational one ﬁts incommensurable
uantities, but in nowise numbers. Whence it is manifest that
e whole consideration of ratio concerns geometry, becaqﬁe
every ratio is of magnitude, but not every 1'3.th is numerable.

Bradwardine’s explanation of ratios rests initially, then, on the logical distinction
between things which have a common denominator and those which do not. He was
not primarily interested, however, in demonstrating this distinction mathematically.
In evaluating this feature of Bradwardine’s ratio theory, Molland suggests that

Bradwardine’s ﬂexibility on this point helped him to develop his broader theories of

ratios in series, or, in other words, his theory of proportions.31

At the heart of Bradwardine’s theory of proportions is the concept of
denomination, that is, the quantity or quality by which two commensurable things
can be compared. He points out that both rational and irrational ratios can be

denominated, though, of course, in different ways:

A rational ratio therefore is immediately denominated by some
certain number, for, since it is of commensurable quantities, it
is necessary that the lesser or some part of the lesser should
number the reater according to some number, on account of
which Euclici says that of any two commensurable quantities
the ratio of one to the other 15 that of a number to a number,
and this will be clearer below. This species is divided in every
mode, in which ratio is divided in arithmetic. For one is a ratio
of equality, another of inequality. . . .

An irrational ratio is not in this way immediately
denominated by some numerical ratio, because it is not
possible that some part of the lesser should be number the

eater according to some number. But it turns out that an
irrational ratio may be mediately denominated by number.
For exam le, the ratio of the diagonal [of a square] to the side
is half 0 a double ratio, and so ether species of this ratio
receive denominations by number.3

Bradwardine’s logical analysis of irrational ratios continues with a further
distinction, ﬁrst introduced by Euclid, between ratios of lines which are

commensurable in length only and ratios of lines which are commensurable in

87

respect of both length and power. He provides a method for producing an inﬁnite
series of irrational ratios by manipulating terms of previous ratios through division:
Each species can be divided into as many species as there are
ways for lines to be thus or thus incommensurable, for not only
can lines be incommensurable in length only when they are as
diagonal and square, but in other ways perhaps inﬁnite [in
number]. I speak similarly of lines incommensurable in length
and power, because they are not only those that are taken as
means between side and diagonal, and the means between the
mean and them, and further the means between?) these and
those, and so on indeﬁnitely, but also many others.
Although it is expressed primarily in abstract terms in the Geametria speculativa, this
logical framework of ratio theory is the starting point in the De prapartianibus for
further consideration of a physical phenomenon, motion.

When Bradwardine returned later to the problem of ratio and
proportionality, his intentions were much more speciﬁc; and the resulting work was
much more original. He nevertheless drew on a large body of commentary whose
contributors spanned the classical and medieval periods. As the Geametria
speculativa indicates, proportional theory was widely discussed among Latin and
Muslim mathematicians and was applied to the problems of arithmetic, algebra and
geometry. Bradwardine expanded the scope of proportional theory in the De
prapartianibus by applying it to physics as well.34 It was at this stage that his
tendency towards realism, ﬁrst suggested in the Geametria speculativa, fully emerged
and his dedication to an Aristotelian physical theory became ﬁrmly established.

Bradwardine’s originality lay not so much in his support for the idea that
mathematics should be at the disposal of natural philosophy, for, as we have seen,
he was not the ﬁrst to make this claim. His reputation as an innovator rests instead
on his fortunate application of proportional theory to a mechanical problem which

had previously deﬁed mathematical analysis. Bradwardine did not, of course, come

close to articulating the principles of advanced mathematics which later allowed

88

Newton to explain the properties of motion more elegantly and, in a modern sense,
more accurately; but his recognition that elementary geometry and algebra are
inadequate for describing such concepts as force, velocity and resistance had a
profound effect on future scientiﬁc investigation. Bradwardine’s insight that the
natural philosopher required a better mathematical language, coupled with his
conviction that natural philosophy could not be well understood without
mathematics, explains why historians associate Bradwardine with Galileo as
formulators of modern scientiﬁc thought.

In the De prapartianibus.~ Bradwardine was chieﬂy concerned with
demonstrating how the theory of proportions could be applied to the study of
velocity so as to defend Aristotle’s laws concerning natural motion.35 According to
Aristotle, the universe is ﬁnite, and the change which occurs within it is successive
and takes place within time. Aristotle went on to deﬁne change as a kind of motion:
change takes place as motion overcomes natural resistance in a successive, though
not necessarily uniform, manner. Change, then, requires space, time and the
superiority of a moving force over a resisting force. Yet Aristotle also admitted that
some kinds of change do not appear to ﬁt this deﬁnition. He afﬁrmed, for example,
that the heavenly bodies move even though they are not subject to any resistance;
and although the heavenly bodies cannot be equated with time, an observer can
measure time by marking their movements.

As we have already seen in the discussion of Averroes’ criticism of Aristotle’s
view of time, Aristotle himself neither resolved this problem nor provided enough
information for his successors to do so on his behalf. Medieval Aristotelians were
willing to accept that a distinction had to be made between the two kinds of natural
motion, that is, motion against resistance along straight lines as experienced on
earth (rectilinear motion) and the free motion in the celestial sphere. They

nevertheless believed that both kinds of motion should conform to the same laws.36

89

The search for these laws within the framework of Aristotelian physics as it was
understood in the thirteenth and fourteenth centuries provides the context for
Bradwardine’s thesis about proportions.

In the thirteenth century considerations of the nature of motion focused on
the differing explanations of two Muslim thinkers, Avempace and Averroes.
Avempace’s approach to the problem of the relationship of resistance to force in
motion, based as it was on logical deﬁnitions of the celestial sphere, was essentially
Platonic. He argued that, because heavenly bodies move at a steady rate and do not
appear to encounter any resistance, the resistance which affects sublunary motion
must be impeding a force which would otherwise move at a steady, absolute
speed.37 In other words, all motion would proceed at a determinate rate both in
heaven and on earth if resistance were eliminated. Avempace reduced this theory
to a simple arithmetic equation: v=f-r, that is, the velocity of an object is equal to
the amount of force which overcomes the resistance which impedes it. This theory
was in conﬂict with Aristotelian principles because it was based on a narrower
deﬁnition of motion than Aristotle would accept. Avempace assumed that all
motion is fundamentally regular, orderly, and consistent, which directly contradicted
Aristotle’s observation that motion is a kind of change. According to Aristotle,
many motions, such as the motion of ﬁre or that of a growing plant, are too irregular
and complex to be accurately described with a simple mathematical formula like
Avempace’s.

Admittedly, Aristotle and his followers failed to provide an alternative
theory. Averroes in particular struggled with this problem without producing a
coherent solution. His suggestion, for example, that the heavenly bodies actually do
encounter resistance, on the grounds that resistance is a necessary cause of the
successive nature of motion, led him to conclusions which contradicted other

Aristotelian positions and did not shed much light on the problem of comparing

90

different types of motion.38 Nevertheless, Averroes’ criticism of Avempace’s theory
of motion focused attention on the weaknesses of classical physics and stimulated
discussions of those weaknesses throughout the thirteenth century. In spite of
Averroes’ objections, however, the simplicity of Avempace’s explanation of force
made it appear the more reasonable approach, and it won adherents even among
those who sympathized most with Aristotle. H. Lamar Crosby observes that
Thomas Aquinas, Roger Bacon, Pierre Jean Olivi and Duns Scotus were all
inﬂuenced to some extent by Avempace’s view.39

Bradwardine’s contribution to this debate involved his mathematical insight
into the rather vague use of the concept "ratio" within the Aristotelian tradition.
Aristotle’s law of motion states that the speed of a moving object depends on the
ratio of its motive power (force) and its resistance: v=f/ r; but his analysis of the
relationship between force and resistance suggests that he had no rule in mind for
calculating the force of any particular moving object. When Averroes turned to the
same problem, he restated Aristotle’s position without making it clear whether he
believed that the ratio between force and resistance was a simple proportion or, if
so, how such a simple proportion could explain changing rates of speed or irregular
motions. Averroes simply declared, in opposition to Avempace, that "it is necessary
that between the mover rand the thing moved there be a resistance. . . . [Therefore,]
every motion will be according to the excess of the potency of the mover over the
thing moved, and the diversity of motions in speed and slowness is according to this
proportion which is between the two potencies and these resistances."”’0

What came to interest Bradwardine was the notion of "diversity of motions in
speed and slowness." He was not satisﬁed simply to know that such a diversity had
to exist whenever motion varied according to speed and slowness but wanted to be

able to calculate this diversity mathematically. Thus, after giving an extensive

review of the mathematics of ratio in the De prapartianibus, he turned in the second

91

chapter to a refutation of common assumptions about the nature of motion.
Bradwardine’s ﬁrst target was Avempace, whose theory be challenged on

Aristotelian lines:

Having looked into these introductory matters, let us now
proceed with the undertaking which was ro osed at the
outset. At ﬁrst, after the manner of Aristot e, et us criticize
erroneous theories so that the truth may be the more a parent.

There are four false theories to be roposed as re evant to
our investigation, the ﬁrst of which hoids that: the proportion
between the speeds with which motions take place varies as the
difference whereby the paw‘ff of the mover exceeds the resistance
offered by the thing moved. '

Bradwardine based his criticism of Avempace on the observation
(mathematical, of course, not experimental) that the halving or doubling of a force
does not result directly in the halving or doubling of velocity. The relationship
between force and resistance is proportional, so the change in velocity must proceed

geometrically (that is, exponentially), not arithmetically:

. . . it follows from [Avempace’s] theory that, given two movers
moving two mabilia through e ual distances in equal times, the
two movers, conjoined, wo d not move the two mabilia,
conjoined, through an exactly equal distance in an equal time,
but, instead, throuih double that distance. This consequence
follows necessarily ecause the excess of the two movers, taken
together, is twice the excess of each of them over its own
mobile; for, just as anything having a value of 2 exceeds uni
by 1, so two such ‘2’5’ (which make 4) exceed two ‘1’5’ (whic
make 2) b 2, which is twice the excess of 2 over 1. The
foregoing olds in all cases in which two subtrahends are
equally exceeded by two minuends.

That the above consequence is false is evident from the
foregoing argument in Aristotle, in Book VII of his Physics,
where he demonstrates the following conclusion: ‘If two
powers move two mabilia separately, through equal distances
1n equal times, those powers con'oined, will move the two
mabi ia conjoined, through an equ distance in a time equal to
the former one.’ This argument of Aristotle is sufficient proof
that the relationship between a single mover and its mobile,
and 45 compound mover and its mabilia, is a proportional
one.

92

Bradwardine defended both Aristotle and Averroes from the charge that

they perceived the diversity of motions as a matter of simple proportions:
Nor can it be legitimately maintained that, in the passages

cited, Aristotle and Averroes understand by the words

‘proportion’ and ‘analogy,’ arithmetic pro ortionali (that is,

equali of differences), as some have c aimed. deed, in

book I of the Physics, Aristotle proves this conclusion: ‘If a

given power moves a given mobile through a given distance in a

given time, half of that power will move half the mobile

through an equal distance in an equal time, because,

‘analogically,’ the relation of half the mover to half the mobile

is simrlar to that of the whole mover to the whole mabile.’

Such a statement, interpreted as referring to arithmetic

pro ortionality, is discerni 1y false (as has already been made

su cientl clear in the ﬁrst argument raised against the

present t eory). Moreover, regarding the same passage,

Averroes says that the proportion will be the same ‘int e gense

that geometricians universally employ in demonstrations.’
Even as Bradwardine defended the Aristotelian position, however, he enhanced it to
make it conform to his own more sophisticated understanding of ratio theory. He
similarly dismissed the next three theories, which relate to particular aspects of
Avempace’s original assertion. Throughout this discussion, Bradwardine repeatedly
vindicated Aristotle and Averroes against the misjudgments of Avempace and his
followers.

In his third chapter, Bradwardine suspended his criticism of others and
offered a more positive approach to the problem of proportional motion, declaring
conﬁdently: "Now that these fogs of ignorance, these winds of demonstration, have
been put to ﬂight, it remains for the light of knowledge and of truth to shine forth.
For true knowledge possesses a ﬁfth theory which states that the proportion of the
speeds of motions varies in accordance with the proportion of power of the mover to
the power of the thing moved."44 Arguing again that this proposition was
thoroughly in keeping with the ideas of Aristotle and Averroes, Bradwardine
actually suggested here a much more complex principle than any of his predecessors

had ever stated either explicitly or implicitly.

93

Bradwardine’s theory of the "proportionality of proportions," as it later came
to be called, was based on his rejection of the traditional formulation of Aristotle’s
law of motion which claimed that velocity could be doubled either by doubling the
force or halving the resistance. In the ﬁrst place, although this particular ratio of
force to resistance might be true in some cases, it could not be applied to all motion:
most motions do not conform to a strict two-to-one ratio. Second, Bradwardine
believed that a simplistic interpretation of Aristotle’s law would suggest that any
force can move any object, when in fact motion only takes place when force exceeds
resistance. What was required instead was a new interpretation of the laws of
motion which took into account the exponential character of force: to double a
velocity, Bradwardine concluded, one does not double the force but squares it. Or,
as Weisheipl explains,

Bradwardine proposed a new law, maintaining that a double

velocity must follow from the entire ower-to-resistance ratio

duplata, i. e., not multiplied by two, ut squared, for twice a

prapartia tripla is one which contains the ratio 3:1 twice. But

only the square of the ratio, i. e., only 9:1, contains twice the

prapartia tn'pla, for the ratio 9:1 is composed of 9/3'3/1. Thus

only the ratio 5 uared can ive twice the velocity. Similarly,

triple velocity fo lows from t e ratio tn'plata, i. e., raised to the

thrrd power. Conversely, half the velocity would follow from

the medietas of the ratio, that is, the square root of the ratio;

one third of the velocity follows from the cube root, and so

forth; thus the mover can never be less than the resistance.

Bradwardine’s exponential function was theoretically valid for

all cases, and it eliminated the possibility of zero-veloci .

Today the5 latter situation is taken care of by a logarithrruc

functron.
It is worth noting that, in spite of Bradwardine’s originality in devising this ﬁfth
theory, neither he nor his contemporaries realized how great an advance he had
made over his predecessors. Bradwardine, with abiding respect for Aristotle, merely
assumed that he had discovered Aristotle’s original intention; and his

contemporaries responded to the ﬁfth theory not so much because they perceived it

94

to be original as because it presented a plausible explanation of Aristotle’s law of
motion.46

In the ﬁnal chapter of the De prapartianibus, Bradwardine addresses the
special problems of circular motion which Avempace’s references to the celestial
sphere had prompted. Bradwardine acknowledged that rectilinear and circular
motion had different characteristics but insisted that both kinds of motion were
subject to the same laws of proportionality. The purpose of the fourth chapter,
therefore, was to demonstrate the inﬂuence of proportionality on the motions of
geometrically different entities. His conclusion was, essentially, that proportional
motion applies equally to a body moving in a circle or in a straight line. The speed
of the moving body, not its path, is the most important factor for consideration.“

Thus Bradwardine united into one comprehensive rule the principles of
linear and circular motion. His theory of proportionality could be used to explain
both kinds of motion and to compare them to each other with a mathematical
precision which had never been possible before. Because his system was purely
descriptive and was based on no experimental evidence, Bradwardine did not realize
that many of his speciﬁc claims do not actually correspond to the realities of motion.
His main purpose, to defend Aristotle from claims that his laws of motion were
vague and self-contradictory, was well fulﬁlled in the De' prapartianibus. More
important for the history of science, his underlying assumption that acceleration
involves geometrical proportionality was substantially correct, and his presentation
of that thesis stimulated more successful studies of the problem of motion. His
greatest contribution, however, was his enthusiastic demonstration that mathematics
could and should be applied to practical problems in natural philosophy.

What does the De prapartianibus tell us about Bradwardine’s view of time?

In answering this question it is important to remember that Bradwardine does not

discuss time as a distinct concept in this treatise but refers to it only in reference to

95

other concepts, such as motion, velocity, distance and magnitude. Similarly, one
must keep in mind the strong philosophical orientation of the treatise which is
heavily inﬂuenced by his interpretation of Aristotelian physics. We can assume,
then, that, in the context of this treatise, Bradwardine accepts Aristotle’s deﬁnition
of time as the number or measure of motion. Bradwardine takes it for granted that
the most efﬁcient way of comparing two motions is to compare the amount of time
it takes for the moving bodies to traverse a given distance. Like Aristotle,
moreover, he is always careful to include the aspect of time in calculations involving
change or motion.

In Bradwardine’s more elaborate system for relating the factors which
inﬂuence motion, however, time becomes a more sophisticated entity than it was for
Aristotle. Like distance or any other factor in the process of motion, time can be
measured and is subject to the same kind of proportional analysis. Bradwardine
makes this point most succinctly in his discussion of Aristotle’s view of yet another
factor in motion, the relative density of the medium through which an object moves.
Bradwardine believes that in both the Physics and the De caela Aristotle manifestly
proves that time itself has a proportional character, that is, times can be compared
to each other in simple ratios, since "the proportion of the times measuring . . .
motions varies also in accordance with the proportion of the media (namely, that
the longer time corresponds to the motion through the denser medium and the
shorter time through the rarer medium)."48 There is little doubt, therefore, that
Bradwardine’s approach to time in the De prapartianibus was based both on
Aristotle’s concrete association of time with motion and also on his own more
specialized understanding of the proportionality of motion.

Weisheipl observes, "The aim of Bradwardine’s treatise was to determine a
universal rule that would govern proportions between moving power and resistance,

on the one hand, and distance and time on the other."49 Implicit in Bradwardine’s

96

rule was the notion that time is a measure of motion, because the time it takes for a
motion to be completed determines the "quantity" of motion, just as the intensity of
a motion determines its "quality."50 This emphasis on time as a measure of motion
accounts for Bradwardine’s frequent references to "equal times" both in his
quotations from Aristotle and in his own commentary. Discussions of "equal times"
in the De prapartianibus give one the impression, however, that Bradwardine, like
Aristotle, 'was little interested in actually measuring motions. His acceptance of
Aristotle’s deﬁnitions of time and motion and his own mathematical instinct
conﬁrmed that time and distance were related to force and intensity in motion;
moreover, Bradwardine realized that, for the sake of mathematical proofs, times
and distances often had to be deﬁned as equal, in spite of practical difﬁculties
involved in making accurate measurements. Indeed, Bradwardine routinely ignored
the empirical problem of measurement, preferring instead to prove his assertions
through pure mathematical logic. His few attempts to support his assertions with
empirical evidence amounted to the use of simple examples from everyday
experience, such as Aristotle himself had often given. Thus, for example, he ended
his refutation of Avempace with the common observation that,

if a given mover were to exceed its resistance by a greater

amount than another mover exceeded its own resrstance, the

former motion would be faster. Then, since a strong man

exceeds anythrn he moves by a greater excess of power than a

weaker mover gsuch as a boy, or a ﬂy, or something of that

sort) exceeds what it moves, he should move it more rapidly.

Expenence, however, teaches us to the contrary, for we see

that a ﬂy carryrng some small particle ﬂies very rapidly, and

that a boy also moves a small object rather rapidly. A strong

man, on the other hand, moving some lar e object which he

can scarcely budge, moves it very slowly, an even if there were

added to what he moves a quantity larger than either the ﬂy or

the boy can move, the man will ghen move the whole not much

more slowly than he did before.
This appeal to common sense certainly involved no experimentation and hardly

illustrates the problem of force and resistance in motion. As an item of proof, it was

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added merely to suggest a logical relationship between the "quality" and the
"quantity" of motion.
The question now arises whether Bradwardine was aware, as he wrote the De
prapartianibus, of the phi1050phical implications of his new theory about motion for
other scientiﬁc or theological topics, including time. Because he thought of the
treatise as a clariﬁcation of what Aristotle had already said, we should not expect
the De prapartianibus to contain a self-conscious statement of its originality either as
a scientiﬁc or as a philosophical text. Some historians regard the De prapartianibus
as an almost purely mathematical work which only indirectly addressed underlying
philosophical issues. Thus Crosby says:
Approaching the problem of establishing an adequate law of
motion from the standpoint of a mathematician rather than
that of a philosopher, 1t is the mathematical formulae which
appear explicitly, and the philosophical theory on which the
are ultimately grounded, t at remains implicrt. It is indee ,
quite conceivable that Bradwardine might have been almost
wholly unconcerned with the philoso hical issues involved, but
simply interested in demonstratin t e mathematical fallacies
implied in previous theories an in showing how a proper
understanding of mathematics involved in the manipulation of
exponential series could solve any objections against the classic
notion 5éhat velocities are proportional to proportions of
forces.

In Crosby’s view, then, Bradwardine perhaps unknowingly made philosophical

assumptions that served his mathematics, but not the other way around.

Other historians have observed, however, that Bradwardine’s approach to the
problem of motion, though we might label it mathematical, had a ﬁrm and conscious
philosophical basis. They see works like the De prapartianibus as evidence of a
general development in early fourteenth-century thought towards a new
epistemology. In this context, Crombie remarks: "when Bradwardine rejected
Avempace’s ‘laws of motion,’ he made use of arguments similar to Ockham’s, and it

is difﬁcult not to see a connexion in the common shift of the problem from the ‘why’

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to the ‘how’ which Ockham made as a logician and Bradwardine as a mathematical
physicist."53 Crombie bases this statement on the observation that, in his Expositia
super libras physicarum, Ockham not only repudiated Avempace’s doctrine but did
so by relying on the same concepts of distance, time and force which form the
foundation of Bradwardine’s theory.54 This is not to say, of course, that Ockham’s
approach to this topic was structurally identical to Bradwardine’s. Quite the
contrary: Ockham relied on logical distinctions and deﬁnitions which he expressed,
for the most part, in a completely non-mathematical vocabulary,55 whereas, as we
have seen, Bradwardine’s logic was fundamentally a mathematical or geometrical '
exercise. The convergence of Ockham’s and Bradwardine’s philosophy cannot be
seen readily in the De prapartianibus, but it becomes strikingly apparent in other
works in which Bradwardine addresses broader philosophical problems such as
inﬁnity, continuity and contingency. We shall return to this point. Here it is
sufﬁcient to note that Bradwardine’s mathematical studies can be seen to have a
philosophical origin.

One of the major questions about early fourteenth-century philosophy
involves the extent to which thinkers were empiricists. In pulling away from the
debates about the "whys" of the physical world in favor of concentration on the
"hows," fourteenth-century philosophers often had to leave the familiar ground of
Aristotelian or Neoplatonic physics; and their success in making the transition to a
new cosmology has often been questioned. In an attempt to defend late medieval
philosophy from the complaint that the shift from metaphysical to empirical inquiry
represents a decline, Ernest Moody argues that late medieval philosophy moved
from a scholastic, theological orientation towards a more modern scientiﬁc
outlook.56 Moody sees the period in which Bradwardine lived and worked as a
formative age when the cosmological and speculative philosophy of ' the Greeks

became analytical, critical and modern.57

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Moody’s rather strong statement has been modiﬁed in recent years as further
research on early fourteenth-century philosophy has uncovered more of the
complexity of intellectual developments in this period. Thus John Murdoch has
remarked that, if late medieval scholars seemed to turn away from traditional
questions, it was not because they? had lost interest in them but because they were
searching for better ways of investigating them.58 New analytical methods, the new
language of proportions and new approaches to logic all advanced philosophical
thought and theological speculation. In the absence of effective techniques for
experimentation, thinkers who wanted to apply these philasaphical innovations to
physical problems were faced with the knowledge that they could not easily explain
the realities of nature. Although their efforts to integrate philosophy and science
were not immediately fruitful, however, their work provided a foundation for
continued development in many branches of scientiﬁc and philosophical inquiry.

The contents and structure of the De prapartianibus indicate that
Bradwardine did in fact have a clear philosophical orientation when he wrote this
work, even though his intention was not primarily to treat the problem of motion
philosophically. He approached Aristotle’s law of motion mathematically in the
conviction that anything less than the precision of a geometrical method could not
adequately express what Aristotle had meant. Bradwardine’s geometrical language
of proportions possesses its own order and logic, while the shape of its arguments
rests on his analysis of the propositions of Aristotle, Averroes and their opponents.
Crosby is correct, of course, in stating that in the De prapartianibus Bradwardine did
not attempt to consider explicitly the broader philosophical implications of his
mathematical approach to motion. Full discussions of time, space and continuity, all
of which have bearing on the problem of motion, are clearly absent. We should not
assume, however, that Bradwardine had no thoughts on these matters, for he

reﬂected upon them at length in other treatises. It is possible that Bradwardine had

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only begun to work out his opinions on these issues when he wrote the De
prapartianibus. In any event, the clarity and orderliness of expression in this work
serve to emphasize its mathematical orientation. One can therefore understand
Crosby’s identiﬁcation of the text as one which, "through the introduction of
mathematical analysis, . . . sets the stage for the quantitative measurement of
physical processes, and, hence, that typically modern physics which was to appear
with Galileo’s wedding of mathematics and experimental observation."59
Still, the richness of the De prapartianibus goes well beyond the mathematical
concepts that it develops. The treatise establishes Bradwardine’s Aristotelian
inclinations as well as his capacity for revision of his predecessors’ ideas. More
important for this study, the De prapartianibus introduces us to Bradwardine’s way of
thinking about physical problems such as time: although he shows a tendency
towards realism and empiricism, his grasp of abstract mathematics was too acute for
us to assume that he had not learned much from the Platonic tradition as well. In
fact, Bradwardine’s treatment of time in the De prapartianibus in light of
Aristotelian and Platonic notions reﬂects his particular interest in a much larger
medieval debate about the physical reality of time.60 Eventually, as the conclusion
of the De prapartianibus suggests, Bradwardine would be prepared to consider as
well the theological dimensions of his work on proportions:
Thus comes to completion this work, concerning the
Broeiortion betfvfl‘iailt tirfoetereeder gritihwviihirhh a11111031??? takerplacei
aiid lfetgvilgceen oWhom and the thing H: moves ihecigsegigtgeiio
proportion - to Whgin be honor and glory as long as there is
any motion. Amen.

We shall soon see how Bradwardine’s mathematical thought came to inﬂuence both

his philosophy of time and his understanding of God as Primary Mover.

CHAPTER FIVE
TIME AND CONTINUITY

Although the De prapartianibus offers the best general introduction to
Bradwardine’s mathematical method and his Aristotelian leanings in natural
philosophy, his Tractatus de continua gives much more speciﬁc indications of his
view of time. Bradwardine had already touched on certain aspects of continuity as
early as 1323 in a treatise on beginning and ceasing1 but his most sophisticated
treatment of continuity dates from the late 13205, shortly after the composition of
the De prapartianibus. Similar to the De prapartianibus in method and tone, the De
continua surpasses Bradwardine’s previous mathematical works to the extent that it
confronts directly the fundamental problems surrounding inﬁnity and continuity
which underlay all medieval discussions of natural philosophy. In the De continua
Bradwardine relied almost entirely on Euclidean geometry to prove that continuous
entities are inﬁnitely divisible.2 Bradwardine’s main achievement in this treatise
was to establish a theoretical correspondence between such abstract mathematical
continua as lines, planes and spheres and the physical continua of temperature,
motion and time. In this way be transformed a previously philosophical problem
into a physical one which could be analyzed mathematically. A5 in the De
prapartianibus, Bradwardine went far beyond Aristotle in rationalizing and
mathematizing the natural philosopher’s approach to motion and change without
deviating from the basic principles of Aristotelian physics.

Unlike the De prapartianibus, however, the De continua was a polemical work

directed against a vocal group of contemporaries who claimed that continua are

101

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composed of indivisible parts or atoms. Bradwardine, following Euclid and
Aristotle, argued instead that all parts of a continuum must be inﬁnitely divisible.
By writing the De continua Bradwardine entered into one of the most contentious
philosophical and logical debates of the late Middle Ages. There has been some
confusion over Bradwardine’s position in this debate. Some historians, noting the
signiﬁcant differences between Bradwardine’s and Ockham’s approaches to
Aristotelian physics, have assumed that Bradwardine had Ockham in mind when he
wrote the De continua. This interpretation fails to account for many similarities in
their perceptions of natural philosophy. In fact, Bradwardine and Ockham agreed
on many Aristotelian concepts, including the deﬁnition of continuity and the
characterization of time. and motion as physical continua. They even shared, to
some extent, a common method for analyzing continuity and other physical
problems. As Weisheipl has pointed out, Ockham and Bradwardine stood on the
same side of the medieval debate about physics: Grosseteste, Walter Chatton and
Henry of Harclay were the real targets of the De continua, not Ockham.3

The topic of time provides a good focus for exploring the positions of both
Ockham and Bradwardine in the larger debate over continuity which dominated
thirteenth- and fourteenth-century studies of natural philosophy. Because they
regarded time as the continuum which deﬁnes all other mathematical and physical
continua, both Ockham and Bradwardine paid special attention to time in their
discussions of continuity. Although they agreed completely on the nature of time
itself, however, they disagreed about the nature of time’s relationship to created
matter. It is in this context, not in that of the inherent continuity of time that
Ockham’s rejection and Bradwardine’s afﬁrmation of Aristotelian physics must be
seen.

The purpose of this chapter is to examine the late medieval debate about

continuity in order to reveal the main features of Ockham’s' and Bradwardine’s

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conceptions of time. The ﬁrst part of this chapter reviews the thirteenth-century
controversy over Aristotle’s confusing writings about continuity, to which
Bradwardine and his contemporaries responded early in the fourteenth century. A
second section explores Ockham’s strategy for reconciling his Aristotelian ideas
about time with a distinctly non-Aristotelian metaphysical system. A ﬁnal section
considers Bradwardine’s view of time, as he expressed it in the De continua, in light
of Ockham’s position. These discussions not only will help to isolate the source of
conﬂict between Bradwardine’s and Ockham’s approaches to natural philosophy but
also illustrate the centrality of temporal continuity in Bradwardine’s own physical
system.

Ockham’s and Bradwardine’s views about time were shaped by classical
discussions which were revived by natural philosophers in the thirteenth century.
All fourteenth-century studies of earthly or celestial motion, change and time
required some reference to the deﬁnitions of inﬁnity and continuity which Aristotle
had originally proposed in his treatments of these topics. In fact, despite the
tremendous variety of scientiﬁc subjects which late thirteenth- and fourteenth-
century thinkers pursued, questions about continuity and inﬁnity were at the root of
almost all of them.4

It was Aristotle’s portrayal of the interrelationship of continuity, motion and
change that stimulated late medieval natural philosophy. In his discussions of
motion, for example, Aristotle always contended that all sorts of movement and
change, even if discontinuous, could be observed and measured because all change
occurs within the framework of continuous time. This theme, which Aristotle
developed most explicitly in his Physics and De caela, is so prevalent in the whole of
his natural philosophy that his medieval successors could hardly have avoided some
consideration of its Bradwardine and his contemporaries at Oxford were deeply

inﬂuenced by the Aristotelian preoccupation with inﬁnity and continuity. Some,

104

however, tried to reconcile Aristotelian physics with the symbolic mathematics of
the Platonic tradition, which led, predictably, to serious disagreements.

The main controversy in the late medieval debate over continuity had its
origins in classical discussions of atomism. Aristotle, who devoted a large portion of
his writings on physics to refuting the atomists, developed a theory about the inﬁnite
divisibility of continua which enjoyed wide acceptance in his own time and
throughout the Middle Ages. Aristotle identiﬁed Democritus and Zeno as the chief
proponents of the atonrist theory. According to Democritus, all being consists of
distinct, invisibly small atoms which are in perpetual motion in a void. Although
they are all made of the same substance, atoms come in many shapes and sizes. The
variety of objects which we observe in the material world is the product of the
interaction of the atoms as they collide in space. All physical change results from
the combination and recombination of these essential materials. Democritus
applied his atomic theory to psychical change as well, claiming that even the
immaterial world of soul and spirit is composed of atoms. To support the atomist
theory Democritus devised an entire system of physical laws which explained how
atoms maintain the constant motion necessary for development in a dynamic
universe.6

Although Democritus’ theory of atoms seemed to account for both the
variety and change of the sensible world, it was immediately criticized for its
emphasis on perpetual motion in a void: most ancient Greek philosophers believed
that both perpetual motion and the existence of a void were impossible. Aristotle
disagreed with the notion that atoms of matter could be isolated and indivisible and
argued instead that the physical world was whole, continuous and uniﬁed.
Aristotle’s criticism of Zeno took a slightly different form from his criticism of
Democritus. Whereas his objection to Democritus was essentially cosmological, he

attacked Zeno primarily on logical grounds. Aristotle would not accept the validity

105

of Zeno’s paradoxes which denied the reality of motion and change. Zeno was not
in fact an atomist, but he cleverly exploited certain logical features in the Euclidean
deﬁnition of continuity to the advantage of the atomists. Through his paradoxes
Zeno tried to defend Parmenides’ assertion that only one thing exists by exposing
the contradictions in seeing nature as many bodies in motion. The essence of his
argument was that, if every motion, time and distance were inﬁnitely divisible, it
would be impossible to traverse any given segment of a continuum: the runner of a
race, for example, could never reach the ﬁnish line, no matter how he close got to it,
because his distance from it would remain inﬁnitely divisible at every point. Thus
Zeno actually accepted the inﬁnite divisibility of continua on the grounds that this
principle proved the impossibility of motion. Of course, atomists, both classical and
medieval, used the paradoxes not to deny motion as such but to put the discussion of
motion on a different footing. For them, motion of a body only made sense as a
reﬂection of the motions of the indivisible atoms which composed it. Although they
regarded Zeno’s view of motion as absurd, the late medieval atomists skillfully used
his analysis of continuity to discredit the Euclidean position on inﬁnite divisibility.7
Through his elaborate refutation of Zeno, Aristotle unwittingly encouraged this
alliance between Zeno and the atomists by showing how the paradoxes could be
used to support atomist theory.8

Aristotle’s criticism of Zeno had a much more positive inﬂuence, however,
on natural philosophers like Bradwardine, who accepted the Euclidean deﬁnition of
continuity. At the heart of Aristotle’s attack on Zeno was his refusal to accept the
premise of Zeno’s paradoxes that the oneness of matter makes motion impossible.
Aristotle also dismissed those philosophers who claimed that the universe is one and
immovable because they could not explain change. Although their reasoning might
be impeccable, their conclusions make no sense: "For indeed," says Aristotle, "no

lunatic seems to be so far out of his senses as to suppose that ﬁre and ice are one: it

106

is only between what is right, and what seems right from habit, that some people are
mad enough to see no difference."9 The only sensible way to approach nature,
according to Aristotle, was to accept that change exists and to try to characterize it.
In Book V of his Physics, Aristotle deﬁned continuity in terms which would
eventually allow him to characterize change, time, space and matter as continuous.
His deﬁnitions of the adjectives "successive," "contiguous" and "continuous" imply
that continuity is the most specialized of the three because 'it contains elements of
all three in unity. Since Aristotle’s deﬁnitions of these concepts prevailed

throughout the medieval period, they are worth presenting in their original form:

A thing is in succession when it is after the beginning in
position or in form or in some other respect in which rt is
deﬁnitely so regarded, and when further there is nothing of the
same kind as itself between it and that to which 1t is in
succession, e. g. a line or lines if it is a line, a unit or units if it
is a unit, a house if it is a house (there is nothing to prevent
something of a diﬁ’erent kind being between). For that which is
in succession is in succession to a particular thing, and is
something posterior; for one is not in succession to two, nor is
the ﬁrst day of the month to the second: in each case the later
is in succession to the former.

A thing that is in succession and touches is contiguous.
The continuous is a subdivision of the conti ous: things are
called continuous when the touching limits 0 each become one
and the same and are, as the word implies, contained in each
other: continuity is impossible if the extremities are two. This
deﬁnition makes it plain that continuity belongs to things that
naturally in virtue 0 their mutual contact form a unity. And in
whatever way that which holds them together is one, so too the
whole III” be one, e. g. by a rivet or glue or contact or organic
union.

Aristotle then distinguished successive from continuous beings, borrowing from the
language of geometry. Although points and units can both be successive, only points
can be continuous, since units represent distinct entities (like whole numbers) but
points do not: points can touch each other and more points can exist between

points, but no whole number can exist between the numbers one and two.11

107

These deﬁnitions are the foundation of Aristotle’s theory of divisibility.
According to Aristotle, nothing that is continuous can be composed of indivisible
parts because continuity requires each part to be connected to another part.
Therefore, each part possesses some aspect which belongs to other elements in the
series and some aspect which does not. For example:

a line cannot be composed of points, the line being continuous
and the oint indivisrble. For the extremrtres of the two omts
can nei er be ene smce of an mdrvrsrble there can e no
extremity as distrnct om some other part) nor together (since

that which has no parts can have no extremity, the extremity
and the thing of w '

 

1ch it is the extremity being distinct). . . .
Nor, again, can a point be in succession to a point or a now to a
now in such a way that length can be composed of points or
time of nows; for things are 1n succession if there is nothing of
their own kind intermediate between them, whereas
intermediate between points there is always a line and between
nows a period of time. . . . [Therefore,] everythiné continuous
is divisible into divisibles that are always divisrble.

Thus Aristotle concludes that time, magnitude and motion are all subject to the
same theoretical principles that govern continuity.

Indeed, for Aristotle, continuity is the universal concept which links motion,
time and space. In the case of magnitude, for example, the inﬁnity of a line is

equivalent to that of time and motion:

Since every motion is in time and motion may occupy any time,
and the motion of everything that is in motion may be quicker
or slower, both quicker and slower motion may occupy any
time: and this berng so, it necessaril follows that time also is
continuous. By continuous I mean that which is divisible into
divisibles that are always divisible . . . . And at the same time it
is clear that all magnitude is also continuous; for the divisions
of which time and magnitude respectively are susceptible are
the same and equal. . . . [Therefore] if time is 1nﬁnite in
respect of its extremities, length is also rnﬁnite in respect of its
extremities; if time is inﬁnite in respect of divisibility, length is
also inﬁnite in respect of divisibility; and if time is inﬁnite in
both respects, magnitude is also inﬁnite in both respects.

108

Moreover, because magnitude is continuous, movement along a magnitude is

continuous, as is the time in which the movement occurs. So Aristotle remarks in
Book IV of the Physics:
Now we perceive movement and time together; for even
when it is dar and we are not being affected through the body,
if any movement takes place in the mind we at once suppose
that some time has indeed elapsed; and not only that but also,
when some time is thought to have passed, some movement
also along with it seems to have taken place. Hence time is
either a movement of something or that which belongs to
movement. Since then it is not movement, it must be the
other.
But what is moved is moved from something to something,
and all magnitude is continuous. Therefore the movement
goes with the magrutude. Because the magrutude 15
continuous, the movement too 15 continuous, and 1f the
movement, then the time; for the time that haslpassed away is
always thought to be as great as the movement.
Aristotle presents us, then, with a view of motion, time and space which depends on
the inherent continuity of each quality. Because they are all related to each other,
time cannot be atomic if magnitude is not: in proving that a line is not composed of
a ﬁnite number of distinct points, one can prove that time does not consist of
indivisible instants.15 In fact, although it is possible to conceive of an atomic theory
of magnitude which does not require an atomic view of time, Aristotle so closely
binds together time and motion that he is unable to see how the one could be
atomic and the other not.16
Medieval debates about continuity reﬂect the legacy of Aristotle’s criticism
of atomism and his alternative approach. The Muslim philosophers were keenly
interested in continuity, and some of them responded to Aristotle and Zeno by
advocating a modiﬁed form of classical atomism. Both Muslim atomism and the
objections of certain Muslim philosophers to Greek atomism inﬂuenced Latin
thinkers.17 Classical philosophers had either conﬁned their discussion of atomism

entirely to the physical world or, like Democritus, left their speculations about the

109

non-material world largely undeveloped. Medieval thinkers, however, took a wider
approach to these topics. Of particular interest was the question of how inﬁnity and
continuity applied to God and his creation. Thirteenth- and early fourteenth-
century scholars made the debate about inﬁnity and continuity more complex by
trying to analyze these concepts both as features of observable phenomena and as .
expressions of divine omnipotence. Thus Murdoch suggests: ". . . since God’s
absolute power extended to everything that did not include a contradiction, to
invoke this power in examining inﬁnity or continuity was to transfer one’s analysis
from the realm of the physically possible (within the conﬁnes of Aristotelian natural
philosophy) to the broader realm of the logically possible."18 This new way of
thinking led to new approaches and innovative solutions to a problem which
nevertheless retained its classical characteristics.

The late medieval discussions of continuity revolved around the classical
debate over atoms or "indivisibles" but it was also tied to a newer preoccupation
with inﬁnity. In Book III of the Physics, Aristotle had denied actual inﬁnity on the
grounds that the universe is ﬁnite. The only inﬁnity Aristotle would admit was the
potentially inﬁnite divisibility of a continuum: "since no sensible magnitude is
inﬁnite, it is impossible to exceed every deﬁnite magnitude; for if it were possible,
there would be something bigger than the heavens."19 Medieval philosophers
generally accepted Aristotle’s authority concerning inﬁnity in the physical world but
they went on to consider the possibilities of the actual inﬁnities which God might
create. From this avenue of speculation came the "paradox of unequal inﬁnities"
which Bonaventure helped to popularize in his discussion of the eternity of the
world. Murdoch deﬁnes this paradox in this way: "if one allows the existence of
actual inﬁnities, then it appears that some inﬁnities will clearly be greater than
other inﬁnities which are equally clearly part of the former; but it is axiomatic that

all inﬁnities are equal; therefore, in this instance a part is not less than, but equal to,

110

its whole - which is absurd."20 Bonaventure’s use of this paradox in his treatment of
eternity stimulated a wide range of commentary21 and reinforced the link between
inﬁnity and time.

While some philosophers resolved the paradox simply by using it to prove the
impossibility of actual inﬁnities, others faced the problem more directly by analyzing
the differences between actual and potential inﬁnities. These investigations were
directly concerned with continua because, by virtue of its composition from inﬁnitely
divisible elements, a continuum is potentially inﬁnite. The characteristics of
potential inﬁnities were investigated from a variety of perspectives, but most
thinkers began their studies with mathematical analysis. Aristotle, of course, had
said a great deal about the general nature of continua and the continuous quality of
physical forces; but Euclid contributed an essential technical vocabulary for the
study of inﬁnity and so provided a mathematical framework for analyzing
continua.22

Averroes’ treatment of inﬁnity, which was so inﬂuential in late medieval
discussions of continuity, was based on just such a Euclidean framework for sorting
out Aristotle’s various comments about continua. In Book V of his commentary on
Aristotle’s Physics, for example, Averroes tried to simplify Aristotle’s deﬁnition of
the continuous as a special kind of contiguity. Averroes recognized that Aristotle
had been correct to link continuity and contiguity in the case of physical entities but
he pointed out how difﬁcult it is to express this link with Euclidean mathematics.
Two physical bodies must be contiguous for there to be any continuity between
them; but, in abstract mathematics, it is not necessary to hold tightly to this
deﬁnition. Instead, it is more convenient to say of mathematical entities (for
example, lines, surfaces or solids) that, when two such bodies come together, their
extremities are not contiguous but superimposed on each other: the extremities of

each become one.23

111

Albertus Magnus helped to disseminate this notion of superposition in
mathematical continua in the West by emphasizing superposition in his own
commentary on Aristotle. In wrongly attributing the idea to Euclid instead of
Averroes, Albertus put the whole discussion of continuity into a form which stressed
the geometrical nature rather than the philosophical signiﬁcance of the
continuum.24 As far as Albertus was concerned, it was Euclid who had provided the
necessary vocabulary for explaining the contiguous qualities of mathematical
entities, so the supposition theory should be credited to him as well.25 Although
Averroes’ ideas undoubtedly inﬂuenced Albertus’ approach, Albertus preferred to
stress Euclidean themes in his study of Aristotelian continuity. Albertus thus helped
to legitimize a geometrical approach to natural philosophy by illustrating how
Euclid’s methods for analyzing abstract entities could be applied to mathematical
continua, and, by analogy, to physical continua as well.

Other attempts to apply Euclidean geometry to the problem of continuity led
to controversy. Henry of Harclay, Chancellor of Oxford in 1312, believed, for
example, that actual inﬁnities could exist and that continua were composed of
indivisibles. His solution to the inﬁnity paradox rested on his acceptance of unequal
inﬁnities. Like Averroes and Albertus, Harclay used a Euclidean principle to
distinguish between natural and mathematical continua. He agreed with Euclid’s
axiom that, in nature, every whole is greater than its parts. In abstract mathematics,
however, a broader axiom could be exploited. Henry assumed that every inﬁnity is
whole in itself, even if it is a subset of another inﬁnity: "that which (e. g., an inﬁnite
set) contains another thing (e. g., an inﬁnite proper subset) and something else
beyond it, or in addition to (praeter) it, is a whole with respect to the other thing."26

This assumption was soon criticized for its ambiguous interpretation of
Euclid and its misrepresentation of Aristotle. The Franciscan William of Alnwick

pointed out that Henry’s distinction between inﬁnities and their proper inﬁnite

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subsets did not imply that the latter were smaller, because only ﬁnite things have
quantity, the necessary prerequisite for comparison of size.27 In his commentary on
the Sentences, given in Paris in 1342, Gregory of Rimini enlarged on William’s
observation. Himself an advocate of the existence of actual inﬁnities, Gregory tried
to explain how some inﬁnities can exist as part of other inﬁnities. In the sense that a
whole is made up of parts, he argued, an inﬁnite subset must be considered part of
any inﬁnity which includes it; but considered mathematically, those inﬁnities
become equal because each contains an inﬁnite number of elements.28 The
approaches of William and Gregory to this problem reﬂect the medieval tendency in
natural philosophy to distinguish physical continua from purely mathematical ones.
When Bradwardine set out to deﬁne his own view of continuity in the mid
13205, then, he had to consider two major questions: how well does Aristotle’s
theory of inﬁnite divisibility apply to physical and mathematical continua
respectively; and how appropriate is geometrical analysis to the study of physical
continua such as motion, time and temperature? His efforts to solve these problems
show a striking similarity to those of Ockham. Both approached the subject of
continuity along Aristotelian lines: they largely accepted Aristotle’s method for
refuting the atomist position and explicitly acknowledged the continuous nature of
time and motion. Moreover, both exhibited the same tendency to isolate the
analysis of physical continua from larger metaphysical considerations. In their
works of natural philosophy both Ockham and Bradwardine approached physical
continua as particular mathematical or logical problems and rarely connected such
discussions with considerations of the philosophical signiﬁcance of continuity. In
this sense, their views represent a more authentic Aristotelianism even than those of
their great predecessor Thomas Aquinas, whose discussions of continuity always

began with an analysis of being.29

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The differences between Bradwardine and Ockham on this issue are equally
remarkable, however. Bradwardine was a staunch defender of Aristotelian physics:
his mathematical transformation of Aristotle’s physical theory was done in a spirit of
respect and acceptance. Ockham, on the other hand, openly criticized the
philosophical basis of Aristotle’s physical system, while admitting that many of
Aristotle’s observations concerning motion, time and space were substantially
correct. Nor were the analytical methods of Bradwardine and Ockham entirely
compatible. Bradwardine chose a mathematical method along the lines of
Grosseteste, while Ockham preferred the more traditionally logical approach of
Averroes and Aquinas. If Bradwardine and Ockham actually inﬂuenced each other,
as textual evidence seems to suggest, it is important to examine Bradwardine’s view
of the continuity of time in the context of Ockham’s own views and his criticism of
Aristotle.

In spite of an interrupted academic career and political involvements which
drew him farther and farther away from academic circles in the last two decades of
his life, Ockham is generally regarded as "the most inﬂuential philosopher of the
fourteenth century."30 This does not mean, of course, that he was immune from the
inﬂuence of other thinkers, even young ones like Bradwardine, or that his ideas
were revolutionary in every respect. An accurate appraisal of Ockham’s inﬂuence
must acknowledge both the conventional aspects of his philosophy and the subtle
ways in which his contemporaries modiﬁed his ideas to suit their own arguments.31

Ockham’s views about continuity and time illustrate well the complexity of
the late medieval debate about natural philosophy, as well as Ockham’s formative
position in it, for they reﬂect both hearty acceptance and severe criticism of
orthodox Aristotelianism. In addition to establishing the main features of

Bradwardine’s conception of time, the following comparison of Ockham and

Bradwardine will help to clarify Ockham’s role as a participant in a much larger

114

discussion among thinkers of different talents and at various levels of experience.
Just as Bradwardine’s views of time and continuity depend on an evaluation of his
mathematical thinking, Ockham’s views cannot be understood properly without
reference to his metaphysical system. Although his critics claimed that his
conception of reality made God a capricious and unfathomable force in the universe
and thus undermined faith, Ockham always maintained that his primary goal was to
exalt the complete freedom and omnipotence of God’s will and to elevate faith
above reason. In developing this thoroughly orthodox point of view, Ockham drew
heavily on Aristotle and Averroes and was also deeply inﬂuenced by Duns Scotus,
despite his fundamental disagreement with certain features of Scotist philosophy.32

Like every other thinker of his age, Ockham had to confront the
contradictions in classical metaphysics before attempting to produce his own system.
Along with Thomas Aquinas and Duns Scotus, Ockham wanted to reconcile
Aristotelian philosophy and Christian doctrine but he was deeply dissatisﬁed with
his predecessors’ solutions. Ockham was as troubled by Aquinas’ strong
dependence on Aristotle as he was by the approach favored by Franciscans from
Bonaventure to Scotus, which tried to moderate Aquinas’ system through greater
reference to Plato and Greek Neoplatonism.33 Moreover, Ockham could not
accept the thirteenth-century attempts to reconcile philosophy and theology because
they made use of the principle of realism, deﬁned by Ernest Moody as "the
metaphysical and epistemological doctrine . . . that the human intellect discovers the
particulars apprehended by sense experience in an intelligible order of abstract
essences and necessary relations ontologically prior to particular things and
contingent events, and that from this order the intellect can demonstrate necessary
truths concerning ﬁrst causes and the being and attributes of God."34 The realists,
in keeping with both Platonic and Aristotelian metaphysics, believed that objects

have sensible qualities, such as size, color, number and location,- which have

115

universal reality. A thorough analysis of an object would be impossible, therefore,
without reference to these universals, which have signiﬁcance beyond the individual
characteristics of that object. To the extent that every object has size, for example,
all objects share a common nature with respect to that universal quality. Aristotle’s
entire system of observation of matter involves close attention to this concept of
universal qualities, and his extensive work in this area had a great impact on
medieval investigations into both metaphysics and natural philosophy.

Ockham’s main objection to realism was that it accorded sensible qualities a
reality beyond the reality of a particular thing. Ockham believed instead that the
human mind could directly apprehend the qualities of an object. Weisheipl explains
that

for. Ockham, among the ten ‘cate ories’ of Aristotle, only

individual ‘substances’ and indivi ual ‘ ualities’ were res

absolutae, existing outside the human min . All other things,

such as quantity, motion, time, lace, velocity and causality,

were only temrs (termini) or wor s (namina) to stand for (sup-

panere) nothrng but the mdrvrdual under some consideration of

connotatron of the mind, and did not represent the

apprehension of the mind of some objective reglity distinct

from 1nd1vidual substances or individual qualities.
Ockham’s insistence that descriptive qualities were inherent in objects and had no
independent reality did not constitute an entirely new idea: philosophers before
Ockham had claimed, for example, that universal natures existed only as mental
abstractions.36 Through Ockham’s inﬂuence, however, some young scholars began
to argue that the common natures which the mind can recognize in various objects
have no reality, even potentially or incompletely, but are only mental terms
(intentianes animae) which have logical functions in propositions.37 The adherents
of this position, who came to be known as norrrinalists, not only provided a new

direction for late medieval philosophy but also went far beyond Ockham himself in

their criticism of medieval realism and orthodox metaphysics.

116

Ockham’s views had implications for both natural philosophy and theology.
His denial of the reality of universals outside the mind allowed him to reject the
notion that God created individuals to conform with divine ideas: any similarities
which exist between two individuals are the result of God’s free choice and do not
require an elaborate metaphysical explanation. Therefore the intellect, whether
human or divine, should be directed towards comprehending the individual thing
which exists.38 Such a perspective can, on the one hand, call into question any
intellectual activity which involves deduction from general principles. In this sense,
Ockham’s positions were at odds with the traditional Aristotelianism of medieval
natural philosophy. In fact, Ockham used his new system of propositional logic to
demonstrate that many of the principles which Aristotle had considered necessary
and self-evident were not 50.39 Since Ockham offered no new cosmology to replace
Aristotle’s, one might say that he undermined late medieval science with his
skepticism. On the other hand, Ockham’s assertion that there might be several
possible and equally valid explanations for a particular phenomenon, as well as his
emphasis on the human capacity to analyze individual objects or events, had a
stimulating effect on physical theory throughout the fourteenth century. Indeed,
Moody goes so far as to say that Ockham’s new approach to knowledge was
instrumental in establishing "the intellectual environment in which later fourteenth-
century philosophers explored new physical theories . . . [and so] laid the
foundations for the scientiﬁc revolution of the seventeenth century."40

In his penetrating study of Ockham’s physical theory, Andre Goddu provides
a useful framework for understanding Ockham’s opinions about continuity and time.
According to Goddu, Ockham tried in his natural philosophy to maintain both the
hypothetical necessity and the factual stability of the natural order, while at the
same time defending God’s omnipotence and freedom.41 While he attempted to

include a wide variety of metaphysical, theological and physical questions in his

117

logical system, Ockham realized that certain problems had to be treated in isolation
from others. Goddu contends that Ockham borrowed Aristotle’s methods of
isolation and imagination experiments when he speculated about physical realities
although Ockham’s own ideas about God’s relationship to humanity affected his use
of these methods. Instead of merely accepting the principles of Aristotelian physics,
Ockham was more likely to use isolation and imagination experiments to disprove
their logical necessity and to assert the contrary: that abstract concepts and
connotative terms can be reduced to subjects and their absolute qualities.42
I One of Ockham’s main philosophical goals, therefore, was to disengage
natural philosophy from metaphysics. By emphasizing that sensible qualities are
inherent in and inseparable from matter, Ockham tried to undermine Aquinas’
synthesis of Plato and Aristotle, which established a link between forms in the world
and forms in the mind.43 Although he did not reject all aspects of Aristotle’s
physics out of hand, Ockham claimed that his theories had to be tested empirically,
preferably by focusing on speciﬁc physical phenomena unhindered by metaphysical
considerations. Bradwardine followed a similar analytical method by isolating
physical problems in order to examine them geometrically. Goddu argues that
Ockham’s application of the principle of isolation to Aristotelian physics, together
with other fourteenth-century criticisms of Aristotle, led to the complete rejection of-
Aristotelian natural philosophy by the seventeenth century. Since Ockham relied
simply on logic as his empirical technique, however, he was not able to progress very
far on his own in designing a new physical theory to take the place of the one he
dismantled.44
When we turn to the question of Ockham’s view of continuity, we ﬁnd that he
did not believe in the existence of indivisibles, an opinion which is consistent with
his position on universals. Using the familiar illustration of points in a line, Ockham

argued that one need not think of lines terminating with points: a ﬁnite line is

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simply a line of a particular length.45 In Ockham’s linguistic analysis of points and
lines, only individual, permanent points and lines are real. Ockham regarded
Euclidean terminology as merely symbolic. Words such as "point," "line" or "instant"
are not things in themselves but terms which stand for more complex concepts in a
proposition; similarly, "motion" and "time" are not physical entities distinct from
things which move or exist in time.46

Whenever Ockham approached the problem of time, he used the traditional
Aristotelian vocabulary of motion and change, but his understanding of these
concepts was considerably different from Aristotle’s. Ockham’s reluctance to
consider any aspect of change as distinct from the object undergoing change
constituted a major break with Aristotelian physical theory, especially in regard to
motion and time. Since Aristotle had argued that everything which moves is moved
by something and that all change comes about as the result of some kind of motion,
the Aristotelian concept of motion had great metaphysical signiﬁcance: Aristotle
and his followers took it for granted that motion had a reality and purpose prior to
and distinct from any object experiencing change. Ockham’s identiﬁcation of
qualities with individual objects seriously undermined these metaphysical
distinctions.

By the thirteenth century, as we have seen, discussions about motion, time
and continuity had become extremely sophisticated. Consequently a debate ensued
over whether motion (and, by analogy, time) was a ﬂowing form (fanna ﬂuens), that
is, a distinct, continuous entity, or a ﬂux of form (ﬂuxus farme), in which an object
undergoes successive change.47 In his effort to deﬁne motion as an inherent feature
of a moving object rather than a separate force acting on the object, Ockham clearly
sided with the second position.48 As in all aspects of his philosophical system,

Ockham did not abstract or analyze the characteristics of motion as general

119

principles. He argued that the only way to understand motion is to examine the
motion involved in particular cases."’9

Ockham emphasized the individual experience of change by describing
change as a successive process of internal transformation.50 Although his
description of change as continuous follows Aristotle, Ockham’s assertion that the
form of the object undergoing change actually changes itself is at odds with
Aristotle’s theory of forms. Ockham’s explanation of successive transformation
reduced motion and time to sensible characteristics of objects and stressed the
absolute individuality of every instance of change. Thus Ockham could argue that
broad explanations of natural phenomena based on Aristotle’s theories of motion
were inadequate. The implications of this approach for theology were even more
striking: if God does not need to create according to pre-existing forms and can
change individuals directly without applying external forces such as motion, his
actions cannot be predicted or explained by the Aristotelian or any other
metaphysical system.51

Ockham’s view of time was consistent with his view of motion both in its
Aristotelian origins and in its ultimate emphasis on individual experience.
Throughout his Tractatus de successivis, a compilation of three short works, Ockham
presented the thesis that motion, place and time are inseparable from objects which
are in motion, space or time. This view, Ockham contended, was fully in keeping
with Aristotelian physics.52 In a sense, of course, Ockham’s description of change
did concur with Aristotle’s. It was widely accepted in the fourteenth century that
change is continuous and can be observed only by examining the body undergoing
change. Ockham argued, however, that his position made it easier to explain the

difference between continuous motion (such as that of the heavenly bodies) and

irregular change, a perennial problem for the Aristotelians. Nonetheless, Ockham

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ﬁrmly stated that his theory was sanctioned and even suggested by Aristotelian
physics.

Ockham begins his discussion of time in the T ractatus de successivis by
positing that time, like motion and place, "is not something in itself totally distinct
from a permanent thing."53 He goes on immediately to point out that, as Aristotle
says, time is inextricably bound up with motion and is part of the process by which
an object is changed.54 Time and motion therefore share the characteristic of being
intrinsic in a particular body; they do not exist apart from the reality of matter. This
assertion does not contradict Aristotle, who acknowledged himself that one cannot
observe time without observing change in some physical body. Ockham continues in
his interpretation of Aristotle by developing the orthodox principle that time and
motion are really different aspects of the same phenomenon.55 Because time is the
measure of change in a particular object, moreover, it has no meaning outside the
context of the motion of a physical body.56 While this position is Aristotelian as far
as it goes, Ockham does not develop it further. For Ockham, time is primarily
empirical.57

Although time is an observable phenomenon which accompanies motion, it is
not its own substance and therefore cannot have parts. Ockham clariﬁes the
classical'language about time by arguing that time does not consist of the parts past,
present and future; rather, time is divided into past or future with respect to the
individual objects which endure.58 By analogy, says Ockham, one could imagine
that a length of time is like a line which, being a continuum, can be divided
inﬁnitely. In reality, however, neither lines nor times exist as an inﬁnite series of
atoms or parts.59 Certainly no one could physically divide these entities into as
many parts as is theoretically possible. Thus the inﬁnite divisibility of a continuum
is, as far as Ockham is concerned, a reasonable theoretical and logical deﬁnition but

also, as Aristotle himself freely admits, an extremely difﬁcult one for the human

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mind to comprehend.60 Ockham therefore presents his thesis that time, motion and
place are inherent in objects as a practical solution to the problem of recognizing
inﬁnities in physical matter.

In the case of instants, for example, Ockham argued that, whether they can
be divided inﬁnitely or not, instants nevertheless are inherent in real things and are
not abstract, as some contemporaries (mademi) claim.61 Ockham did not see any
contradiction in holding this view while at the same time using Aristotle’s own
arguments for inﬁnite divisibility of instants to refute Zeno’s half-distance
paradox.62 Yet, while he willingly accepted the traditional position on the
theoretical nature of the divisibility of continua, Ockham was reluctant to minimize
the integrity of individual continuous entities. A continuum is not merely composed
of its divisible parts: a ﬁnite line is simply a line, not an inﬁnite series of points, just
as a ﬁnite period of time is not a procession of individual instants.63

This review of Ockham’s position on continuity and time serves to illustrate
his ready acceptance of certain Aristotelian concepts and his ﬁrm rejection of
others. Ockham had no difﬁculty in seeing time as the measure of motion or as the
number of motion according to before and after.64 He conceived of time as being
both continuous and successive and admitted that time is discrete because "the mind
divides motion into prior and posterior, and numbers the prior and posterior parts
in motion."65 With Aristotle be afﬁrmed that the circular movements of the
heavenly bodies provide a uniform standard by which one can measure other times
and motions.66 In fact, Ockham’s teaching on continuity conforms to Aristotle’s in
every major respect with one signiﬁcant exception. For Ockham, time was not some
relation distinct from permanent things, as Aristotle had claimed, but was a relative
or connotative name. To say "time is" is equivalent to saying "something is moved
whence the mind measures how much another thing is moved."67 This apparently

minor distinction actually reﬂects the main thrust of Ockham’s attack on

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Aristotelian metaphysics, which he pursued in many contexts. In short, Ockham
repeatedly showed his willingness to draw on Aristotle for explanations of certain
natural phenomena but freely interpreted and revised Aristotle when Aristotle’s
ideas conﬂicted with his own logical principles.

In the De continua, Bradwardine sought, as Ockham had sought, a way to
make the concept of continuity more comprehensible. However, whereas Ockham
had relied on propositional logic for this purpose, Bradwardine characteristically
turned to geometry, even, at times, to the point of ignoring major logical problems
which called into question his mathematical calculations.68 Although both
Bradwardine and Ockham conceived of continuity and time primarily in Aristotelian
terms, Euclid’s Elements provided the inspiration for Bradwardine’s approach in the
De continua. As with the De prapartianibus, moreover, Bradwardine emphasized in
the De continua the necessity of applying mathematics to the study of natural
philosophy, remarking:

No one studying physics can hope to succeed unless he uses
hiﬁ‘iﬁi‘h’h‘i‘é‘f Emil? "’ ﬁﬂiﬁé’dtffdmihéfv‘; ’23:”; ’
hiddgn secret, and holds the llileygto every subilety of letter?

whoever, then, presumes to stud physrcs while nelelecting

mathematics should know from t e start t he wi never

make his entry through the portals of wisdom.
In keeping with this assertion, Bradwardine made use of a mathematical argument
in the De continua to try to disprove the atomist position that continua are
composed of indivisibles. In the course of this analysis, Bradwardine encountered
Ockham’s problem of explaining how the theoretically acceptable premise of inﬁnite
divisibility could be demonstrated in the physical world. Unlike Ockham, who had
been content to deﬁne the problem without resolving it, Bradwardine attempted to
devise a mathematical solution. In the De continua, therefore, Bradwardine

examined several kinds of continua, both physical and purely mathematical. In

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general, his analysis of mathematical continua was more successful than his
treatments of various physical continua, although his application of mathematical
models to the continuity of time proved to be extremely fruitful.

Bradwardine tried in the De continua to dismantle the atomists’ position by
demonstrating the absurdity of their main principles. Beginning with an extensive
list of deﬁnitions, Bradwardine went on to develop one hundred and ﬁfty-one
propositions concerning continua, drawing primarily on geometrical arguments to
establish his case against atomism. So mathematically meticulous was his procedure
that he waited until Proposition 141 to state explicitly his thesis that a continuum
cannot be composed of indivisibles.7O This concept is implicit, however, throughout
the work and, it dominates his analysis of both geometrical and physical continua.
In the De continua Bradwardine not only borrowed freely from Aristotelian physical
theory but also derived his own position in favor of inﬁnite divisibility from
Euclidean mathematics. Often, as in the De prapartianibus, Bradwardine used
Euclidian concepts to correct Aristotle’s analysis of a physical problem. In the case
of Bradwardine’s theory of imposition, for example, he demonstrated geometrically
that two continua could overlap to form one continuum in order to avoid Aristotle’s
ambiguous distinction between continuous and contiguous elements.71 The
advantage of this theory for natural philosophy was that Bradwardine could use it to
prove that physical continua such as motion and time can have discrete parts or
segments and still remain connected to the rest of the continuum.

Bradwardine’s main targets in the De continua were the advocates of
immediate indivisibilism, who believed that continua are composed of a series of
indivisible points between which there are no additional points. With the aid of
geometry, Bradwardine successfully refuted them. Realizing, however, that
geometry alone could not conclusively disprove immediate indivisibilism, he did not

even attempt to refute the theory of mediate indivisibility, which posits that between

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any two indivisibles in a continuum there is always another indivisible.72 In spite of
its relatively limited scope, however, the De continua achieved its main aim of
undermining mathematically the principle of indivisibility on which all atomist
theories depend.

Bradwardine begins his refutation of atomism with an examination of several
types of continua, both mathematical and physical, and in the process he explicitly
delineates his view of time. At the outset of the De continua Bradwardine
introduces his conception of time as a continuum in a series of deﬁnitions pertaining
to continuous substances. After deﬁning the continuum itself as a quality whose
parts are mutually connected (ad invicem capulantur), he proceeds to distinguish
between permanent continua, whose parts exist simultaneously, and successive
continua, whose parts, in the words of Aristotle, succeed according to before and
after (succedunt secundum prius et posterius). In deﬁnitions four, ﬁve and six
Bradwardine gives solids, planes and lines as examples of permanent continua.
Deﬁnitions nine and eleven establish time and motion as successive continua.
Deﬁnition ten deﬁnes an instant as an atom of time. In these deﬁnitions,
Bradwardine emphasizes the connection between motion and time by deﬁning
motion as a successive continuum measured by time (continuum successivum
tempare mensuratum). Time, on the other hand, is measured not by motion but by
its own successiveness: tempus est continuum successivum successianem
mensurans.73

In deﬁnitions seventeen to twenty-two Bradwardine explains how the terms
past, present, future, beginning and ending should be applied to successive
continua.74 These deﬁnitions provide the foundation for examining time by
establishing that all successive continua are essentially temporal: they are not
simultaneous but have some parts which exist before other parts. When one wishes

to consider a successive thing or a particular segment of a successive continuum,

125

says Bradwardine, one must determine the ﬁrst and last instants of its existence.
Deﬁnitions nineteen to twenty-two, therefore, provide speciﬁc rules for making
these determinations under various conditions.

In his propositions and corollaries Bradwardine was able to comment at
greater length on the features of time which his deﬁnitions could only imply. Some
aspects of time which Bradwardine considered in the treatise include the inﬁnity of
time, its relation to motion, its composition and the beginnings and endings of time
segments. In pursuing these topics Bradwardine rarely strayed from an Aristotelian
framework. His mathematical approach allowed him to focus on the physical and
geometrical characteristics of time without reference to broader metaphysical or
theological issues. In this way Bradwardine proved himself an advocate of
Ockham’s methods of isolation and imagination experiment. Bradwardine’s analysis
of inﬁnity, for example, rests ﬁrmly on the classical Greek sources, particularly
Aristotle’s Physics.75 Quite apart from any possible theological considerations,
Bradwardine accepts that time is inﬁnite in the Aristotelian sense, that is, it is
inﬁnitely divisible and moves in a forward direction. As a geometer, Bradwardine
prefers to regard inﬁnity as a fundamental concept uncomplicated by inappropriate
logical concerns. He therefore points out the absurdities that could result from
applying the concept of inﬁnity to either singular or universal things.76 In the
process of condemning a logical argument which confuses universals with particular
things, Bradwardine clearly categorizes time and geometrical points as universal
inﬁnities; for although a mountain of gold, say, is continuous throughout, it has
physical limits which time and geometrical entities do not.

It is the inﬁnity of time, moreover, which makes it the measure of ﬁnity in
motion and space.- Bradwardine explicitly states the connection between motion,
time and space in his ﬁrst proposition concerning continua which restates Aristotle’s

thesis that a continuous quality can be divided inﬁnitely:

126

6 - Every body, surface, line and point can be moved uniformly
and continually. 7 - In the case of two local motions which are
continued in the same or equal times, the veloc1ttes and
distances traversed by these [movements] are proportional, 1.
e., as one velocity is to the other, so the space traversed by the
one is to the space traversed by the other. 8 - In the case of
two local motions traversing the same or equal spaces, the
velocities are inversely proportional to time, 1. e., as the first
velocity is to the second, so the time of the second veloc1ty 15 to
the time of the ﬁrst. 9 - A [given] movmg body can be moved
at an speed whatsoever or a [given] space can be traversed by
any [ ody] at all. 10 - The being or non-being [of ﬁmte things]
is measured in a certain time.
In an argument strongly reminiscent of those in the De prapartianibus, Bradwardine
establishes here the Euclidean principles that geometrical entities can be moved
continuously and that the speed and position of a moving object can be varied.
Bradwardine turns next to the theories of proportional velocity which he first
developed in the De prapartianibus to prove that his conclusions about continuous
motion in geometrical entities can be applied equally well to observable motions.
The notable difference between his treatment of this subject in the De continua and
similar ones found in the De prapartianibus is Bradwardine’s explicit recognition in
the De continua of the role of time in the process of measuring motion. Although he
had accounted for time in his calculations in the De prapartianibus, it is only in the
De continua that he deﬁnes time as the continuous, uniform standard by which
velocities can be measured. Moreover, supposition ten accords the continuum of
time an even larger cosmological signiﬁcance, for, if the being or non-being of ﬁnite
things is measured by time, every created thing is subject to temporal limits.78
Since he was not concerned in the De continua to explore the theological
ramiﬁcations of his temporal theory, we should not be surprised to ﬁnd him
concentrating on the mathematical consequences of his very Aristotelian approach
to motion, time and space. The majority of subsequent propositions which mention
time follow the pattern of the De prapartianibus, in which time appears as a

necessary constant in measuring motion. Bradwardine’s characteristic pattern in the

127

De continua was ﬁrst to illustrate some feature of continuity in purely geometrical
terms and then to show how this feature inﬂuenced a physical continuum such as
time, motion or temperature. After describing the continuity of points in a circle,
for example, Bradwardine turns in proposition twenty-four to an analysis of uniform
circular motion in which time-provides the test and measure of uniformity.79 In
making this transition Bradwardine implicitly acknowledges that geometrical
successiveness is a kind of timeless motion. The reality of motion in the physical
world, on the other hand, depends on temporal deﬁnition. Time, therefore, is a
prerequisite for all physical continua whether I successive, as in motion, or
permanent, as in space.

Thus Bradwardine shows early on in the De continua that time is the central
concept in his arguments that the continuity of proportional motion is equivalent to
the continuity of a geometrical line and that motions, like lines, are inﬁnitely
divisible.80 To demonstrate the divisibility of motion, Bradwardine once again
begins with a purely geometrical proof. Propositions thirty-two through forty-two
offer an elaborate Euclidean analysis of the divisibility of lines and angles, as well as
a thorough discussion of the mediate divisibility of points. In the next eight
propositions Bradwardine applies this analysis to motion. Rather than arguing
positively that motion must be divisible, however, Bradwardine focuses on the
absurdities of claiming, like the Pythagoreans and Henry of Harclay, that uniform
motion and time are composed of indivisibles.81 The actual form which this
negative argument takes has little bearing on Bradwardine’s view of time and offers
no additional insight into it. Nevertheless, his constant repetition of the connection
between the continua of time and motion reinforces the Aristotelian deﬁnitions of
time which he presented at the beginning of his treatise.

Bradwardine’s analysis of the composition of continua forced him to think

about a more complicated problem, one which Aristotle himself had only partially

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solved. Bradwardine’s Euclidean models depended on the axiom that geometrical
entities can be divided and that these divisions occur at speciﬁc points. However,
although he could conceive of such points as atoms, he did not consider them
indivisible, as his opponents did. In Bradwardine’s view, physical continua are even
less subject to an atomistic analysis than geometrical ones, which led him to declare
in proposition 100: "It is manifest that no natural substance is composed of ﬁnite
atoms."82 There follows a geometric proof which demonstrates the equivalence of
proportional velocities occurring in equal times by suggesting that the opposite
conclusion, that motions occurring in equal times are not proportional on account of
their composition out of distinct indivisibles, is unreasonable and contrary to
principles already proven in the De prapartianibus.83 Because it was based on a
negative argument, however, Bradwardine’s distinctions between the two
conceptions of the physical composition of continua are not entirely convincing.
Bradwardine’s strategy against the atomists was more successful when he
avoided altogether the issue of indivisible atomism and concentrated instead on the
equivalence of continuity within motion. In proposition 105, for example, he drew
on the principle of equal inﬁnities to prove that equivalent continua have an equal
number of components, whether those components are divisible or indivisible.
Again, the continuum of time served as the necessary standard by which to measure
this equivalence.84 Bradwardine restated this position even more strongly in
proposition 120, in which he added the dimension of varying speeds of velocities.
Here he implied that it is the divisible nature of time which makes it possible to
compare the relative speed of motions.85 These considerations about the continuity
of motion eventually helped Bradwardine to dismiss the theory that continua can be
composed of immediate indivisibles. His whole theory of imposition rested, in fact,
on his assumption that equivalent continua have the same number of components

and so can. be superimposed. In Bradwardine’s view, then, time has the crucial

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function in natural philosophy of bridging gap between the theoretical nature of
geometrical continua and real, physical continua existing within a temporal
framework.

In contrast to the De prapartianibus, then, the De continua provides a
concrete definition of time according to Aristotelian principles. Bradwardine
presents time as a successive continuum which can be divided inﬁnitely into time-
atoms or instants, which are themselves subject to further division. Time is,-
moreover, the single continuum which governs all other physical continua including
motion, space and temperature. For all that, Bradwardine does not invest time with
any independent physical reality, nor does he consider in any depth how time can be
used practically to measure other continua: time is a measure of motion, but
motion is not a measure of time according to Bradwardine’s initial deﬁnitions. This
vagueness actually helps Bradwardine to make time a pivotal concept for comparing
geometrical and physical continua by means of Euclidean language.

Bradwardine’s view of time is thus both strikingly Aristotelian in its
identiﬁcation of time with motion and strikingly non-Aristotelian in its elevation of
mathematical reasoning to a degree not found in any of his predecessors. In this
respect, Bradwardine’s isolation of the problems of time and continuity from other
metaphysical considerations is similar to Ockham’s; and, of course, on a theoretical
level, both of them reach the same conclusions about the nature of permanent and
successive continua. Bradwardine’s implicit acknowledgment that geometrical
ﬁgures do not represent real things indicates, for example, at least partial agreement
with Ockham’s criticism of Aristotelian physics. Both Bradwardine and Ockham
realize that, by interrningling geometrical and physical continua, Aristotle failed to
distinguish them adequately or to take into account the real usefulness of
geometrical continua in the investigation of natural philosophy. In proposition 151,

in fact, Bradwardine actually claims that "there are no surfaces, lines or points at

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all":86 Of course, Bradwardine’s denial of a separate reality for these entities does
not amount to an afﬁrmation of Ockham’s thesis that these concepts have no reality
apart from a real physical object. In the De continua Bradwardine simply wants to
point out the practical difﬁculties of describing physical continua geometrically so
he consciously avoids broader metaphysical considerations. Nevertheless,
pr0position 151 clearly indicates Bradwardine’s conviction that the proper goal of
geometry is to study real solids,87 a position with which Ockham would have
sympathized.

Furthermore, Bradwardine did not follow Ockham in deﬁning motion as an
inherent part of a moving object. Although he did not deve10p the point in the De
continua, Bradwardine maintained the orthodox Aristotelian approach of describing
motion and time as categories of being and consequently failed to identify exactly
how the continuity of space and time inﬂuences the continuity of motion.88
Although Ockham’s approach to the fundamental problem of motion was more
promising, neither Ockham nor his immediate followers solved the problems
presented by physical continua in a way that is more convincing than Bradwardine’s.
Still, Bradwardine and Ockham succeeded not only in providing new ways of
investigating an ancient problem but also in reworking the Aristotelian deﬁnitions

of time and motion found in Averroes and Thomas Aquinas for a more skeptical

fourteenth-century audience.

CHAPTER SIX
TIME AND CONTINGENCY

Closely related to continuity is the problem of contingency, which often
concerns the predictability of continuous events. Unlike continuity, contingency
does not lend itself easily to mathematical analysis. Discussions of contingency in
Aristotle and throughout the medieval period, therefore, are primarily linguistic or
logical in character. Bradwardine’s devotion to Aristotle, who had originally posed
the problem in Book IX of his De interpretatiane, and the importance of this topic in
late medieval scholarly debate stimulated Bradwardine’s interest in contingency in
spite of its fundamentally non-mathematical nature. Although geometry certainly
inﬂuenced his view of contingency, Bradwardine was forced to employ other
methods when he approached this problem.

In the De incipit et destinit and the De ﬁztun's cantingentibus, Bradwardine
examined some of the logical and psychological aspects of time which a purely
mathematical approach could not consider properly. These texts complement his
scientiﬁc writing about time because they present an alternative, more philosophical
view of time based not on its relationship to motion but on its enigmatic capacity to
link the past to the future. Bradwardine’s early work on contingency reveals not
only the complexity of his view of time but also the origins of the mature opinions
concerning predestination and divine foreknowledge which dominate the De causa
Dei. It is in the De incipit et destinit and the De futuris cantingentibus, moreover, that
we ﬁnd the clearest evidence of Bradwardine’s early interaction with the most

inﬂuential logicians of his day, particularly William Ockham.

131

132

The wide variety of medieval discussions about contingency makes it
necessary to restrict this analysis to aspects of the problem which speciﬁcally
concern time as a successive continuum. The previous review of Bradwardine’s
concept of time in the De prapartianibus and the De continua has shown that he
largely accepted Aristotle’s deﬁnition of time as the number or measure of motion
according to before and after. Time, like motion, is successive and inﬁnitely
divisible: Time and motion cannot be conceived, therefore, as separate entities.
These Aristotelian principles deﬁne a rational natural order which can be
investigated through observation and mathematical analysis. Bradwardine found
this notion of rationality very appealing.

Unfortunately, even Aristotle recognized that his deﬁnitions were not
entirely compatible with human perception of time. The ambivalence about time in
Aristotle’s natural philosophy inﬂuenced discussions of contingency throughout the
Middle Ages. In this chapter I shall examine the two aspects of contingency which
have the greatest bearing on Bradwardine’s view of time: prediction in the context
of beginning and ceasing, and the question of whether a future event can be both
contingent and foreknown. Because Bradwardine’s position on contingency was
based on classical as well as contemporary thought, I shall refer extensively to
Aristotle, Boethius, Peter of Spain and William Ockham, all of whom directly
inﬂuenced Bradwardine’s view of contingency, both positively and negatively.

The problem of prediction which features so prominently in Bradwardine’s
view of contingency originated in Aristotle’s physical theory. Bradwardine’s
approach to contingency was also inﬂuenced by the attempts of some medieval
logicians to use the principles of Aristotelian physics to make predictions. Although
the subject of prediction has received relatively little attention from modern
scholars, those who have studied it agree that medieval thinkers often saw the

problem of prediction as a physical one and approached it by analyzing the concepts

of beginning and ceasing. This approach, ﬁrst suggested by Aristotle, involved the
determination of the temporal limits of a process of change by measuring them
against a continuum.1 Having established that time is an inﬁnitely divisible
continuum, like the motion it measures, Aristotle then had to explain how a change
could begin or end in a moment or now of time when a now is both divisible and
singular. Two things cannot occur in the same now, so neither can the process of
moving from a state of rest to a state of motion be described as occurring within a

single now. Aristotle identiﬁed the difﬁculty of assigning a ﬁrst moment of motion

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in Book V of the Physics:

On the basis

surrounding beginning and ceasing resulted directly from his deﬁnition of

continuity:

And not only must that which is changing have changed,
but that which has changed must also previously have been
changing, since everything that has changed from something to
something has changed in a period of time. For suppose that a
thing has changed rom A to B in a now. Now the now in
which it has changed cannot be the same as that in which it is
at A (since in that case it would be A and B at once); for we
have shown above that that which has changed, when it has
changed, is not in that from which it has changed. If, on the
other hand, it is a different now, there will be a period of time
intermediate between the two; for, as we saw, nows are not
consecutive. Since, then, it has changed in a period of time,
and all time is divisible, in half the time it will have corn leted
another change, in a quarter another, and so an ways;
consequently it must have previously been changing.

of this argument, Aristotle went on to show that these ambiguities

So it is evident also that that which has become must
previously have been becoming, and that which is becoming
must reviously have become, everything (that is) that is
divisib e and continuous. . . . So, too, in the case of what is
perishing and that which has perished; for that which becomes
and that which perishes must contain an element of
inﬁniteness since they are continuous things. . . . It is evident,
then, that what has become must previously have been
becoming, and that which is becomin must previously have
gecoigile; for all magnitudes and 1 periods are always

1v151 e.

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In a negative sense, this sort of analysis might thoroughly discourage the observer of
an event from trying to determine its precise duration. On the other hand,
Aristotle’s approach to continuity suggested that one could reconstruct the past and
predict the future (in a limited way, of course) simply by examining a particular
successive continuum in its present state. Although Aristotle’s theory posed serious
difﬁculties for medieval natural philosophers, who wished to measure events clearly
and accurately, it promised tantalizing possibilities to logicians, who welcomed any
method which might help to verify the truth of logical propositions. Much of the
excitement over beginning and ceasing among medieval thinkers grew out of the
philosophical implications of Aristotle’s theory. Because Bradwardine was more
interested in natural philosophy than in pure logic, however, he seemed to ﬁnd the
logical implications of beginning and ceasing somewhat confusing and bewildering.
Aristotle himself was too good an observer of nature to ignore the
impracticality of his theory. He knew from his own experience that the mind can
discern the beginning and the ceasing of motions: to argue otherwise would be to
support, implicitly or explicitly, Zeno’s half-distance paradox. Aristotle thus needed
to ﬁnd a way of assigning the precise instant of initial motion without undermining
his theory of continuity. His solution to the problem, as he outlined it in Book VIII
of the Physics, involved the admission that logical considerations must precede
physical ones in this case since it is impossible physically to isolate the ﬁrst instant of
beginning or ceasing:
It is also plain that unless we hold that the point of time
that divides earlier from later always belon only to the later
so far as the thing is concerned, we shall e involved in the
consequence that the same thing at the same moment is and is
not, and that a thing is not at the moment when it has become.
It is true that the point is common to both times, the earlier as
well as the later, and that, while numerically one and the same,
it is not so in deﬁnition, bein the end of the one and the

beginning of the other; but so ar aslthe thing is concerned, it
always belongs to the later affection.

135

If, then, one can logically attribute only one state of being to a given now, Aristotle
insisted that the emphasis should be placed on the ﬁrst instant of being rather than
on the last instant of non-being. Similarly, when the motion ceases, emphasis should
be placed on the last instant of being instead of the ﬁrst instant of non-being.5

This passage from Aristotle generated a large body of commentary on
beginning and ceasing throughout the Middle Ages, although evidence suggests that
the medieval philosophers usually failed to grasp Aristotle’s exact position on the
subject.6 Whether their approach to the problem of beginning and ceasing resulted
from their familiarity with the Physics or was the consequence of their reading of
some of Aristotle’s grammatical texts,7 it is certain nevertheless that medieval
thinkers approached the problem of beginning and ceasing in classical terms and
regarded the verbs incipere and destinere as logically complex. By the twelfth
century, logicians had begun to include incipere and destinere in lists of
syncategorematic words because, like other syncategorematic words (prepositions,
adverbs, conjunctions and quantiﬁers), they complicate logical propositions. After
syncategorematic analysis, the sentence "Socrates begins to be" becomes "Socrates is
now and was not before," just as "Only man is capable of smiling" becomes "Man is
capable of smiling and nothing that is not man is capable of smiling."8 Although this
approach to the problem of beginning and ceasing is primarily grammatical and
logical, it still exposes the underlying concept of before and after which Aristotle
stressed in all of his writings about time and continuity.

In the introduction to his edition of Bradwardine’s De incipit et destinit, Lauge
Olaf Nielsen reviews both the grammatical and the physical approaches which
thirteenth- and early fourteenth-century philosophers applied to the problem of
beginning and ceasing. According to Nielsen, medieval logicians, having
misunderstood what Aristotle had said about this issue, went in the opposite

direction from Aristotle when they tried to assign temporal limits. Whereas

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Aristotle had always afﬁrmed the ﬁrst and last instants of being in permanent things,
many medieval thinkers afﬁrmed the ﬁrst and last instants of non-being. While
Aristotle would have expounded the sentence "Socrates begins to be" as "Socrates is
now and was not before," the medieval logician usually expounded it as "Socrates is
not now and will be immediately after this." The medieval logicians, therefore,
”negated the present and afﬁrmed the future."9 By Bradwardine’s day all
discussions of beginning and ceasing stressed this grammatical aspect of the
problem, although several scholars, including Bradwardine, also investigated some
of its physical aspects.

Nielsen compares Bradwardine’s position on beginning and ceasing to the
views of his slightly older contemporaries, William Sherwood, Peter of Spain and
Walter Burley, to show that a late medieval philosopher’s view of time could
inﬂuence his analysis of the problem as much as his assumptions about grammar.10
According to Nielsen, Sherwood and Burley rejected both Aristotle’s view of time
and his solution to the problem of beginning and ceasing. In his Treatise on
Syncategarimatic Words, for example, Sherwood tried to refute a variety of current
proposals for establishing limits for permanent and successive continua and for
describing the transition from a permanent to a successive continuum. His most
signiﬁcant contribution to the general debate was his logical analysis of different
kinds of transition. His thesis concerning beginning and ceasing depended,
however, on the presupposition that a point dividing a line cannot be common to
two adjacent segments. Sherwood therefore compromised Aristotle’s view of
time.11

Burley came to the same conclusion as Sherwood in his De prima et ultimo
instanti, in which he examined the problem of determining beginning- and end-

points in various types of continuous entities. Following Sherwood, Burley relied on

a logical argument to prove that a point dividing time into two segments cannot be

137

common to both segments. In Nielsen’s view, this un-Aristotelian assumption
allowed "the logical necessity of attributing a dividing point to only one segment [to]
become an attribute of time itself."12 Thus Sherwood’s and Burley’s preference for
logic forced them to conceive of time as composed of indivisibles. Because these
discussions were primarily logical, and so did not even address the physical aspects
of time which feature so prominently in Aristotle’s treatment of beginning and
ceasing, it is not entirely clear whether Sherwood and Burley were aware of the
implications of their solutions for natural philosophy as a whole. Nevertheless,
insights into beginning and ceasing substantially enriched the purely logical
approaches which characterized most early medieval studies of time. Even if they
did not have Book VIII of the Physics in mind when they formulated their
arguments, their general knowledge of Aristotelian physics served to make their
criticism of previous theories more sophisticated because it allowed them to
supplement logical arguments with appropriate concepts from Aristotelian natural
philosophy.13 Though they did not perceive beginning and ceasing as a physical
problem, their implicit attitudes about time as a complex problem for both logicians
and natural philosophers represent a signiﬁcant advance in the medieval approach
to the subject. '

The tendency to consider beginning and ceasing as at least partially a
physical question was more pronounced in the writing of Peter of Spain. In his
Tractatus syncategarimatum, Peter supplemented his assessment of the logical
functions of the words incipere and destinere with an analysis of permanent and
successive continua. He considered the problem of before and after both
grammatically as a matter of tense and physically in terms of the nature of time. 14
Unlike Sherwood and Burley, Peter proposed a solution that concurred with
Aristotle’s view of time and provided a model for Bradwardine to follow in his own

early attempts to understand beginning and ceasing. The characteristic feature of

138

Peter’s analysis is his emphasis on the inﬁnite divisibility of permanent and
successive continua. After brieﬂy explaining why he classiﬁes incipere and destinere
as syncategorematic words, he devotes a major portion of his discussion to the
physical properties of different kinds of continua. In distinguishing permanent from

successive continua he points out that

the being of permanent things is a whole at one and the same
time while the bein of successive things is not a whole at one
and the same time ut only in a succession of parts. . . . It is
impossible that more than one time occur at one and the same
time, . . . [P]ermanent things are naturally prior and successive
things naturally posterior, smce permanent things are the cause
of successive things. . . . [Moreover,] permanent things are
intrinsically limited while successive thin s are not limited
intrinsically but are limited by permanent ﬁngs - for example,
a change is limited by a quantity or quality. *5

 

 

 

 

In other words, Peter employs an Aristotelian argument to prove that continua are
limited in different ways depending on how they exist in time.
These considerations, Peter goes on to say, play an important role in the

assignment of actual limits:

Thus as regards permanent things the being of which is
obtained in an indivisible [instant], one can 've the ﬁrst
instant of their bein and 0 their non being a terwards, but
one cannot 've the ast instant of their not being beforehand
nor of their ing. . . . But as regards successive things - being
of which is not obtained in an instant, one gives neither the
ﬁrst not the last instant of their being but gives the last instant
of their not being beforehand and their ﬁrst instant of their not
being afterwards. For while they have their being in a certain
time. they have not being at the limit of that time; and just as
there is no interval between time and itﬁgmit, so there is none
between their being and their not bein .

Although permanent continua necessarily exist in time, their temporal limits are
relatively unambiguous: one merely follows the Aristotelian principle of afﬁrming

the ﬁrst and last instants of being. Because successive continua run parallel with

time, however, one cannot so easily assess ﬁrst and last instants: if time is a

139

continuous entity, divided into segments by nows, the ﬁrst and last instants of a time
segment cannot properly be considered part of the successive entity. This
perspective comes directly from Aristotle’s description of continuity in the Physics.
Although he recognized the logical dilemmas that could arise from accepting
Aristotle’s deﬁnitions, Peter was not overly disturbed by them. In the tradition of
Aristotle himself, in fact, Peter devised a linguistic solution to the problem of
beginning and ceasing which accounted for both Aristotelian physics and
contemporary logical studies. The vocabulary which Peter used to express his
solution became widely known and had a particularly strong inﬂuence on
Bradwardine. His solution takes the form of ﬁve rules concerning the meaning and

usage of incipere:

Rule One. When the verb ‘begins’ occurs with permanent
things the being of which is obtained at an indivisible [instant],
it indicates an assertion of the present and the negation of the

ast. . . .
p Rule Two. When the verb ‘begins’ occurs with successive
things or with permanent things the being of which is not
obtained in an instant, it indicates a negation of the present
and an assertion of the future, because successive things do not
have bein at their outset. . . .

Rule ree. When being is added to the verb ‘ceases’ it
indicates a negation of the resent and an assertion of the past,
no matter what sort of 'ng it occurs together with. The
reason for this is that one cannot give the last instant of a
thin ’s bein whether the thing is permanent or successive. . . .

IRule our]. Similarly, when the not being of thin that
are simply permanent is added to the verb ‘ceases,’ it in 'cates
a ne ation of the gresent and an assertion of the past. . . .

Rule Five]. ut when the not being of successive things is
added to ‘ceases,’ it indicates an assertion of the present and a
negation of the future, since onelgloes not give the last instant
of not being to successive things.

Peter’s analysis of beginning and ceasing had direct bearing on Bradwardine’s view
of time for several reasons. Most obvious, Bradwardine adopted Peter’s method for

assigning limits in almost every respect in his own treatise on beginning and ceasing,

to the point of incorporating large portions of Peter’s treatise in his own work.

140

Peter’s study encouraged Bradwardine to think about continuity along the
Aristotelian lines which already appealed to him and provided a ready-made
vocabulary for expressing his own views about continuity. Moreover, though it is not
itself a mathematical work, the Tractatus syncategarimatum stands in the late
medieval tradition of applying Aristotelian physics to apparently non-physical
problems and so possibly contributed to the ﬂourishing of mathematical studies
among the Mertonians.18 Most important, Peter’s contentions about ceasing in
Rule Five reemphasized Aristotle’s suggestion that syncategorematic terms might be
used to predict the future. Peter did not develop this idea, but later thinkers,
including Bradwardine, paid this suggestion considerable attention.

Bradwardine’s De incipit et destinit and his Geametria speculativa were both
written in the early 13205 and so represent his ﬁrst academic efforts. Because of
their geometrical nature, topics involving beginning and ceasing, continuity and
inﬁnity attracted his attention at an early stage of his advanced studies; judging from
the content of subsequent work, moreover, these topics continued to fascinate him
even after he began to concentrate on theology. Nielsen has established that
Bradwardine wrote the De incipit et destinit in 1323, while he was in the middle of his
arts course. The form and content of the text indicate that Bradwardine wrote it
shortly after completing the part of the curriculum devoted to logic. In fact,
according to Nielsen, the word igitur in the ﬁrst sentence of the text suggests that the
discussion of beginning and ceasing might have been part of a larger work listing the
functions of several syncategorematic words.19

One need not look far to ﬁnd a reason for the survival of this particular
section if Nielsen’s conjecture about its relation to Ockham’s Summa Lagicae is
correct. Nielsen argues that Bradwardine presented his position on beginning and
ceasing in response to Ockham’s treatment of the same subject in the ﬁrst book of

the Summa Lagicae, which Ockham had completed by 1323. In Book II of the

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Summa Lagicae, ﬁnished after 1323, Ockham presented a revised view on the same
topic. Nielsen’s analysis of these passages suggests that Ockham not only
considerably modiﬁed his position on beginning and ceasing after 1323 but did so
directly in accordance with Bradwardine’s criticisms of his original position.20 If the
young student of arts was able to persuade Ockham to change his mind on this issue,
it might be wise to reconsider the precise nature of their relationship. Most
comparisons of Ockham and Bradwardine emphasize Ockham’s inﬂuence on
Bradwardine’s theology, especially in the negative sense that Ockham’s views
prompted a ﬁerce response on Bradwardine’s part. Nielsen’s research indicates,
however, that the connection between the two thinkers was probably much more
complex, positive and mutually beneﬁcial than the conventional interpretation of
their interaction has recognized.

Another indication of the date of the De incipit et destinit is its strong reliance
on Aristotelian physics. In this treatise Bradwardine tried to resolve the problem of
assigning limits to permanent and successive things within the context of Aristotle’s
teaching on the continuum. Since the text represents Bradwardine’s earliest
reﬂections on the subject, it is not surprising that his approach was conservative.
Not only did he borrow heavily from Aristotle and Peter of Spain, but he also
conﬁned his discussion speciﬁcally to logical questions which did not have a
theological dimension. The main theme of the work is the mind’s inability to
acquire determinate knowledge about future events. Thus the future, from the
human perspective, is entirely contingent.21 Although this position seems contrary
to the more deterministic approach which he later took in the De futuris
cantingentibus and in the De causa Dei, his conscious decision to consider
contingency without reference to God gave him the freedom to side-step aspects of
the problem which involve divine causation or prescience. Subsequent discussions

of beginning and ceasing in the De continua conﬁrm Bradwardine’s tendency in

142

earlier works to treat logical and physical problems separately from theological
ones.22

More compelling evidence for the early date of the De incipit et destinit is
Bradwardine’s use of Aristotle and Peter of Spain. His uncritical acceptance of
Aristotle’s view of time and continuity indicates a basic knowledge of the Physics but
his arguments do not convey the originality which he later demonstrated in
reevaluating Aristotle in the De prapartianibus and the De continua. Even this early
effort, however, the text is structured as a series of geometric proofs, in spite of its
essentially non-geometrical subject. This Euclidean approach to a logical problem
reﬂects Bradwardine’s growing interest in mathematics, a feature of his thought
which left its mark on all of his writings, including those devoted to theology. It is
revealing to note in this context that, even though both his topic and his method
were logical, he tried as often as possible in the De incipit et destinit to explain his
theories in terms of physical concepts such as motion and time and even stated
explicitly in the text that he wished to speak as a natural philosopher not a
logician.23

Like Peter of Spain, Bradwardine focuses in this text on the notion that the
inﬁnite divisibility of continua seriously complicates the task of assigning limits.
Bradwardine’s ﬁrst two propositions essentially restate Peter’s distinctions between
permanent and successive continua and he concludes along with Peter that, in the
case of permanent continua, one should afﬁrm the ﬁrst and last instants of being. In
the third proposition Bradwardine tries to work out in a series of detailed corollaries
how the problem of beginning and ceasing affects the analysis of successive things
such as motion in which a single instant cannot truly constitute being. He therefore
asserts, following Aristotle, that it is impossible to determine logically or physically

when a motion begins to be, since one would have to isolate the instant at which the

motion did not yet exist but would exist immediately afterward.24 Working out the

143

implications of this proposition for the study of motion is the chief burden of the De
incipit et destinit. To [shed light on this dilemma, Bradwardine devotes the
corollaries of the third proposition to a comparison between successive continua and
permanent continua which are not so seriously affected by the problem of beginning
and ceasing.

Having analyzed at length the problem of assessing beginning- and end-
points for permanent and successive things respectively, Bradwardine turned very
brieﬂy in proposition four to the subject of things which possess being in only one
instant, a notion which Burley had ﬁrst introduced to the discussion of beginning
and ceasing in the 13105. Not entirely convinced that instantaneous things could
really exist, however, Bradwardine addressed the issue only perfunctorily.25 In the
ﬁnal proposition Bradwardine summarized his conclusions with a series of rules,
based on Peter of Spain’s method for analyzing propositions containing the verbs
incipere and destinere. Bradwardine’s entire conception of time in this treatise, in
fact, parallels that of Peter of Spain: time is both the medium in which permanent
things exist and also a successive continuum in its own right which measures and
limits other successive things. In the case of a permanent thing, the inﬁnitely
divisible nature of time makes it impossible to determine the exact moment the
thing comes into being or ceases to be: one must choose to afﬁrm either the ﬁrst
and last instants of being or the last and ﬁrst instants of non-being. Following Peter,
Bradwardine claims that one should always affirm the ﬁrst and last instants of being
in cases of permanent things. Moreover, one cannot predict the future of a
permanent thing merely by afﬁrming its beginning in the present. He rejects the
logic which expounds the sentence "Socrates begins to be" as "Socrates is now,
therefore Socrates will be" on the grounds that such an exposition uses the same
instant to afﬁrm both Socrates’ present and future state. On this basis, he questions

the general assumption that propositions in the future tense can reveal the truth

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about a permanent object.26 Relying heavily on Aristotelian physical theory,
therefore, Bradwardine concedes that the future state of permanent things can be
predicted but only in a limited and artiﬁcial way. Logical analysis can predict that
something which is will continue until it ceases to be, but this revelation offers no
concrete information about the actual future state of that thing.

In the case of successive things, Bradwardine contends, again along
, Aristotelian lines, that it is impossible to make any true statements about them
except retrospectively.27 His ﬁrst argument against predicting the future of a
successive entity relates to Aristotle’s initial problem of designating ﬁrst and last
instants of being. To predict the future state of a successive thing, such as motion,
one would have to know the next adjacent instant, something which the inﬁnite
divisibility of time makes extremely difﬁcult. If one cannot even designate a
beginning-point for a motion, says Bradwardine, one can hardly be expected to
determine what will follow after it.28 A more signiﬁcant obstacle to knowing the
future of a successive thing is that successive things unfold themselves in time. One
cannot fully know something which has not yet happened and therefore does not
exist. Bradwardine again goes back to Aristotle in distinguishing between our
perception of what might happen in the future and the sensible reality of the
present. Even our sensible perception of present motion is suspect, however, since
neither the senses nor the mind can tell us exactly when a motion in the present has
begun. Under these circumstances it is clearly impossible to make predictions about
a future motion which is completely beyond our experience.29 Bradwardine is not
denying here the common experience of motion or even the human capacity to
measure it. He simply rejects the notion that one can know in the present the future
state of a successive thing because knowledge of any physical being requires sensory

experience, which is impossible to obtain for a future event.

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The ﬁnal argument against the possibility of certain knowledge about the
future state of successive things contains the treatise’s most explicit statement about
the nature of time. The basis of Bradwardine’s argument is Aristotle’s insistence
that the successive nature of time makes it impossible to designate an instant in the
future before it actually occurs. Such a designation would require the measurement
a motion from outside of time, which violates the deﬁnitions of both motion and
time.30 In the subsequent analysis of this problem, Bradwardine develops at length
the thesis that the future of successive things lies beyond certain human knowledge
because time, space and motion are all interrelated. As parallel successive
continua, all three are subject to the ambiguities which result from their inﬁnite
divisibility.31 In other words, Bradwardine implies that one cannot use
syncategorematic terms to draw conclusions about the future, for the transition from
present to future is a physical not a logical process. As far as Bradwardine is
concerned, then, incipere and destinere are only really useful in affirming the present
state of permanent things; their utility in afﬁrming the present state of successive
things is limited; and they cannot function at all as true indicators of future states in
logical propositions.

When Bradwardine returned to the problem of beginning and ceasing in the
De continua, he treated it geometrically, without signiﬁcant reference to
syncategorematic words. He paid little attention, moreover, to the question of
contingency, presumably because it did not lend itself to mathematical analysis and
he had already dealt with that aspect of the subject in the De ﬁtmn's cantingentibus.
Although it makes no reference to contingency, however, the De continua
reconﬁrmed, and indeed expanded upon, the underlying theory about time which
informed Bradwardine’s views on beginning and ceasing. In his initial deﬁnitions,
for example, Bradwardine restated with mathematical precision the Aristotelian

position on continuity which governs all statements involving before and after. His

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seventeenth deﬁnition states that "for something to be, to have been, or to be about
to be after another thing, is the same as to be, to have been, or to be about to be with
a mean between those things." Deﬁnition eighteen says that "for something to be, to
have been, or to be about to be immediately after another thing, is the same as to be,
to have been, or to be about to be without a mean [between those things]."32 The
purpose of deﬁnition eighteen was to affirm Aristotle’s assertion that beginning and
ceasing occur in the same instant, or as Bradwardine later expressed the idea in
proposition twenty-seven, "every beginning or ending is not measured in time, but in
an instant."33 .

Bradwardine then went on to distinguish between the beginnings of
permanent things, which have ﬁrst and last instants of being and successive things
which have ﬁrst and last instants of non-being. In other words, permanent things are
intrinsically bounded while successive things are extrinsically bounded. To say
otherwise, one would have to assume that a thing must have both a last instant of
non-being and a ﬁrst instant of being and, consequently, that continua are composed
of immediate indivisibles}4 According to Murdoch, Bradwardine’s views about
beginning and ceasing had an important function in his overall strategy against the
atomists. Bradwardine’s success in this enterprise rested on his ability to perceive
the inconsistencies of the atomist position and to tailor Aristotelian physical theory
to suit the particulars of the debate.35 By popularizing Bradwardine’s criticisms of
the atomists the De continua contributed to the achievement of fourteenth-century
philosophers who greatly clariﬁed the nature of continuity through their
investigations of successive continua.36

In the De incipit et destinit and the De continua Bradwardine presented a
physical rather than a psychological view of time. Even on those occasions when he

admitted the role of human perception in deﬁning time, he discussed this perception

in Aristotelian terms. By consciously avoiding the issue of divine knowledge he was

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able to describe time and motion as successive continua whose natures and
directions are determined by natural law. Such a secular view of time was extremely
useful in his mathematical studies, encouraged his respect for Aristotle and satisﬁed
his desire to ﬁnd order in the natural world. Nevertheless, Bradwardine could not
escape from the inﬂuence of contemporary speculation at Oxford about
contingency, which called into question the validity of a human-centered approach
. to time. Aristotle himself had addressed the problem of contingency, much in the
same way as he had tried to solve the problem of beginning and ceasing, and so
made an important contribution to an extremely complex debate. In the De incipit
et destinit Bradwardine consciously avoided, as Aristotle had done, any
consideration of broader philosophical or theological implications of contingency.
By the fourteenth century, however, it was impossible to do full justice to the topic
of contingency without taking into account the work of the Christian thinkers who
had transformed contingency from a merely logical problem into a potent
theological one. Their continuing efforts to establish a relationship between God’s
certain knowledge about the future and human uncertainty led to subsidiary
discussions about a wide variety of difﬁcult theological topics including
predestination, free will and divine causation. Medieval theologians, in fact, made
signiﬁcant progress in bridging the gap between contingency as a logical problem
and the temporal aspects of God’s relationship with his creation.

The De ﬁzturis cantingentibus, composed shortly after the De incipit et destinit
while Bradwardine was still a master of arts, represents one of Bradwardine’s ﬁrst
attempts to sort out the philosophical implications of contingency and to consider
whether and to what extent the future has been predetermined. He had already
shown in the De incipit et destinit that the future seems to be contingent from the
human perspective because we cannot attain certain knowledge of the future

through logical analysis of propositions or observation of nature. This does not

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mean, however, that the future is also contingent to God. In the De futuris
cantingentibus Bradwardine explored, perhaps for the ﬁrst time in his career, certain
aspects of the transition from past to future which he later reﬁned in the De causa
Dei. His initial attempt to resolve the problem of contingency can be seen as a
perceptive but youthful response to a complex body of authority ranging from
Aristotle’s metaphysical works to Ockham’s studies of divine causation.

Aristotle’s main contribution to the medieval debate about contingency
comes from his discussion of truth in Book IX of the De interpretatiane. The passage
which Aristotle devoted to future contingents is, unfortunately, so confusing that
neither medieval nor modern scholars have been able to agree on precisely what he
was trying to prove about the truth of future events.37 In his analysis of the passage,
Jaakko Hintikka suggests that the source of Aristotle’s difficulty with contingency,
like his problem with beginning and ceasing, was his inability to offer on the basis of
his physical system simple, unambiguous answers to questions about the truth of
temporally indeﬁnite sentences.38 Aristotle approached the problem of
contingency by distinguishing generally between things that are necessarily true for a
given time and those which are only possible. He offered no ﬁrm criteria, however,
for determining the relative truth of various kinds of statements about the future.
Although he admitted that some events might be eternally necessary, he believed
that most truths tend to be contingent, claiming that

not everything is or happens of necessity: some things happen
as chance has it, and o the afﬁrmation and negation neither is
true rather than the other; with other things it is one rather
than the other and as a rule, but still it is possible for the other
to happen instead. . . . Clearly, then, it is not necessary that of
every afﬁrmation and opposite negation one should be true
and the other false. For what holds of things that are do§§ not
hold for things that are not but may possibly be or not be.

This rather vague doctrine suggests that the contingency of an event or thing is

based on whether it is necessary both now and in the future. While it is logically

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necessary that a certain future thing will either be or not be, one cannot prove its
future existence or non-existence in the present. From the human point of view,
then, future things are almost entirely contingent. Whereas all true statements
about the past are necessary, most future statements must wait for retrospective
veriﬁcation.40 From the perspective of contingency, then, past and future are
fundamentally different states of time.

Because of its large scope and obvious theological implications, the problem
of contingency received much greater attention throughout the Middle Ages than
the more specialized problem of beginning and ceasing. Although he had not yet
begun his theological studies when he wrote the De ﬁzturis cantingentibus,
Bradwardine’s philosophical training had advanced enough so that he was prepared
to consider more than just the physical and logical aspects of contingency.41 In
developing his own philosophical approach to contingency, Bradwardine was guided
by the work of Augustine and Boethius, who came to be, along with Aristotle,
Bradwardine’s favored authorities.

Augustine’s approach to contingency appealed to Bradwardine chieﬂy
because it considered contingency as much a physical problem as a theological one.
Augustine supplemented Aristotle’s view of contingency by paying greater attention
to its moral implications and offered an alternative method for deﬁning the
problem. Whereas Aristotle concerned himself mostly with the issue of truth in
temporally indeﬁnite statements, Augustine considered the human perspective on
contingency in future events. In Book V, Chapter 9, of the City of God, Augustine
presents his own view of contingency through his criticism of Cicero’s cosmology.
According to Augustine, Cicero’s major error was his unreasonable denial of any
kind of foreknowledge or fate, which was due to his fear of rigid predestination. For
Cicero, said Augustine, it would be far better to deny fate or God altogether than to

live believing that there is no opportunity for independent will or action. In making

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this claim, Cicero assumed that human acknowledgement of divine prescience
amounts to the surrender of individual freedom.42

Augustine rejected Cicero’s assessment of the relationship between the
human and the divine will and thus dismissed Cicero’s insistence on viewing
contingency from the divine perspective. In Augustine’s opinion, God’s
foreknowledge does not interfere with the exercise of human will; on the contrary,
God’s foreknowledge actually enhances and protects human freedom. As the ﬁrst
efficient cause of every event, God gives to his creatures a world in which they can
exercise their wills freely according to their abilities: "their future strength is
completely determined and their future achievements utterly assured."43
Augustine’s conception of the will not only preserved both God’s prescience and
human freedom but also placed the question of contingency in a human context.
God’s knowledge of the future does not make human knowledge of a particular
future event any more certain, except in instances of prophesies, and even here we
do know exactly how or when God will fulﬁll them. Augustine’s position on
contingency was entirely consistent, therefore, with his view of time, which also
stressed human perception. God made time so that his creatures would have a
sensible reference for ordering their existence and to give them a place in history.
Thus time and contingency must always be related to eternal being.44 In this sense,
Augustine’s approach to contingency had a metaphysical signiﬁcance which
Aristotle’s lacked. Nevertheless, both Aristotle and Augustine emphasized, in
different ways, the necessity of separating absolute truth from human perception of
truth.

In the Consolation of Philosophy Boethius offers an interpretation of
contingency which lies somewhere between Aristotle’s and Augustine’s. Like
Aristotle, Boethius wanted to establish degrees of necessity and was, in fact, much

more successful than Aristotle had been in Book IX of the De interpretatiane. In

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Boethius’ view, the order of the natural world depends on the absolute necessity of
certain events such as the rising and setting of the sun. As for contingent things,
Boethius makes the further distinction between cases in which the possibility of one
outcome is equal to another and cases in which a certain outcome is extremely
unlikely but still possible. Boethius also maintains Aristotle’s position that a true
prediction concerning a future event cannot be considered necessary solely on the
grounds that the prediction turns out to be correct: only individual events in time
which are always true should be considered necessary.45
Through his consideration of the theological aspects of contingency, however,

Boethius arrived at a position on the function of will in determining future events
which closely resembles Augustine’s. In the ﬁrst place, God is not subject to the
same kind of observation of past, present and future that his creatures experience
because he is outside of time. God’s foreknowledge does not involve the kind of
control which Cicero and others have attributed to him. In fact, his inﬂuence is of
an entirely different order:

since God abides for ever in an eternal present, His

knowled .e, also transcending all movement of time, dwells in

the simp icity of its own changeless present, and, embracing the

whole inﬁnite sweep of the past and future, contemplates all

that falls within its simple cognition as if it were now taking

place. . And therefore, if thou wilt carefully consider .that

immediate presentment whereby it discriirunates all things,

thou Wilt more rightly deem it not foreknowledge as of

somethin future, ut knowledge of a moment. that never

passes. or this cause the name chosen to describe it is not

prevision, but providence, because, since utterly removed in

nature from things mean and trivial, its outlook embraces all

things as from some lofty height. Why then dost thou insist

that the things which are surveyed by the Divine eye are

involved in necessity, whereaibclearly men impose no necessity

on the things which they see?
Boethius again echoes Augustine on the question of the human response to
contingency. He contends that, while many unexpected events seem to be chance,

they really occur as the result of "causes [arising] from that inevitable chain of order,

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which, ﬂowing from the fountainhead of Providence, disposes all things in their due
time and place."47 Moreover, in establishing that order, God has provided for the
human will to exercise freedom in choosing future actions. The freedom of a human
soul is relative to its capacity to use freedom wisely.48 So while emphasizing the
Aristotelian distinctions between necessity and possibility, Boethius also places
contingency in a broader cosmological context which links human freedom with the
obligation to recognize moral and natural order.

Medieval discussions of contingency bear the inﬂuence of Aristotle,
Augustine and Boethius in varying degrees.49 Anselm, for example, used Boethius’
distinction between different levels of possibility to draw his own distinctions about
necessity. Thus he differentiated between "antecedent" necessity, which is absolute,
and "subsequent" necessity, in which God’s foreknowledge does not interfere with
free choice. In Anselm’s view, only the rigid "antecedent" necessity could impair the
free exercise of choice.50 Similarly, Peter Abelard concluded from his reﬂections
on Aristotle’s discussion of future contingent sentences that God knows and can
reveal contingent truths without enforcing determinism or yielding divine
infallibility.51 Peter Lombard later introduced a more sophisticated approach to
contingency which involved the question of whether God can know what he does not
know, thus making an initial distinction between that which is necessary and that
which is immutable.52 Robert Grosseteste went on to distinguish further between
simple necessity (those things, like mathematical principles, which would be the
same regardless of the course of history) and immutable truths, which can not
change once they have been established. Grosseteste’s theories about the
relationship between past and future necessity stimulated a heated debate about the
modal aspects of contingency which continued well into the fourteenth century.53
Aquinas, in keeping with Boethius, went back to the familiar notions that God’s

being in the eternal present allows him to know the future without determining it

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and that God’s knowledge that a person will make a particular choice does not
detract from the freedom of that choice.54 In response to Aquinas Duns Scotus
argued that there is an objective difference between past and future which God
experiences as much as humans do. For Duns, contingency depends on God’s power
to will the opposite of anything that he wills.SS This outpouring of theories about
contingency in the thirteenth century provides the context for Bradwardine’s
dialogue with Ockham on contingency in the fourteenth century.

The philosophers who inﬂuenced Bradwardine most immediately in the De
ﬁzturis cantingentibus were Peter Aureoli and William Ockham. It was Aureoli who
suggested the principles about contingency which Ockham later developed into a
sophisticated logical theory of necessity. Bradwardine ﬁrst challenged this theory in
the De futun's cantingentibus, then expanded his criticism of it much more skillfully in
the De causa Dei. Aureoli’s argument was based on the assumption that a thing
which is immutable in a particular state must therefore be necessary in that state.
From this premise he tried to prove that a true statement about the future is both
immutable and necessary. Aureoli was fully aware of the central dilemma of this
thesis: a statement which is true both in the present and at the time of its fulﬁllment
leaves no room for contingency or choice. He therefore softened his original
position by expanding the role of contingent statements about the future, which, he
claimed, need not be either true or false in the present.56 In this way he saved the
logician from the necessity of verifying future truths in the present, but he put his
whole theory in doubt by failing to explain how something could be true about the
future but not true in the present. Aureoli left it to others, such [as Ockham and
Gregory of Rimini, to address the logical difﬁculties which arose from this new
proposal. His use of arguments from Aristotle, Grosseteste and Lombard ensured,
however, that his ideas would be widely publicized, if not precisely followed,

throughout the fourteenth and ﬁfteenth centuries.57

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Ockham’s speculations about contingency appear in many of his
philosophical writings. In addition to discussions in the Summa Lagicae and the
Quadlibeta, the Tractatus de praedestinatiane et de praescientia Dei et de M
cantingentibus provides an extended treatment of Ockham’s view of contingency. In
the Tractatus de praedestinatiane Ockham is particularly interested in addressing the
question of how the necessity of a statement varies according to whether it refers to
a past, present or 'future time. He also makes a distinction here between the
necessity of statements about things which God has predetermined and that of
purely logical statements which do not reveal whether God’s predestination is
involved in them. According to Philotheus Boehner, who has edited the Tractatus de
praedestinatiane and several other of Ockham’s works, Ockham conceives of
contingency as a fundamentally logical and linguistic problem, although he admits
that contingency also has some signiﬁcant theological ramifications.58

The thrust of Ockham’s analysis in the Tractatus de praedestinatiane,
reminiscent of treatises on syncategorematic words, is to decide whether verbs such
as praedestinare and reprobare refer primarily to the present or to the future. Since
statements about the future cannot be veriﬁed as true or false, he argued, one
cannot detemiine whether they are absolutely necessary as one can when the
statement is about the past. Even a statement containing the word praedestinare or
reprabare in the past tense, however, still refers to the future until the event in
question takes place and can be veriﬁed. On the other hand, God knows the truth
of every proposition whether it applies to the past or present, in which it is possible
for us to share in his knowledge, or to the future, in which it is not. Therefore, there
cannot be any proposition which is neither true nor false. Moreover, if a statement
about the future is true, it is necessarily true only after the instant in time at which
God fulﬁlls the prophecy. Until this instant, the statement could be true but would

not be necessarily true, since an action can only be necessary after it has been

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completed.59 Ockham’s logic is based on the observation that human and divine
perceptions of the future are entirely different in character and scope.

Ockham then must explain how it is that God can know the future without
depriving humanity of its free will. In contrast to many of his predecessors, who
placed God outside of time, Ockham credits God with an immediate experience of
time which resembles a human one. In the sixth assumption of the Tractatus dc
praedestinatiane Ockham maintains that God’s capacity to know the future is a

logical, not a cosmological reality:

It must be held beyond question that God knows with certainty
all future contingents - i. e., He knows with certainty which part
of the contradiction is true and which false. . . . It is difficult,
however, to see how He knows this [with certainty], since one
part [of the contradiction] is no more determined to truth than
the other. . . . For that reason, I maintain that it is impossible
to express clearly the way God knows future contingents.
Nevertheless it must be held that He does so, but contingently.

Despite [the impossibility of expressin it clearly], the
following way [of knowing future contingentsfcan be ascribed
[to God]. Just as the [human] intellect on the basis of one and
the same [intuitive] cognition of certain non-complexes can
have evident cognition of contradictory contingent propositions
such as ‘A exists,’ ‘A does not exist,’ in the same way it can be
granted that the divine essence is intuitive cognition that is so
perfect, so clear, that it is evident cognition of all things past
and future, so that it knows which part of a «gantradiction
[involving such things] is true and which part false.

Though more perfect than human knowledge in every respect, God’s knowledge of
the future is still contingent. By drawing an analogy between human and divine
knowledge of contingent events, Ockham suggests that God’s experience of the
future is comparable to ours: like us, he is waiting for the future to come into being
so that his knowledge of the future can be necessitated.

Ockham’s discussion of whether God’s knowledge of the future can change
further emphasizes God’s temporality. In Ockham’s view, one of God’s supreme

powers is his capacity to know the truth of changing propositions without changing

himself. Moreover, Ockham argues that in certain cases God does not know future

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events, but his lack of knowledge in no way impairs his perfect understanding of the
_ future:
[Some contingents] that are future as regards their wording
suggest (implicant) that present or past things are future.
Suppose, for example, that the roposition ‘Socrates will sit
down at tl’ is asserted after t1. is suggests that past things
are future - viz. that t1 is future and that Sitting down is future.
Such a proposition about the future can change from truth to
falsity, since before t1 it was true and after t it is false. And
God can not know such a future contin ent a er He did know
it, as a result of chan e of thgrigs an the passage of time,
without any change on is part.
This argument not only ﬁrmly places God inside time but also preserves, albeit in a
limited way, the contingency of future events at the expense of God’s absolute
knowledge.

Ockham admitted that he could not easily prove his theories about
contingency with human reason alone. He considered faith, rooted in Scripture and
the saints, to be the best form of verification.62 This admission did not spare him,
however, from the criticism that his conception of divine foreknowledge directly
contradicted patristic views. His acknowledged inability to explain his logical
theories in terms of the orthodox position on God’s relationship to time made
Ockham’s views on contingency the subject of considerable debate. While he was
relatively successful philosophically in placing his theories about contingency in a
context of a changing physical universe, he had more trouble in convincing his
colleagues of the religious merit of his logic. At the heart of his difﬁculty lay his
view of time, which seemed to contend that God experiences time in the same
Aristotelian way of motion and change as his creatures experience it.63

Bradwardine’s chief objective in the De ﬁltwis cantingentibus was to refute
the human-centered view of divine time expressed by Ockham and some of his

contemporaries. Bradwardine agreed with Ockham that Aristotelian physics

provides a good explanation of time as a natural phenomenon but he refused to

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believe that God shared in any way the human experience of time. Because the De
ﬁlturis cantingentibus posited such a rigid separation of God from time and
advocated such a ﬁrm commitment to the notion of God’s absolute prescience, it
could give the impression that Bradwardine saw practically no role at all for human
free will. Later, in the De causa Dei, he would treat the subject of contingency with
much greater subtlety and balance. In his ﬁrst attempt, however, his inexperience in
dealing with complex philosophical and theological questions led him to
uncompromising positions and exposed his lack of expertise in philosophical inquiry.
On the subsidiary issue of whether God causes sin by virtue of his prior knowledge
of it, for example, Bradwardine had little to offer beyond an apology for not yet
having mastered the problem.64 Nevertheless the De ﬁ4turis cantingentibus
demonstrated Bradwardine’s general familiarity with the contemporary state of the
debate over contingency and offered a criticism of Ockham’s position which was
clear and relatively well developed in spite of its failure to present a satisfactory
alternative.

Bradwardine set out in the De futuris cantingentibus to prove that God has
complete foreknowledge of all future contingents by virtue of his eternal nature. In
the sixth opinion, Bradwardine deﬁned the temporal basis for his view of
contingency, which echoed Boethius’ and Anselm’s assertion that everything is
eternally present to God and therefore God has complete knowledge of every future
event.65 Bradwardine thus stressed the difference between the creature, whose
knowledge of the future is necessarily contingent because of his position in time, and
God, who knows everything there is to know simultaneously. Bradwardine
reinforced his contention that God knows all things in an eternal present by
stressing God’s immutability. In contrast to Ockham’s conception of God,
Bradwardine’s view did not admit that God experiences change and time. There is

no reason to consider the question of whether God can change his mind about the

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truth of a future statement because God knows eternally the truth of every
proposition. Not even God’s willingness to respond to his creation undermines his
immutability.66 Bradwardine then demonstrated in the same way that his view of
God is thoroughly consistent with revelations about God’s nature in Scripture.
God’s knowledge of future events ensures that his revelations were, are and will be
true, whether they come to us through prophecy or through another means, such as
created knowledge.67
When it came to explaining how human free will could be accommodated in
his theory of God’s unchanging omniscience, however, Bradwardine had nothing
very original to offer. He derived his main argument about free will from
Augustine’s criticism of the Stoics in Book V of the City of God, in which Augustine
had claimed that God allows the human will to participate freely in his eternal
plan.68 This and several other similar references to Augustine and Boethius
indicate that Bradwardine adopted, essentially uncritically, their conception of the
relationship between God’s future knowledge and the human will.69 Bradwardine’s
deﬁnition of divinity, based as it was on the classical and patristic principles of
omniscience, immutability, eternity and omnipotence, gave him little choice but to
acknowledge God’s capacity for complete knowledge of future contingent events.
Bradwardine’s youth and relative inexperience with theological matters
apparently led him to a rigid and uncompromising position in the De futuris
cantingentibus. The conclusion of the treatise left no room for doubt that he was
comforted much more by arguments which demonstrated God’s absolute prescience
than by those which emphasized free will. Bradwardine was content simply to
acknowledge that some kind of free will must be possible since both Scripture and
Christian writers have afﬁrmed it. Nor did he show any inclination to deﬁne free
will so that it was compatible with his deterministic view of necessity. Bradwardine’s

ﬁnal word on contingency in the De ﬁltun's cantingentibus was that, while the

159

capacity to know the truth of a future contingent statement is beyond the capacity of
man, God, with his absolute power, is not constrained by human weakness.70
Signiﬁcantly, Bradwardine was not opposed to Aristotle’s position on contingency as
such; his concern was only to deﬁne contingency so that it did not minimize God’s
non-temporal knowledge of future contingent events.

Bradwardine’s early position on contingency, as it was expressed in the De
incipit et destinit and the De futuris cantingentibus, was based on the tension which be
perceived between two equally compelling temporal theories. As a mathematician
and natural philosopher, Bradwardine found Aristotle’s deﬁnition of time both
reasonable and useful; as a Christian philosopher, he was attracted to Augustine’s
and Boethius’ more psychological conception of time, which seemed to offer a
better explanation of time’s relationship to eternity. In both treatises on
contingency Bradwardine exhibited a tendency towards rigid, almost dogmatic, logic,
as if he was trying to express his philosophical opinions as mathematically precise
truths. Thus his commitment to the thesis that the continuous nature of time
prohibits logical predictions about the future was just as strong as his
pronouncement that God’s perfect foreknowledge repudiates real contingency. At
the heart of this apparent contradiction lies Bradwardine’s even more fundamental
belief that Aristotle’s description of time and other features of the natural world
accurately reﬂects God’s creation. Although he realized that one could never hope
to determine God’s temporal relationship to his creation using natural philosophy
alone, Bradwardine thought that Aristotelian physics allowed the natural
philosopher to study the world from the human perspective and in human terms.

These writings on contingency also say much about Bradwardine’s academic
personality in 13205. He was at once receptive to the ideas of his thirteenth-century
predecessors and deﬁant in support of the positions which attracted his interest. If

Nielsen’s assessment of Bradwardine’s interaction with Ockham in the De incipit et

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destinit is correct, the De futuris cantingentibus also clearly indicates Bradwardine’s
ability as a young scholar to debate and even instruct his more established peers.
Although it would be too much to expect complete consistency in his early treatises,
Bradwardine’s work on contingency, along with his mathematical studies of
proportionality and continuity, provide a good indication of his intellectual outlook.
While he did not conﬁne his studies to problems which could be solved easily with
mathematics, he applied mathematical methods to his subjects whenever possible.
Underlying all of his main positions was the assumption that there is an order in
nature which can be understood mathematically, not in the purely symbolic sense of
Platonic mathematics but in the active observation and description of natural
phenomena according to Aristotelian physics.

As a concept which has both cosmological and physical signiﬁcance, time
emerged again and again in Bradwardine’s early writings, though he did not, so far
as we know, devote a separate treatise to the problem of time. In his early treatises
the problem of time always arose in the context of proportional velocity, continuity
or contingency. While his studies of motion in the De prapartianibus, the De
continua and the De incipit et destinit all depend on his Aristotelian understanding of
time as a physical concept, however, the De ﬁltun's cantingentibus attempted to
confront the much more difﬁcult problem of explaining how human beings can
experience contingency in their temporal existence without denying certain
knowledge to God. It was the logical dilemma of contingency in a temporal world
created by a timeless God which troubled Bradwardine in the De futuris
cantingentibus. Although he tried to resolve the dilemma through recourse to
Aristotelian natural philosophy he eventually realized that a purely creature-
oriented view of time only partially explains the cosmological signiﬁcance of the

distinction between time and eternity.

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In the De futuris cantingentibus Bradwardine posed challenging questions
about time and contingency but found himself unable to answer them. By the time
that he wrote the De causa Dei, however, he was able to describe precisely the
distinction between time and eternity, to assess the place of time in his own
cosmological system and to reconcile Aristotelian physics with Augustinian theology.
Bradwardine’s mature view of time undoubtedly grew out of his interaction with
colleagues in the 13305 and was inﬂuenced by his conversion experience.
Nevertheless, his early speculations about time as a physical and logical concept
informed his approach to God’s use of time, which lies at the center of his attack on
the modern Pelagians. Without an understanding of Bradwardine’s mathematical
way of thinking and his devotion to an Aristotelian perspective on nature, it is easy
to underestimate his ability to balance different cosmologies and conciliate opposing
schools of thought in the De causa Dei, a work that is generally portrayed as highly
polemical. The foregoing discussion of Bradwardine’s early attitudes towards time
offers the necessary background, therefore, for exploring the cosmology he

presented in the De causa Dei.

CHAPTER SEVEN
TIME IN THE DE CAUSA DEI

The De causa Dei, Bradwardine’s longest and most inﬂuential work,
represents the only surviving example of his theological method. Although it is as
long as or longer than most contemporary sentence commentaries, the De causa Dei
is a polemical work focused on a single issue: the defense of God’s role as ﬁrst
cause in every created act against the false claims of the modern Pelagians, as
Bradwardine referred to his opponents. In spite of its theological orientation,
however, the De causa Dei follows the same style as Bradwardine’s works of natural
philosophy. The text consists of a series of axioms and corollaries arranged and
tested with Bradwardine’s characteristic mathematical precision.

His central thesis that God is the ﬁrst cause of every created act was not
remarkable in itself, since Thomas Aquinas had already developed it at length as
both a philosophical and a theological problem in the Summa thealagica.
Bradwardine’s capacity for precise mathematical reasoning, however, combined with
his passionate disdain for the contemporary suggestion that grace need not precede
a meritorious act, gave his analysis of the ﬁrst cause a special sharpness and urgency.
Bradwardine fully appreciated the implications of his view of the ﬁrst cause for
other theological questions, such as contingency, free will, grace, and
predestination. Indeed, the burden of the three books of the De causa Dei was to
illustrate both philosophically and theologically how the human will can be guided

at all times by God’s will and yet remain free.

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The deterministic nature of Bradwardine’s arguments made the De causa Dei
a controversial work when it was published in 1344 and it remains so today.
Bradwardine’s activities in the 13405 helped, in fact, to ensure that the De causa Dei
would reach a wide and varied audience. By the late 1330s, he had attracted
powerful ecclesiastical patronage and was enjoying the prominence of his position as
chancellor of St. Paul’s and chaplain to Edward III. In spite of his new
responsibilities, Bradwardine had been able to maintain close ties with his former
colleagues at Merton: he dedicated the De causa Dei to the Mertonians, who had
urged him to put his complaints. against the "modern Pelagians" into writing.
Bradwardine’s reputation as a learned and saintly man and his strident claims about
topics of contemporary interest assured a large audience for the De causa Dei. Any
analysis of this work must consider, therefore, both the context of the academic
debate which shaped its contents and the inﬂuential position of its author.

Modern readers of the De causa Dei, like their medieval counterparts,
respond to the polemical tone of the work and sense in it some of the confusion of
mid-fourteenth century theological discourse which Bradwardine tried to overcome.
Although they all concede the importance of the work, historians disagree strongly
about why it was signiﬁcant. In spite of their different interpretations of
Bradwardine’s purpose, for example, both Leff and Oberman contend that the De
causa Dei is almost wholly theological in character. According to Leff,
"Bradwardine eschewed philosophy and metaphysics. He was not primarily
concerned with the problems of being or its nature, nor with the scope of human
knowledge."1 After acknowledging the philosophical interest of the text, Oberman
also argues that Bradwardine was "ﬁrst and foremost a theologian, for whom
philosophy served as a necessary means for the expression of theological thoughts."2
Other historians contend, however, that it was Bradwardine’s distinctive

philosophical outlook which gives the De causa Dei its remarkable character. In his

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assessment of Bradwardine’s criticism of the "modern Pelagians," F. C. Copelston
portrays Bradwardine as a metaphysician who based his doctrine of grace on the
Aristotelian principle that whatever is moved is moved by something else; and, as a
Christian, Bradwardine merely speciﬁed that the ﬁrst cause of any movement
ultimately is God.3 Unlike Augustine and Boethius, who used a psychological
argument to explain how God causes the human will to act predictably and freely,
Bradwardine relied ﬁrmly on Aristotelian cosmology in his analysis of the problem.4
Bradwardine’s views of time provide a good means for assessing the extent to
which his theology was shaped by Aristotelian metaphysics. Time, the continuum
which distinguishes limited created being from the eternal perfection of God, has
both physical and theological signiﬁcance in Bradwardine’s cosmology. The variety
of contexts in which the problem of time arises throughout the De causa Dei reveals
the importance of time in Bradwardine’s attempt to reconcile his Aristotelian
natural philosophy with the doctrine of grace and justiﬁcation which he derived
from Augustine. In this chapter, I shall trace Bradwardine’s treatment of time under
three broad headings - the role of time in creation, the philosophical enigma of
time, and the function of time in theological discussions of sin and grace - in order
to examine Bradwardine’s method of synthesizing Aristotelian natural philosophy
with Augustinian theology. This analysis of Bradwardine’s view of time in the De
causa Dei will demonstrate that the problem of time held a central place in
Bradwardine’s metaphysical system as well as in his conception of God’s absolute
power because it is the distinction between time and eternity which reveals how God
can create an orderly universe and participate in every created motion or act
without being constrained by the rules which he has established for his creation.
Since one of the central purposes of the De causa Dei was to explain God’s
activity in the world, the subject of creation arose in it continually. As a devoted

follower of Aristotle and a gifted natural philosopher in his own right, Bradwardine

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remained committed even in his theology to the validity of Aristotelian natural
philosophy. In the tradition of Thomas Aquinas, Bradwardine had advocated in his
earlier works the exploration of natural phenomena through human reason. By the
time of the writing of the De causa Dei, however, he had become more interested in
the long-standing problem of reconciling reason with faith. Bradwardine’s ﬁrst
attempt to integrate his Augustinian-Boethian view of eternity with his Aristotelian
view of time in the De ﬁzturis cantingentibus, in which he seemed to rule out the
possibility that the human and divine minds could share a common experience of
time, was not entirely successful. Some nineteenth- and early twentieth-century
historians, such as Lechler, Workman and Laun saw the De causa Dei as a further
attempt to separate humanity from God. In more recent times this view has been
defended and enlarged upon by Leff and Robson, who, like their predecessors, see
both Bradwardine and Wyclif as advocates of an extreme predestinarianism.5
Because he held that God in his absolute power can do anything and insisted that
God participates directly in every human act, Bradwardine has been accused both of
determinism and of drastically diminishing the human capacity for creativity or
independence.

If one keeps in mind Bradwardine’s Aristotelian outlook on the world,
however, another interpretation of the De causa Dei becomes possible.
Bradwardine the scientist wished to ﬁnd order and rationality in the created
universe; and, like all theologians of his age, he looked to God to ﬁnd the source of
that order. In an intellectual environment of intense speculation about what God
could or could not do, Bradwardine’s approach to God can be seen as optimistic and
a positive inducement to all kinds of human endeavor rather than a grim, paralyzing
sort of determinism. For Bradwardine, the notion of presdestination was in fact a
consolation to those who were anxious about the state of their relationship with

God: he intended not to frighten people but to reassure them, in the face of

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disquieting remarks by some theologians that God might intervene in the world
without observing his own natural laws or that his knowledge of the future might be
altered by acts of human will.6 In Bradwardine’s opinion, God has created the
world in such a way that its orderly development in time in no way restricts his
power, in his eternal present, to participate in his creation. On the contrary, God’s
constant involvement with his creation ensures order and goodness without fear of
divine capriciousness.

The main theses of the three books of the De causa Dei give an indication of
how Bradwardine envisioned God’s activity in the world.7 In Book I Bradwardine
argues that God is the source of every good act: "Grace, which is a habit freely
given by God, together with the human will is the proper efficient cause of whatever
good and meritorious act man performs."8 Moreover, although the human will must
cooperate in the process of causing a good act, the gift of grace is "naturally prior" to
the human will.9 Book II develops the idea that God has created the human will in
such a way that it can freely choose one course of action or another. In this sense,
the human will is undetermined and its future is contingent. At the same time, any
act of the created will requires God, who in his inﬁnite and perfect knowledge
knows what choice will be made, to be its coeffector.10 In Book III Bradwardine
explores the implications of this principle of "antecedent necessity" for the temporal
order of creation. Here Bradwardine tries to explain how God’s function as ﬁrst
cause inﬂuences the past, present and future of every aspect of his creation.11 All
three theses stress the creature’s experience of God rather than God’s experience of
creation: God intervenes in the world and directs its entire development without
being changed himself.

Bradwardine’s conception of God’s relationship to creation rests on the
premise that the physical world exists in time and operates according to natural laws

established by God. In his view of matter, for example, Bradwardine restates the

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Aristotelian deﬁnition of matter as a formless, potential substance which only
becomes a real being when a form is added to it. Along with Aquinas, Bradwardine
contends that God has created both matter itself and the forms which shape matter
into real things.12 All things, therefore, come into being in accordance with the
divine plan. God’s love ensures that everything which he creates is good, so that
nature itself is fundamentally good. 13 Because God not only gives matter its form
but also determines the laws which govern all motion and change, God must be seen
as the prime mover in every act.14
Bradwardine bases this thesis ﬁrmly on the philosophical and logical studies
of Aristotle, who had argued that every effect must be caused by something.
Therefore, every individual act, and indeed creation as a whole, proceeds from God
as the ﬁrst cause.15 Bradwardine obviously did not see a contradiction between his
belief in God as a direct and primary participant in the world and Aristotelian
explanations for how the world actually operates. In fact, Aristotle’s initial
observation that all effects in the physical world have causes stands as the
underlying principle both of Bradwardine’s natural philosophy and of his theology.
Although he accepted Aristotle’s deﬁnition of matter and his theory of
causation, Bradwardine could not agree with his conviction that the world is eternal.
We have already seen how closely Bradwardine followed Aristotle’s conception of
time in his works of natural philosophy. There is no reason to suppose that in the
De causa Dei Bradwardine rejected the An'stotelian principles concerning time’s
continuity, its inﬁnite divisibility or its relationship to motion after having proven
their validity so successfully in his works of natural philosophy. Nevertheless,
Bradwardine made it clear in several passages in the De causa Dei that the idea of a
created world of inﬁnite duration cannot be sustained.16 Bradwardine contended
that none of the classical philosophers, including Plato and Aristotle, had been able

to prove that the universe has existed from eternity. Aristotle’s theory of causation

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in fact suggested the contrary, he said, since the motion of the universe must have
been caused initially by something. In keeping with the medieval interpretation of
Aristotle, Bradwardine attributed to God this initial motion, which began the
process of creation.17

Bradwardine therefore tried in the De causa Dei to illustrate precisely how
all created acts proceed initially from God. The idea of couching the story of
creation in myth, as Plato had done in the Timaeus, held no appeal for Bradwardine.
The truth, Bradwardine contended, should be clear both to natural philosophers and
to theologians: since it consists of real being, the universe must have been created;
and logic, observation of the natural world and revelation all point to creation by
God. Bradwardine did not think speculation on how God created the universe or
how he could exercise his absolute power over it was particularly useful, for the
human mind cannot grasp the full meaning of creation. This notion lies at the heart
of Bradwardine’s criticism of his opponents’ alternative approaches to God’s
absolute power. Bradwardine was much more intrigued by the question of how
God, despite existing in an eternal present, nonetheless continues to participate
actively in the historical development of his creation.

In Book 1, chapter 1, of the De causa Dei Bradwardine defends the theses
that God is the greatest and most perfect goodness and that every created thing has
a deﬁnite beginning, concluding along Thomist lines that all things proceed from a
ﬁrst cause which is God.18 Later, two long corollaries explore the metaphysical and
logical reasons for afﬁrming the creation of the world and God’s power to direct
it.19 As we might expect from a specialist in natural philosophy, Bradwardine’s
arguments for creation are particularly effective when he illustrates the difference
between God’s eternal present and the temporal limits of created being with
concrete references to natural phenomena. In corollary 40, for example,

Bradwardine embarks on an extensive attack on the physical theory of those

169

philosophers, including Aristotle, Plato, Anaxagoras and Averroes, who persist in
claiming that the universe is eternal in spite of irrefutable cosmological evidence to
the contrary.20

In addition to logical arguments against the eternity of the world,
Bradwardine adds the ingenious reasoning that the principles of Euclidean
geometry preclude the possibility of a universe limitless in space and time.
Bradwardine’s understanding of continuity and the problem of beginning and
ceasing are crucial in this context; for, as he points out, the majority of classical
philosophers, including Democritus, Aristotle and Epicurus, agreed that permanent
continua have external limits.21 It is the existence of external limits which allows
objects, whether physical or purely mathematical, to be compared.22 Bradwardine
therefore adopted a mathematical argument concerning the external limits of
permanent continua to verify the theological truth that God creates and provides
spacial and temporal limits for every existing thing.

The question of temporal limits for created things has additional signiﬁcance
for Bradwardine’s theology because time distinguishes created being from eternal
being. Whether a thing is permanent or successive, it exists in time and therefore
has limits. All successive continua such as motion or temperature share the
characteristics of ﬁnity and inﬁnity: while they are potentially inﬁnite in respect of
their divisibility, they do not have limitless duration.23 By placing his creation
within time, God ensures that it remains distinct from himself and has limits.
Indeed, Bradwardine goes so far as to say that God cannot create something which

24 In spite

is necessary and limitless in itself, for only God can have these qualities.
of its negative wording, this assertion is not meant to restrict God’s power in any
way. Rather, it serves to emphasize Bradwardine’s larger contention that the
created world is not only distinct from God but also receives its goodness directly

from God. Bradwardine’s use of a mathematical argument to disprove the

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possibility of an eternal universe indicates the extent to which his natural philosophy
informed his theological views. It is evident from Corollary 40 that he had no
difﬁculty in reconciling his opinions about continuity, inﬁnity, time and motion with
his belief in the supreme power of God. Bradwardine maintained, in fact, that
Aristotle and other classical philosophers contributed directly to his proof of the
ﬁnity of the created world despite their conviction that the world is inﬁnite. In
contrast to Bradwardine’s former efforts to explain and redeﬁne Aristotelian
principles, his discussion of time and eternity in the De causa Dei amounts to a self-
conscious rejection of certain Aristotelian principles and a thoughtful revision of
others.

Bradwardine’s profound belief in God the creator led him to adopt a
cosmology which emphasized the Augustinian and Boethian distinction between
divine eternity and the imperfect changeability of the created world. Echoing
certain themes from the Timaeus, Bradwardine conceived of creation as neither
corrupt nor fundamentally evil simply because it changes and exists in time: the
very fact that God has made the world and loves it makes it good.25 Nor did he
think that human reason .is inadequate to the task of investigating the natural order
which God has made.26 Nevertheless, Bradwardine had to come to terms with the
dilemma posed by the central theses of the De causa Dei: God is both an active
participant in every aspect of creation and yet distinct from it because he is inﬁnite
and immutable. In resolving this dilemma Bradwardine returned to the conception
of time which he had ﬁrst developed in the De ﬁtturis cantingentibus.

Bradwardine considered it a matter of primary importance to prove that God
is not affected by time but has a kind of being which transcends the temporal order
of his creation. One of the ﬁrst objections Bradwardine made in the De causa Dei
was directed against those who try to make God more accessible to human

experience by likening him to created things. In an impressively thorough

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repudiation of the polytheism of the ancient world, Bradwardine warned against the
error of reducing the manifest greatness of God’s creation to pantheism by
worshipping as gods things such as trees, the sun or the moon.27 Since nature-
worship was not a wide-spread heresy in mid-fourteenth-century England, one might
wonder why he should have focused so much attention on it. Part of the explanation
lies, of course, in his effort to provide encyclopaedic coverage of all challenges to
God’s cause. Although Bradwardine could not have worried seriously about
Babylonian, Egyptian or Roman religious practices, he was extremely distressed by
the assumption which underlay them all that the world had formed itself out of
primordial chaos rather than being created from nothing by God. Bradwardine
therefore used the subject of polytheism to make the larger point that God cannot
be conceived as "temporal, created or corruptible."28 It is in this context that
Bradwardine laments the human failure, both in ancient times and in his own, to
recognize God’s transcendence over his creation.29

Bradwardine further emphasizes God’s distinctiveness by asserting that God
remains inﬁnite and eternal despite his capacity to enter into the created world.
Bradwardine develops this point most thoroughly in the second chapter of Book I,
which demonstrates why God necessarily is the ﬁrst cause in every human act. In
this passage Bradwardine explicitly states his thesis, which he derived from Aristotle,
Avicenna and Algazali, that God is the ﬁrst cause from which all effects proceed.
God is not, however, simply a craftsman who, having created the world, leaves it to
operate according to its own mechanisms and by its own energy. Instead, God, as
the ﬁrst cause of every created act, is always directly involved in his creation. Leff
observes that Bradwardine uses here the terms of Aristotelian metaphysics to

portray God as the "triple cause, formal, efﬁcient and ﬁnal," of every created act:

formal, because he establishes the conditions in which the act will take place;

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efficient, because he actively participates in every phase of the act; and ﬁnal,
because his participation makes a potential act real and actual.30

From a cosmological point of view, God’s most mysterious power is his
ability to participate so fully in creation and to encompass all creation within himself
without being changed, limited or corrupted}1 Bradwardine draws on a long
tradition of metaphysical speculation when he accords to God a perfect, uncreated
being. Following Augustine, he attributes great signiﬁcance to God’s response to
Moses in the Book of Exodus. In replying "I am who I am," God has offered
humanity an insight into his true nature as simple, perfect and universal being.32 By
his very nature, God cannot be other than distinct from created things, which are
changeable, have limits, pass in and out of existence and lack the perfection of the
creator. Bradwardine’s Platonic interpretation of the passage from Exodus exposes
his dependence on Augustine for his view of God. Like Augustine, Bradwardine is
able to accept both Platonic statements about God’s perfection and completeness
and revelation through Scripture, in spite of his preference for Aristotelian natural
philosophy. Bradwardine’s conception of God as distinct and changeless plays a key
role in his solution to the philosophical and theological problem of God’s
intervention in a changeable but largely rational world.

Bradwardine’s statements about time in the De causa Dei, therefore, need to
be examined primarily in the context of his conception of God’s distinctiveness from
creation. Bradwardine considers it a mistake to think that time is not in itself a
creation and, unlike other creations, had no beginning and will have no end. For
Bradwardine, time provides a frame of reference for creation. No created thing
exists which does not exist in time; indeed, time is such a fundamental concept in
creation that God alone can exist outside time. If one accepts the premise that God
is perfect being and the ﬁrst cause of every created act, says Bradwardine, one must

also admit that God created the world from nothing and placed his creation within

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the limits of time. To say otherwise would be to claim the existence of other kinds
of pre-temporal being which share in God’s eternity and inﬁnity. Even Aristotle,
who thought that the world is eternal, proved through his natural philosophy that
the world could not have been made from pre-existing material.33 God alone, then,
is free from the constraints of time; and time, as the medium of creation, assures us
of God’s eternal, inﬁnite and perfect being. God is able to exist outside time yet still
participate in the lives of his creatures because he sees all of his creation from an
eternal present. God knows all things simultaneously and eternally, and there is
nothing to obscure his vision at any instant of creation: he does not need to wait for '
his knowledge to be completed or his prophecies fulﬁlled in time.34 Bradwardine
thus supplements his metaphysical argument about God’s relationship to the world
through time with an epistemological one.

In Book I, chapter 6, Bradwardine contends that God has complete
knowledge of every created thing. Relying on a powerful range of authorities,
including Plato, Aristotle, Seneca, Boethius, Augustine and Averroes, Bradwardine
develops a complex logical argument in favor of God’s eternal knowledge. God’s
knowledge is necessary for the existence of every created thing, says Bradwardine,
because it is God’s eternal knowledge of a thing which makes it real. Bradwardine
quotes, for example, from Avicenna’s commentary on Aristotle’s De anima that "all
things of the earth which are past, present or future have being in the mind of the
creator."35 He goes on to suggest that God’s knowledge not only is complete but
also exists in God’s mind in a perfect and universal form. God’s knowledge thus
transcends time and the limitations of created being.36 Having built up an extensive
list of authorities in his favor, Bradwardine considers it a simple matter to prove in a
brief corollary that God, "both omnipotent and omniscient," has complete
knowledge of every created thing, whether it is possible or impossible, whether it

can be veriﬁed by human reason or only imagined.37

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Bradwardine’s strongest statements about the problem of time and eternity
come in chapter 51 of Book III, which is devoted entirely to the topic of eternity.
Once again drawing on authorities from Plato to Averroes, he contrasts the
mutability and limitation of created being with the immutability and inﬁnity of God.
Because he is eternal, neither God nor any of his acts can be measured in time. In
God there is no divisibility; no past, present or future; no succession. God’s
existence is simple, uniﬁed, perfect and simultaneous. The patterns of ﬂux and
change which human beings observe in time are part of a created order which is
separate from God and does not change him. God sees everything in a single
instant.3’8 Throughout this passage Bradwardine reveals his continuing interest in
the physics of motion and succession by using images of nature to define negatively
God’s eternal serenity. Bradwardine suggests, in fact, that knowledge of the
manifestations of God in nature deeply enriches the understanding of the eternal
God. He acknowledges with Plato that it is motion, especially the motion of the
heavenly bodies, the constant pattern of night and day, which distinguishes our
world of time and change from God’s timeless existence.39 In Bradwardine’s view,
then, time as a created being has a central place in the natural order which God has
made for his creatures.

Like Aristotle and Averroes, Bradwardine associates time with motion and
implies that time and motion can be used to measure each other. In the context of
eternity, however, the concept of time has a much more signiﬁcant cosmological
function, for it is the ﬂux of time itself which gives created things their special
character and makes them different from God. To illustrate this point, Bradwardine
appropriately chooses a geometrical metaphor to describe God’s temporal
relationship to his creation: God is a single point on a line; he is a single instant in
time. In his eternal present God does not experience any of the effects of time as

his creatures do, either physically, as in successive continuity, or psychologically, as

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in memory.40 The importance of time in Bradwardine’s cosmology, then, is that it
establishes the praper scope for the study of nature, while its counterpart, eternity,
frees God to participate in his creation without being changed or restricted by it. In
Oberman’s words, "by his theocentric thinking Bradwardine sees the idea of time as
the limiting factor for the creature, characterising the relation between man and
God as an inﬁnite distance, whereas this distance does not exist for God."41

We can conclude, therefore, that although Bradwardine did not present a
systematic analysis of time in the De causa Dei, his view of time had signiﬁcant
bearing on his understanding of creation. In his other works Bradwardine
demonstrated a thorough mastery of Aristotelian natural philosophy and Euclidean
geometry. The De causa Dei allowed him to display commensurate skill in analyzing
other kinds of sources. Plato’s T imaeus, Augustine’s theological works and
Boethius’ Consolation of Philosophy all contributed to Bradwardine’s conception of
eternity and the relationship of eternity to time in creation. As we shall see,
Bradwardine’s reading of Anselm, Aquinas and Duns Scotus enhanced his
conception of time as a philosophical and theological problem. Throughout the De
causa Dei Bradwardine suggested that an Aristotelian approach to natural
philosophy in no way contradicted the notion of an eternal and limitless creator, so
long as one did not try to argue that the world itself is eternal. Bradwardine’s
remarks about time in the De causa Dei indicate that he continued to see time in
Aristotelian terms, as the measure of motion or, more generally, as the successive
continuum which embraces all movement and change in created being. Because
time is created and therefore has a beginning and an end, its regular, successive
nature serves as a frame for all other motions and changes which can be observed in
nature. Like Boethius, however, Bradwardine felt compelled to state that God

exists outside the temporal order; otherwise God would be subject to the same

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forces as created beings and would lose his essential characteristics of inﬁnity,
eternity, immutability and omniscience.

By the time he wrote the De causa Dei, however, Bradwardine had completed
his degree in theology and was thoroughly familiar with the contemporary debates
concerning the nature of God’s involvement in the world. Consequently, he fully
realized how difﬁcult it is to reconcile logically a conception of God as changeless
and eternal with a belief that God participates directly in every aspect of creation.
It is almost impossible for the human mind to grasp how God can be simultaneously
inside and outside time, how God can prophesy and respond to the petitions of his
creatures without himself changing in any way; and yet the educated fourteenth-
century Christian was expected to affirm this complex and apparently self-
contradictory deﬁnition of God. Both Scripture and patristic authority demanded it.

As we have already seen, theologians such as Duns Scotus and Ockham tried
to solve the problem by proposing alternative cosmologies. They argued in various
ways that God, by virtue of his absolute power, has the capacity to change along with
his creation in time without losing his qualities of immutability or omniscience.42 In
this way the contingency of at least some acts of the human will could be preserved.
Ockham was particularly aware of the dilemma of maintaining God’s omniscience
while safeguarding human freedom: he ultimately concluded that reason cannot
resolve this dilemma and that certain truths about God’s essential nature have to be
accepted by faith alone.43

Because Bradwardine refused to admit the possibility of change in God, even
to preserve the freedom of the human will, he had to consider an alternative
approach to contingency in the De causa Dei. His conception of God as distinct
from the created world, coupled with his conviction that God participates directly in
every human act, made it necessary for him to work out a theory of contingency

which respected both positions. Although his treatment of contingency was much

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more sophisticated in the De causa Dei than it had been in the De futuris
cantingentibus, Bradwardine maintained the same thesis in the later work and
continued to regard contingency primarily as a philosophical problem. His greater
success in the De causa Dei results from his superior knowledge of the early
fourteenth-century debates about contingency as well as his readiness, where
appropriate, to consider some of the theological implications of his theory of
contingency. In fact, Bradwardine took the same step as Ockham in contending that
some mysteries of God’s power have to be taken on faith. Nevertheless, in his
characteristically optimistic portrayal of the power of human reason, Bradwardine
tried to show that faith can serve the pursuit of knowledge: to a certain extent at
least, he thought, one can use the same methods to learn about God as one might
use to investigate the natural world.44

In all of his discussions of contingency Bradwardine attempted to prove that
God in his absolute power knows all future contingents but is still able to ensure the
freedom of the human will: God "causes the human will to act predictably but
freely."45 Bradwardine shared with Ockham the idea that God in his absolute
power can change anything in the universe at will, although they interpreted the
signiﬁcance of this power in different ways. Ockham took what might be called a
psychological view of contingency, claiming that because the ﬁnite mind cannot
reconcile divine foreknowledge with human contingency we must accept
contingency as a feature of consciousness and divine foreknowledge as a matter of
faith.45 Consequently, we must admit that God can act in unpredictable ways. As a
metaphysician and natural philosopher, Bradwardine assumed that, although God
could act in apparently confusing or unpredictable ways, his constant participation in
the activities of creation assures a kind of order which the human mind can observe
and comprehend. In any event, God’s knowledge that an individual will make a

particular choice does not make the choice any less free from the human point of

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view. By emphasizing free will from the human perspective, both Ockham and
Bradwardine echo Augustine. They differed primarily in their approach to the role
of divine foreknowledge as a factor in human decision-making.

In his discussion of late medieval approaches to contingency, Calvin
Normore argues that views of time and modality usually inﬂuenced opinions about
contingency. In the case of Duns Scotus, who helped to focus Bradwardine’s
attention on God as ﬁrst cause, contingency relates to the necessity of the past,
present and future. Duns thought that, while the past is necessary because it has
already happened, neither the present nor the future are necessary. According to
Normore, Duns contended that "God’s knowledge is a single act which never ‘passes
into the past’ and so is as contingent as any present act. God knows what will
happen, but he can know otherwise than he knows."47 Ockham, on the other hand,
was convinced that both the past and present are necessary since, once they have
happened, they can no longer be changed. Ockham rejected a claim made originally
by Grosseteste that for God to know something he must be in a particular state.
Using a linguistic argument, Ockham tried to show that Grosseteste’s claim is true
only for the human mind because knowing or not knowing a particular thing is the
same for God.48 Being linguistic in nature, Ockham’s argument did not pay so
much attention as Duns’ to the problem of transition from past to future. Even so,
both theologians implicitly acknowledged that God’s fundamentally different
perception of time is at the heart of human contingency.49

In contrast to Duns and Ockham, Bradwardine approached contingency in
the De causa Dei in a way that is explicitly temporal. Bradwardine made use of
arguments from Grosseteste’s De libero arbitria, as well as Anselm’s Cur Deus homo,
to support his theory that God’s immutability makes contingency impossible from
the divine perspective.50 Because past, present and future all depend on God’s

knowledge, which is eternal and absolute, it is inconceivable that he could be subject

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to any kind of contingency.51 Indeed, in Bradwardine’s opinion, there is no
objective difference at all between past and future. God’s will simultaneously
directs all things which we see modally as past, present and future. Therefore, God
is not bound by our perception that a future event ﬁnally occurs in time, passes into
the past, and can no longer be changed. Because God is free from the temporal
limits of succession, he does not have to regard past and future as different. The
truth of a past event, like the truth of a future event, is conﬁrmed by God’s will
alone, which is constant, eternal and unchanging. Though we see the future as
contingent and the past as unchangeable, and therefore necessary, God assures the
truth and reality of both in his eternal present.52

This thesis is more or less the same as the one which Bradwardine presented
in the De futuris cantingentibus although, as Normore observes, it is developed with
much greater skill in the De causa Dei. Instead of portraying God’s knowledge of
everything at once as a static and rigid kind of knowledge, Bradwardine again makes
use of a geometrical image to explain how God sees the transition from past to
future without changing himself: God is like a point at the center of a circle, and
the points moving along its circumference are instants of time. Thus God can see a
particular point ﬁrst as future, then as present, and ﬁnally as past in a single
observation.53 This image both illustrates God’s ability to view apparently
contingent things without changing and also reinforces Bradwardine’s larger
contention that God is both distinct from and involved in creation.

Having described in compelling terms God’s capacity to observe the
transition from future to past in his eternal present, Bradwardine is left with the
difﬁculty of deﬁning the scope of the human will: how can one argue that God has
perfect knowledge of every future act without facing the charge of determinism?
Bradwardine was not prepared to deny free will since both Scripture and human

reason point to the fact that individuals constantly make choices, sometimes with

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terrible consequences, without conscious awareness of restraint. Bradwardine, of
course, agreed with Boethius that God’s eternal knowledge of a future event does
not force an individual, living in time, to make predetermined choices. From the
human perspective, God’s foreknowledge does not presuppose determinism.
Whereas in the De futuris cantingentibus, Bradwardine had been content merely to
make this contention and support it with references from relevant authorities, he
tried in the De causa Dei to deﬁne contingency and free will in terms .of axioms
about God’s absolute power over his creation.

Bradwardine based his mature theory of contingency on the principle that
God’s knowledge is complete and therefore necessary for the reality of his creation.
Even free will is "necessary" in the sense that God has created the universe in such a
way that human beings are able to exercise their wills freely within it. If God is the
ﬁrst cause of every act, however, he naturally participates in every act of free will;
indeed, God is the source of free will. This circumstance is, of course, very difﬁcult
to explain. Most of Book III of the De causa Dei is devoted to deﬁning the complex
relationship between the divine and human wills. Throughout his discussion of free
will Bradwardine assumed that, although God permits individuals to use their wills
freely, he does not allow them unlimited choices.54 All of Bradwardine’s assertions
about contingency and free will are based, moreover, on the assumption that human
perceptions of creation are different from God’s.55 While the individual can be
guided by God to choose to act in a particular way, he cannot conceive of the choice
as being predetermined. Human beings must live in and make choices in a world
governed by time: they cannot know with any certainty what will happen in the
future, and, at any rate, the conviction that God knows the future does not allow
them to abrogate their responsibility for their own moral conduct in the present.56

It is for this reason that Bradwardine, returning to an idea which he had

developed at length the De incipit et destinit, strongly denied any possibility of

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prediction in the De causa Dei. In the later work, however, Bradwardine went
beyond the relatively simple issue of logical prediction to condemn the use of
astrology and the unfounded beliefs in fortune or fate. Bradwardine devoted three
chapters to exploring the classical origins of belief in fate and the occult practices of
prediction.57 He then systematically refuted these beliefs, not only by appealing to
Scripture and other established theological authorities but also through reference to
his own cosmological system. Bradwardine considered it wrong to think that the
future will occur in some arbitrary way; but, because the future must unfold
according to plan in the mind of God, it is even worse for the human mind
pretentiously to try to predict the future. Moreover, since the future is not arbitrary,
there is no fate, except in the sense the divine mind knows what will happen and
allows this providence to be fulﬁlled in time.58 Bradwardine concluded his
arguments against fate with the proposition that all things are governed by laws
which are established by divine providence.59

This pervasive emphasis on providence in the De causa Dei has led twentieth-
century historians to focus on, and often exaggerate, Bradwardine’s cautious
approach to contingency. In fact, Bradwardine’s treatment of the relationship
between contingency and will is the central issue in Leff’s and Oberman’s highly
inﬂuential studies of the De causa Dei. Although neither of them examines in detail
the philosophical assumptions about time and eternity which support Bradwardine’s
view of contingency, their approaches to contingency in the De causa Dei provide an
extremely useful framework for evaluating the connection between Bradwardine’s
theology and his ideas about time as a physical principle. The following comparison
of Leff’s and Oberman’s interpretations of Bradwardine’s view of contingency will
serve, therefore, not only to review some of the historiographical issues which have

inﬂuenced studies of Bradwardine’s theology for the last three decades but also to

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suggest opportunities for reevaluating the role of Bradwardine’s approach to time in
the development of his thesis that God is the ﬁrst cause of every human act.
Although they differ greatly on many aspects of Bradwardine’s theology, both

Leff and Oberman agree that, in the case of future contingents Bradwardine sees no
conﬂict between the necessity of an act based on God’s foreknowledge and the
freedom of an individual to choose that act. Unlike Oberman, however, Leff uses
Bradwardine’s view of contingency to emphasize Bradwardine’s determinism. In
Leff’s analysis of the problem of contingency, "Bradwardine regards liberty and
contingency for God’s creatures as relative; as the product of secondary causes they
are equally dependent upon God’s will as their ﬁrst cause."60 For this reason, the
divine will is the source of contingency, for God is not only the ﬁrst cause behind the
chosen act, but creator of the world in which the consequences of the act will
manifest themselves. Indeed, Bradwardine openly acknowledges that God, having
full and absolute knowledge of past, present and future, is able to build the concept
of free will into his creation.61 However, Leff also attributes to Bradwardine the
conviction that the future, like God, is immutable:

Firstly, every act of divine will, past, present and future, must

have existe eternall . Secondly, in the same way, all that is

about to be, and all t at will be, must, of necessity come to be.

Thirdly, that everything, therefore, whether past, present or

future, is subject to the same act of creation, and its temporal

order bears no relation to the certainty and eternity of its

existence in God. The use to which Bradwardine puts these

conclusions shows clearly where he departs from tradition: he

transforms the eternal instant in God to deny the future any

independent existence. Where St. Thomas was content to

allow that God saw everything through His own essence which

in no way necessitated what e foresaw, Bradwardine changes

this neutral intelli ence into active approbation: with him,

what God sees, e forewills. As a result, the future is as

deterngmed as the past and the present: it cannot not come

about
This passage reveals Leffs tendency to interpret Bradwardine’s view of the future in

theological terms and as a restriction of human freedom without accounting for

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Bradwardine’s Boethian emphasis on God’s experience of creation in one eternal
present.

Leff then places Bradwardine’s determinism in the context of the intellectual
radicalism of the late medieval universities. According to Leff, Bradwardine was
driven to such an extreme view on future contingents because of his opposition to
three contemporary schools of thought. Bradwardine’s most obvious opponents
were those Stoic and Islamic philosophers who promoted a kind of determinism in
which God need not be directly involved in the world. In Leff’s view, Bradwardine,
whose own conception of God was heavily dependent on Greco-Arabic deﬁnitions,
was not worried about determinism as such; his chief complaint was that the Stoic
and Islamic philosophers made God too impersonal, too far removed from his own
creation. Bradwardine also attacked a less uniﬁed group of philosophers who went
too far in the opposite direction. These thinkers undermined God’s omniscience
and omnipotence by emphasizing the large scope for free will in human choice.
Bradwardine thoroughly rejected any claim that God does not fully know the future,
either because he has not yet willed the future or because he can only foresee good
and not evil. Even more distressing to Bradwardine was the Pelagian notion that
God waits until an act has been completed to assess its merit. Such a position
"would remove any order between merit, free actions and reward, denying God’s
will to be their cause and making the past, present and future all completely
contingent and free from necessity."63

The third group of opponents angered Bradwardine with their suggestion
that since the future, unlike the past and present, does not yet actually exist, it might
or might not take place at all. This view not only violated Bradwardine’s assumption
that the future already exists in the divine mind but also implied that God can
change his mind about the future and is therefore mutable. Bradwardine’s ﬁerce

rebuttal of this point of view suggests to Leff the collapse in the fourteenth century

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of Aquinas’ moderate balance between contingency and free will. While Aquinas’
metaphysical system allowed God to be the ultimate cause of any human action, it
also posited enough of a connection between created being and God to permit a
more flexible approach to contingency. Leff argues that fourteenth-century
approaches to contingency, on the part of both Bradwardine and of his opponents,
so separated created and uncreated being that philosophers had to favor either free
will or necessity. Bradwardine’s originality, in Leffs opinion, lies in his ardent and
almost solitary defense of the principle of divine necessity.64

At the heart of Bradwardine’s argument about future contingents, says Leff,
is his notion that God’s will deﬁnes what will happen by making choices which stand
for all eternity. Although God could logically have made different choices from the
ones which he has made, his ultimate decisions are eternal: creation is the process
of these decisions coming to fulfillment in time. For God subsequently to make a
different decision he would have to change.65 To change, God would have to make
himself a creature of time. Therefore, to say that God cannot change something
that he has willed is not to doubt God’s absolute freedom but to give God’s free
choices the respect due them as eternal truths. According to Leff, Bradwardine
locates his opponents’ main error "in confusing this eternity in God with temporal
measurements, thereby trying to judge the inﬁnite by finite standards. . . . As a
result, rather than acknowledge the problem of the future, he denies it."66

The main problem with Leff’s approach to Bradwardine’s view of
contingency is that it underestimates the importance of Bradwardine’s
understanding of eternity as both physical and theological concept. As the
examination of Bradwardine’s analysis of the role of time in creation has
demonstrated, it is misleading to say that Bradwardine did not acknowledge the

problem of the future. As we have seen, he paid the problem of the future

considerable attention in the De causa Dei and in other works, though not so much

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in a theological context as in a cosmological one. The image of God as a point in
the center of a circle elegantly conveys Bradwardine’s conception of God’s
relationship with his temporal creation: God’s awareness of past, present and future
in an eternal present ensures the future of the human will without compelling it to
act in a particular way. If we keep this image in mind when reading the De causa
Dei, we discover that Bradwardine’s purpose is not to reduce, either explicitly or
implicitly the scope of human action but to demonstrate how God accommodates
free will eternally into his creation. Bradwardine’s temporal theory therefore
transforms the problem of the future from a logical one into. a cosmological one in
which the distinction between time and eternity, not that between past and future,
becomes crucial in determining the contingency of a particular event.

One of the chief advantages of Oberman’s interpretation of Bradwardine’s
view of contingency over Left’s is that it takes more into account Bradwardine’s
ideas about creation, although here again the emphasis is on a theological not a
philosophical understanding of contingency. Like Leff, Oberman sees
Bradwardine’s approach to contingency as a reﬂection of his conception of eternal
and created being. Oberman, however, stresses more than does Leff Bradwardine’s
attachment to Christian authority in his treatments of necessity and divine
prescience. Oberman reminds us that Bradwardine always works from the
assumption that God is not restricted by time, which only exists for the beneﬁt of his
creation. He points out from the start of his analysis of the De causa Dei that
Bradwardine feels justiﬁed in ignoring certain aspects of the problem of future
contingency which arise only because of "the imperfect human conceptive faculty."67
In the words of D. J. B. Hawkins:

The imaginative difﬁculty which we have to overcome is the
erroneous supposition that He (God) knows actual events as
we know them in a temporal series. He knows them as a

temporal series, but he dggs not know them in a temporal
series of acts of awareness.

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Nevertheless, Bradwardine still has to explain how God can know the outcome of all
future events and still give his creatures the freedom of will which Scripture
promises and human experience seems to require. In Oberman’s view,
Bradwardine’s major task in his discussion of contingency is to explain the
relationship between the omniscient divine will and the temporally limited human
will. '

According to Oberman, Bradwardine, following Bernard of Clairvaux,
deﬁnes the human will at least partially in terms of the divine will: every rational
creature shares with God the capacity to choose freely. The human will is
nevertheless limited in the sense that it cannot choose from an inﬁnite number of
possibilities: it can only choose to accept or refuse a deﬁnite possibility that has
been presented to it. Bradwardine concurs with Hugh of St. Victor and Peter
Lombard that the human will is free not on account of its power to will everything
(which belongs only to God) but because it can act spontaneously according to its
own powers of judgment. Though the human will is more limited than the divine
will, neither will is capricious or arbitrary.69

To acknowledge the will’s capacity to choose, however, does not necessarily
demand acceptance of contingency, since God might predetermine what the choices
will be and know in advance the will’s decision. Oberman agrees with Leff that
Bradwardine’s real difﬁculty with contingency arises from his unwillingness to
diminish in any way God’s knowledge of the future or his role as the ﬁrst cause in
every human act. Bradwardine thus comes to insist that the will cannot function
without grace. He stands in opposition to Ockham and others, who doubted
whether grace, as a theological doctrine, and will, as a philosophical principle, could
be considered together in any treatment of contingency. In Bradwardine’s
cosmology, however, grace and will come from the same source and must be

examined together. Therefore, according to Oberman, Bradwardine always tries to

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interpret will in terms of grace. In Oberman’s view, Bradwardine’s insistence on
combining a theological starting-point with a theocentric approach to contingency
has led many to the assumption that he was a rigid deterrninist.70

Oberman notes, however, that Bradwardine’s method of synthesizing the
views of important authorities with his own profound insights into nature actually
contributed to a ﬂexible view of human will. Bradwardine maintained throughout
the De causa Dei his reliance on Christian authority, especially the views of
Augustine, Anselm and Thomas Aquinas. All of these theologians had emphasized
the importance of grace in guiding the human will and attributed full omniscience to
God. Bradwardine was particularly devoted to Anselm, who in his own struggle with
the problem of necessity concluded along Boethian lines that God does not really
have prescience, but has simple knowledge in his eternal present. By eliminating
tense from the analysis of God’s knowledge, Anselm argued, it is possible to see how
the will can remain free in spite of God’s knowledge of the future.71

Bradwardine also seemed to follow Aquinas almost exactly on two aspects of
the question of necessity. In the ﬁrst place, both agreed that the human will lacks
the capacity for self-conscious conformity to the divine plan because it cannot
envision the ﬁnal aim. Furthermore, even if God were to reveal the ﬁnal aim to
someone, he would not compel that person to conform to it.72 According to
Oberman, Bradwardine’s view of God’s role in this process of directing the human
will is one in which God "moves man according to his own nature, and freely, and
when this is thwarted by sin, He transforms man by His grace."73 In accepting these
positions of Anselm and Aquinas, Bradwardine absorbed the entire Augustinian
tradition of deﬁning free will in terms of grace. The combination of Augustine’s

psychological view of time and his convictions about grace deeply moved

Bradwardine, as it had other theologians in the Augustinian tradition.

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Nevertheless, Bradwardine had a gift for original thought, and he could not
be expected merely to repeat the work of his predecessors. In Oberman’s view, the
uniqueness of his position on contingency lies in the degree to which he elevated the
role of grace in the exercise of human will. In this context, Oberman lists four
factors which give Bradwardine’s approach to contingency its deterministic quality.
First, as we have already observed in the discussion of the De ﬁzturis cantingentibus,
Bradwardine stressed the vast difference between the divine and human experience
of time. He was not very patient with efforts to develop purely psychological or
logical explanations for contingency because he saw human lack of knowledge about
the future as the inevitable condition of the imperfect human mind. Second,
Bradwardine was not satisﬁed by the conclusions of Anselm and Aquinas, which
suggested that God’s prescience guarantees that what was, is and will be cannot at
the same time be what was not, is not and will not be. Bradwardine rejected the
notion that God merely protects his creation from internal contradiction in favor of
a view which places God in the more active role of directing the events which his
creatures perceive in the past, present or future. Third, Bradwardine reinterpreted
the Aristotelian theory that potency precedes every act. Bradwardine’s predecessors
had used this theory to argue that God creates potencies and then allows the will to
participate in the process of transition from potency to act. In Bradwardine’s view,
however, God’s use of the process of potency does not mean that he does not know
whether or how the act will take place. Finally, Bradwardine stressed the
Augustinian argument that the human will does not give up any freedom by
following God; indeed, the human will is in its freest state of all when it acts without
resistance to the divine will.74

Oberman concludes his assessment of Bradwardine’s view of necessity by
noting that, although Bradwardine expressed his ideas in a rigorous and sometimes

extreme form, he did not intend his position on necessity to negate the possibility of

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free will. In Bradwardine’s philosophical and theological system contingency, not
liberty, is the opposite of necessity.75 Oberman recommends that we approach
Bradwardine’s theory of necessity from the perspective of Augustine’s distinction
between "necessitas invita" and "voluntaria":

The former is the Stoical necessity of fate, the latter the

Christian necessity in which God’s world dominion is

confessed. The statement ‘all things that happen, happen of

necessity’ can accordingly he meant in two ways: as an excuse

for ilt with reference to destiny, and asa6confession that God

pe orms everything according to 1118 Will.
Bradwardine routinely took the latter view and argued throughout the De causa Dei
that God’s will constantly guides the course of creation. Bradwardine’s conviction
that God’s will is necessarily fulﬁlled reﬂects his fundamental optimism concerning
the natural order, while his emphasis on grace indicates his belief that the human
will has a crucial role to play in following God freely and participating in the work of
creation. Thus Oberman, like Leff associates almost all aspects of Bradwardine’s
view of time and contingency with such theological issues as grace, will and
prescience.

The pervasiveness of Leffs and Oberman’s theological approach to the De
causa Dei is confirmed by another major study of Bradwardine’s view of
contingency. Donald J. McCarthy argues along the lines of Oberman that
Bradwardine’s approach to the problem of contingency was bound up with his
deﬁnitions of the nature of God.77 Like Oberman, McCarthy tries to avoid Left’s
verdict of severe determinism by evaluating Bradwardine’s conception of the
relationship between the divine and human will within the context of grace.
Whereas Leff sees Bradwardine’s position as a philosophical one dominated by a
particular theological outlook, Oberman and McCarthy portray Bradwardine

primarily as a theologian with considerable skill in philosophy. McCarthy goes

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beyond both Leff and Oberman, however, in stressing the metaphysical and
cosmological factors which shaped Bradwardine’s view of contingency.

McCarthy contends that readers of the De causa Dei must take into account
not only Bradwardine’s sources and conclusions but also the place of the problem of
contingency in his theology as a whole. Unlike many of his contemporaries, who
were more interested in contingency as a philosophical, grammatical or
psychological problem, Bradwardine saw it as a subordinate issue to the more
important one of God’s participation in the creation through grace. Because he
wished more than anything else to prove that God is the ﬁrst cause of every act,
Bradwardine was prepared to minimize the role of free will as a major factor in
determining the outcome of an event. Bradwardine did not want to eliminate free
choice, but he did want to place it ﬁrmly under the direction of divine causality. His
main task, therefore, was not to examine contingency and free will as distinct
doctrines but to devise a theological and philosophical system which allowed "the
greatest possible human liberty consistent with the nature of divine willing."78

Paying careful attention to Bradwardine’s conviction that God’s knowledge is
perfect and quite different from human knowledge, McCarthy examines
Bradwardine’s concept of the future. McCarthy cites Bradwardine’s remark that
God’s knowledge of the future is more complete than an astronomer’s prediction of
an eclipse to illustrate Bradwardine’s thinking about the reality of the future: since
we have not yet experienced it, the future is not real to us, but this does not mean
that it is not real for God, who already knows and wills it.79 Moreover, not only
does God will the future to exist but his will places future events in the future. God
provides whatever being the future has, and without God neither past nor future
would exist.80

McCarthy presents these ideas as a product of Bradwardine’s acceptance of

Augustinian teaching on eternity and grace and of the work of Anselm and Duns

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Scotus on divine causality. Bradwardine proved the existence of God by positing
that creation is a series of causes, with the primary cause existing in God. Having
added all of the other attributes of God which Augustine had included in his vision
of God as first cause, Bradwardine was able to explain the function of human will as
analogous to God’s: in the present a person is free either to do or not do any act of
which he is capable. As long as he is in full possession of his reason and is able to
make a real decision, the consequence is a free act.81 God, too, can perform or not
perform any act, but his omniscience, omnipotence and eternal presentness remove
any limitation on his ability to choose. McCarthy therefore concurs with Oberman ~
that Bradwardine’s approach to free will is only deterministic from the perspective
of God, who, because he has ordained free will as a fundamental feature of rational
being, cannot be seen as an unrelenting or unsympathetic controller of human
activity.

Although all of these discussions of Bradwardine’s view of contingency
recognize implicitly and occasionally even explicitly the crucial role of
Bradwardine’s conception of eternity and time, none of them approach the De causa
Dei primarily from the perspective of Bradwardine’s natural philosophy. The
analysis of various aspects of Bradwardine’s view of time in this dissertation
suggests, however, that Bradwardine’s approach to time and eternity resulted from
his consideration of both philosophical and theological concepts. Indeed, this
examination of Bradwardine’s mathematical and philosophical treatises has
demonstrated that he had an extremely well-developed conception of natural
philosophy which could not have failed to inﬂuence his theological outlook in the De
causa Dei. He was in fact so convinced of the correctness of his views of time and
other natural phenomena that he did not ever attempt to prove them: he
considered a relevant citation from Augustine or Boethius sufﬁcient to verify the

truth of his ideas. Even though the De causa Dei is not primarily a work of natural

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philosophy, Bradwardine drew both on Aristotle’s doctrine of causality and on his
approaches to natural philosophy to show that created being has an entirely
different character from God’s eternal being. Support from Plato, Augustine and
Boethius further enhanced Bradwardine’s own portrayal of the distinction between
the ever-changing world contained within temporal limits and the immutable,
inﬁnite existence of God. Bradwardine’s desire to ﬁnd order in the natural world,
aided by his special ability to see through the complexities of physical, psychological
and philosophical problems, contributed to his success in examining even purely
theological problems from the perspective of his Aristotelian-Augustinian
cosmology.

The inﬂuence of Bradwardine’s cosmology on purely theological matters is
nowhere more evident than in his discussion of the two main theological problems
in the De causa Dei, sin and predestination. In his analysis of sin, Bradwardine has
to explain why God, who is not only supremely good but also the first cause of every
human act, permits and indeed seems to cooperate in sin. The problem of
predestination involves deﬁning the scope of human responsibility in meritorious
acts and the relationship of human merit to eternal salvation. Bradwardine’s
arguments on both subjects are based on his assumption that God sees his creation
in a much simpler and more complete way than his creatures do. God is both inside
creation and distinct from it, like a point in the center of a circle, while his creatures
are restricted both by their temporal existence and their incomplete knowledge.
Although Bradwardine’s discussions of sin and predestination add little to our
understanding of his view of time as such, they are worth considering brieﬂy because
they point to some of the limitations of applying an Aristotelian-Augustinian
cosmology to theological problems.

Bradwardine’s doctrine of sin depended heavily on a definition of evil,

derived from Neoplatonic phi1050phers and Augustine, which holds that evil has no

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being in itself. Therefore evil, and consequently sin, represent not positive forces
but only the absence of God’s goodness. Augustine had, of course, stressed the non-
being of evil in his attack on the Manicheans, who supposed evil to be a powerful
creative force which actively opposed goodness in the world. By Bradwardine’s day,
although the Manichean heresy was no longer considered a serious threat,
Augustine’s approach had become the basis of the orthodox position on evil and sin.
The extensive philosophical and theological debate about evil in the thirteenth and
early fourteenth centuries, however, indicates widespread dissatisfaction with
conventional explanations for the presence of evil in a divinely created world.82

In the face of these debates Bradwardine warmly embraced the Augustinian
position for two reasons. First, Augustine’s denial of the reality of evil supported
Bradwardine’s contention that God acts eternally and positively for the good of his
creation. Second, Augustine’s emphasis on the positive goodness of God
strengthened Bradwardine’s assumptions about the natural order of creation.
Bradwardine was certainly not so naive as to deny the presence or effects of sin, but
he relied on Augustine to show that evil and sin had no power to disturb the orderly
processes of the created world. Bradwardine maintained throughout the De causa
Dei that, since God is the ﬁrst cause and creator of every existing thing, all things
must be good in themselves.83 No action, therefore, is sinful per se, only per
accidens: the same qualities which make homicide and adultery sins are also
present in the good acts of natural death and marriage.84 Sin results from the
deliberate choice to act in a way which removes one from God or which causes one
to deviate from the course of positive obedience to God’s will.

Bradwardine did not agree with Augustine in every respect, however. In
Bradwardine’s view, the intention behind the act and the degree to which such an
act obeys or disobeys God’s will mainly determine whether or not it is a sin.85 Thus,

for example, the acts of a child or a mentally disturbed person cannot be judged in

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the same way as those of rational adults. By stressing the role of intention in sin,
Bradwardine in fact minimizes Augustine’s assertion that all sins, whether
intentional or unintentional, are reﬂections of original sin, which plagues the entire
human race. Bradwardine’s recognition of the role of the will in sin indicates the
inﬂuence of thirteenth- and fourteenth-century reﬂections, particularly those of
Duns Scotus, on Augustine’s doctrine of sin.86

Bradwardine’s answer to the question of why God permits sin in the ﬁrst
place is rooted both in his metaphysical system and in his understanding of the
relationship of the human to the divine will. Because he is the cause of all that
exists and does not exist, God must be seen as the cause of sin as well. It follows
that God must permit sin as a sort of agent of good, and not as an end in itself.87
The contrast of good and evil makes good more obvious. Simple observation of the
natural world reveals that the universe operates on the principle of balancing
opposites, as for example in music, humidity, temperature, weight and shape.88 The
integrity of the entire universe depends on the interaction of natural forces in a state
of ﬂux. This quality of balance of opposites, which distinguishes ever-changing
creation from immutable God, is both good and necessary. So too, then, is the
balance of sin and merit good. Although God does not wish us to sin, he allows us
to exercise our wills even if we end up making wrong decisions.89 Because it is the
consequence of free will, sin is part of the fabric of the universe. We utterly mistake
God’s intentions, and run the risk of attributing to him human goals and
understanding, if we equate the existence of sin with the notion that God creates
evil for its own sake.

In acknowledging God’s active role in creating sin, Bradwardine allows his
cosmological view of God as the ﬁrst cause of every created act to overshadow his

Augustinian conviction that sin represents a turning away from the reality of God’s

goodness. Bradwardine’s positive view of sin put him at odds with tradition and left

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him open, potentially, for attacks on his orthodoxy.90 That he was never seriously
challenged on this point indicates that his opponents understood that his doctrine of
sin could not be separated from his conception of God’s relationship with creation:
to refute Bradwardine’s view of sin would require dismantling his entire cosmology.
Bradwardine’s compelling approach to creation and his fundamentally optimistic
view of sin ensured that his ideas would be comforting to his supporters and
carefully considered by those who disagreed with him.

Bradwardine’s doctrine of predestination, too, is essentially optimistic and
based on faith in a God who is both utterly transcendent and immediately personal.
Bradwardine’s conception of the way in which God decides whom to save is the
central feature of his entire argument against the Pelagians, and it is based ﬁrmly on
the deﬁnition of God as eternal and immutable. According to Bradwardine, our
temporal experience can give us the incorrect impression that God waits to observe
our actions before he decides whether or not we deserve salvation. Justiﬁcation is
actually a completely atemporal phenomenon. Bradwardine therefore questions the
accuracy of the metaphor in Psalms that an individual can be erased from the book
of life:

God knows in advance, before the foundation of the world
He has predestined all who will reign with His Son in eternal
life. Those whom He has enrolled are contained in the book of
life. How can they be erased from a book where they were
never written? This quotation expresses their hope, that is,
they thought themselves to have been entered into the book of
life. What does this mean, ‘Let them be erased from the book
of life’? It is obvious that they were never there to begin with.
Thus, therefore, those who had hoped, by reason of their
righteousness, that they were written in the book of God, when
confronted by their damnation, are made aware that they are
‘erased from the book of life,’ and they realize that they were
never there. The second part of the statement [‘Let them not
be enrolled with the righteous’] explains the ﬁrst part. As I
have said, ‘Let them be erased’ is to be understood to refer to

their vain hopes. And this can lie correctly summarized by
saying ‘Let them not be enrolled.’ .

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This passage brings into sharp focus Bradwardine’s contention that we can only
deceive ourselves by assuming that God, like us, is temporal and changeable.
Although we must wait until the time of our judgment to know whether we have
been saved, God always possesses this knowledge in his eternal present.
Bradwardine makes use of the Aristotelian concept of potency to explain
how the will, acting within the temporal limits of creation, fulﬁlls the eternal

expectation of God by responding to his grace:

Aristotle shows that ower, or capability, is of two kinds, active
and passive. Now t at which is meant b the quotation, ‘He
Eave them power to become sons of Go ,’ is also asserted in

omans, ‘whoever are led by the Spirit of God are sons of
God.’ God gives men power, that is to say, a rational soul and
free will with which man can freely and voluntarily receive
grace in the present and glory in the future so that, in both the
present and the future, they might become sons of God. Thus
in the present, as they are being made sons of God by faith and
prevenient grace, which makes them into adopted sons of God,
they freely accomplish the pleasing work of sons and so freely
persevere in this to such an extent that nafne could take away
their sonship unless they would permit it.

We must recognize, then, that God is unconstrained in matters of time or power in
justifying certain individuals. His decision to save them and his gift of grace amount
to the same act, although the human will experiences grace and justiﬁcation as
sequential. Here, as in the case of sin, Bradwardine subordinates the independent
function of the human will to the demands of his cosmological system but does not
completely undermine it.

Bradwardine relates his doctrines of sin and predestination to his deﬁnition
of God as ﬁrst cause of all creation by repeating St. Paul’s image of God as a potter:

Why do [the Pelagians] not accuse God because He

punishes innocent beasts and baptized infants with no small

physical ain? Indeed He gave up his own most innocent Son,

our Lor Jesus Christ, to a most painful, cruel, and tormenting

unishment. But since God is omnipotent, completely free

rd of his whole creation, whose will alone is the most
righteous law for all creation - if He should eternally punish

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the innocent, articularly since he does it for the perfection of

the universe, or the proﬁt of others, and for the honor of God

Himself, who would resume to dispute with Him, to

contradict Him, or ask ‘ by do you do this?’ I ﬁrmly believe,

no one! ‘Has the potter no right over the clay to make of the

sani’eggump one vessel for honor and another for menial

use.
Not only does God have the right to punish certain creatures for the overall good of
creation, he can also determine whether a punishment should be merely temporal,
eternal or both: "If a man may undergo temporal punishment for the temporal
beneﬁt of others, why should he not be punished temporally and eternally for the
temporal and eternal beneﬁt of the elect, in order that they might all the more ﬂee
from evil and choose the good of the present, that in the future they might have
greater joy, deeper love, and higher praise of God?"94 Thus Bradwardine returns to
the basic concept of God’s absolute goodness and transcendence to justify divine
punishment. In Bradwardine’s conﬁdent and optimistic view, God’s omnipotence
and eternal knowledge ensure that creation will proceed in a way which is ultimately
good. The human will is obliged to respond to God’s love and to refrain as much as
possible from willful disobedience; but, if one has faith in God’s creation, one need
not worry about the philosophical dilemmas surrounding sin and grace.

Even in matters of purely theological interest, therefore, it is difﬁcult to
evaluate Bradwardine’s thought in isolation from his views about creation, time and
eternity. Bradwardine regarded these fundamental concepts as necessary for
describing both God’s essence and his creative activity. Because Bradwardine not
only made metaphysics and logic serve a theological purpose but also used
theological principles to support a cosmological system that depends equally on
God’s will and human perception of creation, the De causa Dei cannot be seen
exclusively as either a philosophical or a theological work.

Although Bradwardine’s main purpose in the De causa Dei, to prove that

God is the first cause, was, of course, unquestionably theological, his interest, as we

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have seen, was not conﬁned to this issue alone. As a natural philosopher,
Bradwardine also wanted to explore the human response to God’s creation and the
signiﬁcance of the natural world to man’s relationship to God. The De causa Dei
gives every indication of Bradwardine’s conﬁdence in the power of human reason to
comprehend the natural world, within the conﬁnes of our temporal existence, so
long as thinkers do not limit God by applying the same standards to him as they
would to physical phenomena. For created beings, he argued, temporal and spacial
limits are good because they allow us to make comparisons, to measure, to study
nature in general. Furthermore, the human mind can even hope to achieve some
success in understanding God once it grasps the fact that God is creator of the laws
which govern creation but is not himself subject to them. While he did not
underestimate the difﬁculty of obtaining certain knowledge about God,
Bradwardine exposed the error of trying to describe God’s nature or powers in
human terms: hence his impatience with contemporary speculation about God’s
experience of time, which inevitably tried to temporalize God. In constantly
emphasizing the distinction between time and eternity, therefore, Bradwardine
presented a view of God which was thoroughly consistent with the whole body of his
scientiﬁc, metaphysical and religious beliefs.

The preceding examination of Bradwardine’s view of time demonstrates that
this distinction between time and eternity represents a unifying theme for his most
important scientiﬁc, philosophical and theological work. For this reason, an
understanding of his conception of time can help to answer some of the unresolved
questions regarding his thought as a whole. The issue of Bradwardine’s
determinism, for example, can only be evaluated properly in the context of his
particular analysis of the relationship between time and grace. There is no doubt
that by the theological standards of his day Bradwardine truly was a determinist: he

afﬁrmed that both past and future are equally dependent on God’s eternal and

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unchanging will, and be readily subordinated the scope of the human will to the
cause of God’s absolute freedom.

Nevertheless, his brand of determinism had a strikingly optimistic, even
humanistic tone. Both his objection to logical prediction in his early treatise on
beginning and ceasing and his rejection of fate in the De causa Dei indicate his
belief that the future should be faced conﬁdently and without fear of divine
repression. To the human mind, the future provides endless opportunities for
choice, for willing cooperation with or conscious disobedience to God’s plan for
creation. God’s participation in our acts, his eternal knowledge of how we will
respond and his ability to take all of these responses into account conﬁrm his power
to create an orderly universe without restricting human freedom. Moreover, from
the human perspective, the future is completely open: so much so, in fact, that we
cannot accurately predict the future, except perhaps in the experimental sense of
astronomical observation. Bradwardine considered this juxtaposition of
determinism and free will one of the chief mysteries of faith, analogous to the
profound cosmological mystery of the juxtaposition of time and eternity.

Those who are inclined to consider Bradwardine a rigid determinist often
accuse him, in one way or another, of refusing to recognize contingency as a valid
philosophical problem and so reﬂect their misunderstanding of Bradwardine’s
cosmological and metaphysical outlook. To be sure, Bradwardine made no attempt
to reconcile his view of contingency with contemporary ones which required
explanations for how God can be immutable and eternal and yet enjoy a temporal
existence. Instead, Bradwardine’s most important contribution to the fourteenth-
century debate over contingency was to offer an alternative approach, based on a
synthesis of Aristotelian, Augustinian, Boethian and Thomist cosmological
principles, to the attempts of such theologians as Peter Aureoli, Duns Scotus and

Ockham to resolve the problem of contingency logically or grammatically. That

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Bradwardine approached contingency in a cosmological way, one which combined a
precise deﬁnition of time’s relationship to eternity with an Augustinian conception
of grace, does not mean, however, that he dismissed everything his contemporaries
had to say about the logical problem of time. Bradwardine in his theology simply
subordinated purely logical considerations to such metaphysical issues as the
difference between created and uncreated being and the principle of God as ﬁrst
cause. Therefore, although it cannot be denied that Bradwardine was a determinist,
it is equally clear that he used the distinction between time and eternity to
ameliorate the consequences of divine determination of human acts.

Bradwardine’s method for constructing his alternative approach to the
problem of contingency brings us to the related question of the orthodoxy of his
synthesis of Aristotelian and Augustinian principles. Oberman portrays
Bradwardine as an orthodox conservative who tried to defend his Augustinian views
from the radical attacks of young, skeptical theologians like Robert Holcot, Thomas
Buckingham and Adam Wodeham. Leff goes even further, claiming that
Bradwardine followed his conservative principles with such unyielding rigor that he
went well beyond the limits of conventional orthodoxy. Both historians point out
that Bradwardine’s views about sin and necessity deviated, sometimes markedly,
from the dominant perspectiVes. As in Bradwardine’s scientiﬁc works, the De causa
Dei clearly shows that he was not afraid to reevaluate or challenge the opinions of
other thinkers, whether they were his own peers, as in the case of Ockham, or
revered authorities like Aristotle or Augustine. All of his works which have been
examined here reﬂect, in fact, Bradwardine’s ability to redeﬁne and clarify problems
by balancing the wisdom of recognized authorities with his own mathematical
insight. He freely took what were to him the most convincing aspects of well-
established arguments and arranged them axiomatically to produce his own

assessments of disputed questions.

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Especially in the case of time, Bradwardine showed allegiance to many
authorities but subservience to none. His view of time combined Aristotelian
deﬁnitions of time with the Augustinian-Boethian explanation of its cosmological
signiﬁcance. When he began to explore the theological implications of his
cosmology, Bradwardine gathered support from every possible source. Although
some conclusions in the De causa Dei may appear extreme because of his axiomatic
organization of ideas or his uncompromising manner of expression, he based every
argument on principles of such wide acceptance that no contemporary seriously
challenged either his orthodoxy or his reputation as a gifted thinker. Like other
fourteenth-century theologians at Oxford and Paris, Bradwardine took a keen
interest in certain ancient philosophical and theological problems which, on account
of the contributions of Aquinas and Duns Scotus in the thirteenth century, had
become even more complex by the early fourteenth century. Bradwardine shared
with Ockham in particular the desire to push the debates about these problems in
new directions without sacriﬁcing the commitment to Christian authority. On the
issue of time, as we have seen, their main difference was that Bradwardine
developed an approach which permitted him to avoid certain aspects of contingency
which openly contradicted his cosmology, whereas these very aspects fascinated
Ockham and deeply inﬂuenced his philosophical system. To the extent that they
each achieved major innovations in investigating complicated philosophical and
theological problems while remaining faithful to the same body of Christian
doctrine, however, both must be seen as conservative theologians.

In the introduction to Bradwardine’s Senna Epinicius, which commemorates
the English victory at Crécy, Weisheipl makes the important observation that it is
Bradwardine’s unique analytical style, not the unconventionality of his opinions,
which makes his writing so compelling. Weisheipl contends that the theology of the

De causa Dei is perfectly in line with Thomist teaching about God as the ﬁrst cause.

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The impact of the work has been so strong, no less today than in the fourteenth
century, because Bradwardine far surpassed his contemporaries in grasping the
implications of traditional metaphysics and in conveying his insights to a large
audience.95 His inﬂuence and popularity as a thinker are proven by his remarkable
success within and outside of academic circles. His brilliant public career enabled
him, in turn, to popularize his essentially traditional views of nature and God among
both learned and lay communities. Weisheipl’s observation holds as well for.
Bradwardine’s other works. His ideas about geometry, proportionality and
continuity also attracted large audiences because they displayed his skill in
presenting Euclidean geometry and Aristotelian natural philosophy rationally and in
a highly original form. Even his early and relatively immature opinions about
beginning and ceasing forced more advanced scholars to reconsider their views. In
spite of its awkwardness, moreover, the De ﬁttun's cantingentibus demonstrates that
Bradwardine was prepared by the late 13205 to apply his exceptional analytical
talents to a new range of difﬁcult theological questions.

The De causa Dei was the product of Bradwardine’s attempt to place his well-
developed assumptions about the natural world in a broader context and to explain
how God uses the physical and spiritual forces which are observed in nature and
revealed in Scripture to create a uniﬁed, balanced and orderly universe. This study
of the De causa Dei has shown that the distinction between time and eternity, which
lies at the heart of both Bradwardine’s natural philosophy and his theology, became
the major link between them in his mature thought and has suggested that no
attempt to understand the development of Bradwardine’s views or to assess his role
as preserver and transformer of traditional positions can be complete without some

reference to his conception of time.

CONCLUSION

In this dissertation the physical, philosophical and theological elements of
Bradwardine’s view of time and eternity have been examined in the context of
ancient and medieval approaches to the problem of time. Chapters Two and Three
trace the development of the large body of speculative literature on this subject
from the classical period to the end of the thirteenth century. These chapters reveal
not only the general importance of the problem of time in the Western
philosophical tradition, but also the complexity and subtlety of the various solutions
to the problem of time. The main conclusion to be drawn from this review is that
medieval thinkers inherited an approach to time which tried to balance the poetical
cosmology of Plato’s T imaeus with Aristotle’s more concrete natural philosophy.
Christian philosophers from Augustine to Aquinas reinterpreted Plato’s and
Aristotle’s views of time in light of SCripture, but they based their arguments about
time almost entirely on classical formulations.

Chapters Four through Seven of this dissertation explore the inﬂuence of
both classical and Christian approaches of time on the views of one of the
fourteenth century’s most prominent natural philosophers and theologians. Chapter
Four indicates how Bradwardine’s axiomatic method of combining Euclidean
mathematics and Aristotelian physics allowed him to remain ﬁrmly committed to
Aristotle without losing the analytical beneﬁts of a more Platonic approach to
mathematics. Bradwardine’s use of time in his analysis of ratios suggests that he
fully accepted the physical validity of Aristotle’s deﬁnition of time as the number or

measure of motion.

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Chapter Five, which focuses on Bradwardine’s inﬂuential work on continuity,
develops further the theme of his preference for Aristotelian natural philosophy. In
the De continua, Bradwardine explicitly deﬁned time as the successive continuum
which contains and measures all other continua, whether successive or permanent.
This treatise not only reafﬁrms Bradwardine’s commitment to Aristotelian natural
philosophy but also presents unambiguously his notion that inﬁnity in the created
world is a matter of inﬁnite divisibility, not of inﬁnite duration or dimension.
Although he made no attempt in the De continua to compare the continuity of
created matter with the inﬁnity or eternity of God, he developed a theory of

continuity which is consistent with the cosmology which he later described in the De

‘ causa Dei.

Chapter Six contrasts Bradwardine’s early views on beginning and ceasing
with his ﬁrst speculations on contingency. This analysis emphasizes Bradwardine’s
growing awareness of the difference between the human perception of time and
change on the one hand and the divine experience of eternity and immutability on
the other. In the De incipit et destinit, which consciously excludes the issue of divine
foreknowledge, Bradwardine fearlessly proves through Aristotelian principles that
the future is undetermined and completely unpredictable. The De ﬁttun's
cantingentibus explores much more cautiously the true relationship between God’s
knowledge and human perception of the future. By rigidly interpreting the
Augustinian-Boethian view of eternity, Bradwardine seems to deny any possibility of
contingency at all, suggesting an almost complete reversal of his opinion in the De
incipit et destinit.

Chapter Seven attempts to resolve this apparent dilemma by examining
Bradwardine’s mature thought about time and eternity as he expressed it in the De
causa Dei. In this work Bradwardine presents a cosmology which admits no human

capacity to attain certain knowledge of the future through logical prediction1 and

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which recognizes man’s perception of the future as contingent and yet ultimately
dependent on the eternal, immutable will of God. By subordinating every created
act to God as ﬁrst cause, Bradwardine placed God at the center of both the physical
and temporal order. Although it was not primarily a work of natural philosophy, the
De causa Dei was based on a view of time and eternity which enlarged Augustinian
notions of eternity and grace with the principles of Aristotelian physics.

This study of Bradwardine’s conception of time in scientiﬁc, philosophical
and theological contexts demonstrates several important points about Bradwardine’s
thought and fourteenth-century intellectual life as a whole. First, although
Bradwardine was perfectly capable of distinguishing among the logical, physical,
metaphysical and spiritual aspects of time and eternity, he considered it neither
necessary nor desirable to approach time in one way exclusively. All of his works
show his awareness of the classical and medieval debates about speciﬁc topics such
as time, continuity and proportionality, as well as the larger contemporary debate
about the validity of Aristotelian natural philosophy. Nowhere does Bradwardine
show more clearly his afﬁnity for the philosophy of Thomas Aquinas than in his
multi-faceted treatment of time for, to reconcile Augustine and Aristotle, both
theologians had to confront the conﬂicting approaches to time and eternity which
these two authorities present.

Second, Bradwardine’s view of time and eternity, in spite of its clear basis in
Aristotelian physics and Euclidean mathematics, helped him to deﬁne the
cosmological principles which supported his theological positions on grace, free will,
justiﬁcation and sin. In fact, his axiomatic approach to metaphysical problems
allowed him to retain and balance what he considered to be the most convincing
aspects of the Aristotelian and Augustinian-Boethian temporal theories.
Bradwardine’s method allowed him to afﬁrm the accuracy of human observation of

change and motion while acknowledging God’s different perspective on creation.

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Bradwardine’s technical understanding of inﬁnity, continuity, proportionality and
limits lent authority to his conception of God as eternal, immutable, omnipotent and
the ﬁrst cause of every created act.

Third, Bradwardine’s treatment of time illustrates one of the most
characteristic features of his analytical method: his ability to refute his opponents,
not by debating every aspect of a problem under discussion, but by systematically
eroding the validity of one or two crucial underlying assumptions. Thus, one of
Bradwardine’s most effective challenges to contemporary speculation about
contingency, logical prediction and free will arose directly out of his deﬁnition of
time as a created entity, dependent on God for its existence and with no power to
encompass or restrict him. Bradwardine’s view of time illustrates, therefore, how
misleading it is to study his natural philosophy and theology as unrelated features of
his thought.

Another theme which has been stressed in this dissertation is that, despite
the remarkable originality of his methods and the unusual clarity of his style,
Bradwardine was a member an academic community. His achievements, therefore,
cannot be seen in isolation from those of his colleagues. Except perhaps for the
Geametn'a speculativa, all of Bradwardine’s major works addressed disputes of great
contemporary interest. Whether the topic was physical, philosophical or theological,
Bradwardine and his fellow scholars referred to the same body of authority, made
use of the same analytical methods and constantly emphasized the orthodoxy of
their arguments. For this reason, the dilemma of time’s relationship to eternity,
unresolved since the classical period, is a recurrent, if implicit, theme in mid-
fourteenth-century thought.

Although Ockham and Bradwardine were two of the few thinkers explicitly
to examine time as both a physical and theological problem, the issue of time

emerged implicitly in a much wider range of discussions concerning free will,

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contingency and God’s absolute power. Ockham contributed to this discussion by
introducing new techniques for evaluating the truth of logical propositions.
Bradwardine, as a natural philosopher, helped to focus attention on the
cosmological assumptions which theologians must make whenever they try to deﬁne
the relationship between God and man. Bradwardine’s most positive role in these
debates, however, was to suggest that no explanation of the operation of human or
divine will in the created world is valid if it fails to acknowledge the distinction
between God’s atemporal existence and the human experience of constant change.

It would be wrong to suggest that these debates did not sometimes lead to
serious disagreement and personal antagonism, but it is equally inaccurate to
exaggerate the differences among the participants, who were, after all, trained for
critical disputation in the search for truth. The current trend in historical analysis of
late medieval thought, therefore, is to step back from the earlier interpretation of
fourteenth-century intellectual life as a clear-cut debate between advocates of a
radical skepticism and conservative Augustinianism. The main impetus behind this
shift has been a reevaluation of Ockham’s role as an intellectual leader in the early
decades of the fourteenth century. While the originality of Ockham’s thought has
never been doubted, he is being portrayed increasingly as a rather conservative
Franciscan, who inﬂuenced, but certainly did not dominate, those younger scholars
whose views were eventually condemned in Paris in 1347.2 Recent research on such
men as Thomas Buckingham, Robert Holcot, Adam Wodeham, John of Mirecourt
and Gregory of Rimini underlines the complexity of their thought and provides a
better framework for understanding their debates with each other and with so-called
conservative opponents like Bradwardine and Richard F itzRalph.

Because he was a major contributor to the fourteenth-century academic
debates, Bradwardine’s relationship with his contemporaries also deserves to be

reconsidered. Unfortunately, most of the standard interpretive studies of

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Bradwardine either have concentrated almost entirely on his contributions to
natural philosophy or have placed his theological views, embodied in the De causa
Dei, in the context of a ﬁerce religious dispute. Because very few treatments of
Bradwardine’s thought have tried to explain how his views about natural philosophy
inﬂuenced his theology and because most studies have contrasted his positions with
those of a speciﬁc group of opponents, Bradwardine’s position in the fourteenth-
century debates has been somewhat misconstrued: he has been labeled a
conservative on account of his opposition to "Ockhamist" assertions about God’s
absolute power, in spite of his own equally emphatic advocacy of that principle; he
has been called an "inhumane genius" in spite of his constant acknowledgement of
human reason and his unfailing optimism about the goodness of man’s relationship
with God.3 Moreover, the literature on Bradwardine consistently gives the
impression that, although he was an active natural philosopher, his scientiﬁc views
generated little controversy whereas his theological opinions involved him in a
hostile struggle with the nominalists which ended for him only at his death - a view
which fails to account for key features of Bradwardine’s argumentative style. As we
have seen, even his scientiﬁc works were polemical and were directed against ideas
rather than individual thinkers.4 The same observation needs to be made about
Bradwardine’s theological views.

These features of the traditional approach to fourteenth-century intellectual
life are particularly evident in the studies of Leff and Oberman. Despite their vastly
different opinions about the basic direction of Bradwardine’s theology, both Leff
and Oberman portray Bradwardine as a self-conscious opponent of Ockham and his
followers. Because each is chieﬂy concerned with philosophical and theological
questions, however, neither Leff nor Oberman considers other aspects of academic
debate in the mid-fourteenth century. Their decision to stress theology over natural

philosophy leads occasionally to misinterpretations not only of Bradwardine but of

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Ockham. As recent studies of Ockham have shown, even his most innovative and
controversial views about faith and reason depend on his acceptance both of
Aristotelian physics and of Franciscan theology. This combination of inﬂuences
from natural philosophy and theology applies to Bradwardine’s work as well.

The tendency among historians to separate the scientiﬁc theories of medieval
authors from their theological views is, of course, mostly a matter of convenience:
individual scholars often lack expertise in some of the ﬁelds which have bearing on
their multi-disciplinary approaches to cosmological problems. The reason for
focusing attention on Ockham as the leader of a new, skeptical intellectual
movement in the early fourteenth century, however, is primarily historiographical.
The thesis that Ockham initiated a direct challenge to orthodoxy, one which was
checked only temporarily by the Paris condemnations of 1347 and the Black Death,
originated at the end of the nineteenth century and was pursued with vigor for many
decades. Its elegance and internal consistency caused it to persist even in the
absence of direct evidence either to prove or to disprove it.5

One of the most eloquent and inﬂuential proponents of the traditional view
of the fourteenth-century intellectual climate has been Etienne Gilson, who argued
that Ockham almost single-handedly changed the tone of late medieval philosophy.
By divorcing faith and reason, says Gilson, Ockham jeopardized the delicate balance
between theology and philosophy which his thirteenth-century predecessors had
crafted and so brought about the disintegration of scholastic unity:

The practical effect of [Ockham’s] theology was to nullify, in
many minds, the effort of what might be called the classical
scholasticism of the thirteenth centu , including; He of
Ghent and Duns Scotus. Of the ration understanding of aith
attempted by Bonaventure, Albert the Great, Thomas Aquinas
and their contemporaries, very little, if anything, was left after
Ockham. This is the reason why we described Ockhamism as
markin the end of the golden age of scholasticism. Faith was
intact, ut to follow Ockham was to give up any hope of

achieving, in this life, a positive philasaphical understanding of
its intelligible meaning. . . . In this sense, it can be said that the

 

210

doctrine of Ockham marked a turnin point in the history of
philosophy as well as of theology. In t eolo his doctrine was
paving the way to the ‘positive theology’ o the moderns. In

hilosophy, it was paving the way to modern empirigism. In
Both cases it really was a via modema: a modern way.

In Gilson’s view, then, Ockham transformed the late medieval intellectual
community by rejecting completely the philosophical and theological principles
which supported the views of his predecessors.

Gilson subsequently described the effect of Ockham’s thought on his
contemporaries. According to Gilson, Ockham quickly acquired a loyal group of
followers who intensiﬁed the attack on traditional beliefs. These men came to be

known as the "nominalists":

The e ressions ‘nominalists’ and ‘realists’ (nominates,
reales) had een in use as early as the twelfth century. In the
thirteenth centu , Albert the Great had spoken of the
‘nominalists’ as a men who placed community in the intellect
only. . . . But there have been few nominalists in the thirteenth
century. After Ockham, this ancient appellation was used to
designate his disciples. Hence a new doctrinal alignment.
Despite their constant controversies, Thomists and Scotists
were lumped together and made up the class of the ‘realists,’ or
partisans of the ‘ancient way’ in phi1050phy and theology (via
antiqua); the nominalists or terminists (naminales, terministae)
were also called the modems (mademi), not because they
intended to abandon Aristotle, but because they were following
a new way (via madema) in interpreting it. . . . On December
29, 1340, some nominalistic theses were prohibited by the '
[Parisian Facul of Arts], but these measures no more stopped
the spread a Ockhamism than the thirteenth-century
interdictions to teach Aristotle had prevented Aristotelianism
from invading the mediaeval schools.

 

This interpretation of Ockham’s role in fourteenth-century intellectual life
encouraged the notion that there was a single debate between clearly deﬁned
parties and suggested that Ockham led his adherents in a blatant attack on
traditional views.

In his analysis of nominalism, Gilson equated Ockham’s apparent reluctance

to accept the possibility of certain knowledge, either of nature or of God, with the

211

principle of skepticism. Gilson portrayed Ockham as at odds generally with all
thirteenth-century attempts to reconcile Christian faith with Aristotelian natural
philosophy and speciﬁcally with Duns Scotus’ philosophical reﬁnement of this

synthesis:

The God in whom Ockham believes is Yahweh, who obeys
nothin , not even Ideas. Duns Scotus had submitted to the
free wi l of God the choice of essences to be created; instead of
letting God be free to choose between essences, Ockham
suppresses them. Abelard had made Ideas the privilege of the
divine mind; Ockham suppresses universals even in God. It is
because there are no universal Ideas in God that there is no
universality in things. The so-called Ideas are nothing but the
very things produci le by God. God needs no Ideas g1 order to
know; by the very fact that God is God, he knows all.

Thus, although protecting himself with the orthodox claim that God, in his absolute
power, could do anything, Ockham completely dismantled the rational
underpinnings for reconciling faith and reason. In doing so, he negated the work of
thirteenth-century theologians whose outstanding achievement had been to
demonstrate that such a reconciliation was possible.

According to Gilson, Ockham’s rejection of Aristotelian metaphysics further
eroded the attempt to reconcile faith and reason. Ockham’s approach to knowledge
made it impossible for him or his followers to establish either a philosophical basis
for faith or even a rational certainty about natural phenomena. In spite of their
closeness to modern views of certainty, Ockham’s views posed serious and disruptive
theological questions in the fourteenth century:

Like Thomas Aquinas and Duns Scotus, Ockham was ﬁrst
and last a theologian using certain philosophical doctrines in
order to elaborate his own understanding of Christian faith.
The dissolving inﬂuence exercised by his doctrine in the history
of mediaeval scholasticism is due to the fact that, professing as
he did a radical em iricism in philosophy, he had to reduce the
understanding of aith to a bare minimum. An Ockhamist
intellect is as badly equipped as possible for metaphysical

cognition, and since where t ere is no metaphysical knowledge
theology can expect little help from philosophy, te

212

consequence of Ockhamism was to substitute for the positive

collaboration of faith and reason which obtained in the golden

age of scholasticism, a new and much looser regime in which

the absolute and self-sufﬁcient attitude 9of faith was only

backed by mere philosophical probabilities.
By presenting "Ockhamism" as an anti-Averroist theological reaction, moreover,
Gilson stressed Ockham’s position as the leader of a group with a well-deﬁned
agenda of opposition to thirteenth-century approaches to Aristotle.10 Although it
had more lasting effects than the initial criticisms of Aristotle in the twelfth and
thirteenth centuries and displayed a more sophisticated understanding of
Aristotelian natural philosophy, Ockham’s nominalist school arose, in Gilson’s view,
from a similar distrust of classical approaches to knowledge.

Gilson’s interpretation of Ockham and his followers, though it is an extreme
one, provided a model for almost all subsequent discussions of Bradwardine’s
cosmology. Bradwardine’s criticism of the modern Pelagians, who seemed to lack
conﬁdence both in the natural order of the universe and in God’s complete
knowledge of it, points the reader of the De causa Dei to the group of people whom
Gilson identiﬁed as the "Ockhamists." Not surprisingly, therefore, the standard
treatments of Bradwardine’s theology routinely have compared Bradwardine to
Ockham and his nominalist followers, including Robert Holcot, Thomas
Buckingham, Adam Wodeham, Gregory of Rimini and John Mirecourt.
Comparisons have been made because these men have been considered
"Ockhamists," sometimes despite the lack of any speciﬁc evidence suggesting that
the "Ockhamist" label was legitimate. Of course, if these men really did try
systematically to destroy the Aristotelian foundations of thirteenth-century theology,
Bradwardine surely would have opposed them, if only on the grounds that their
skepticism undermined the profession of a lively and conﬁdent faith. In fact, the

attitudes of Bradwardine’s contemporaries to Aristotle were varied and complex.

Thus comparisons of their views can provide many useful insights into late medieval

213

thought, but only so long as we resist the temptation to separate these thinkers into
distinct schools.

We have already seen, for example, that Ockham, in spite of his real
differences from Bradwardine, was perhaps not quite so radical as Gilson and others
have made him out to be. Ockham presented his contemporaries with
epistemological and logical, not so much cosmological, speculations: he was
concerned not with what exists but with how we can know about what exists.
Nonetheless, his skepticism about the possibility of certain knowledge paralleled
Bradwardine’s own concerns on this issue and his method for expressing this
uncertainty was analogous to Bradwardine’s sharp division between the
characteristics of created and divine being. Moreover, both theologians accepted
the fundamental truth of Aristotelian natural philosophy and both based their
theology on the conviction that God, in his absolute power, can do anything.
Indeed, in certain respects, Bradwardine pushed this point farther than Ockham.

Similar observations could be made concerning Bradwardine’s relationship
with the "Ockhamists." Gilson, Leff and Oberman all maintained that Ockham had
followers who together represented the radical challenge which Bradwardine tried
to combat in the De causa Dei. Because they expressed some of the logical
skepticism about knowledge which Ockham had introduced in his philosophical
works, these scholars could easily be identiﬁed as the modern Pelagians whose
notions so distressed Bradwardine. In order to evaluate the extent to which these
men really opposed Bradwardine, historians have focused on their divergent
opinions about the nature of God’s absolute power. The usual assumption is that, in
following Ockham’s conception of God’s absolute power, the ”Ockhamists"
developed a theological perspective that undermined the balance of faith and
reason advocated by Augustine and Aquinas. Little attention has been paid to the

greater likelihood that Bradwardine disagreed with the "Ockhamists" in direct

214

proportion to their acceptance of a cosmology which temporalized God and made
the future contingent not only to man but to God.

According to Leff, for example, the "Ockhamist" insistence that God’s
absolute power allows him to do anything calls into question the necessity of an
orderly, predictable universe. Although God, through his ordained powers, gives
the impression of rationality, he is not compelled always to act according to these
powers. God’s absolute power is an attribute "outside all space and time and not
directed to any speciﬁc universe, or to sustaining any ﬁxed order."11 This
conception of God’s absolute power is, in Leff’s view, the source of skepticism

throughout the whole nominalist movement because

it combined [the] three features of mutability, possibility and
indeterminacy, and applied them to God and revelation. Its
central theme was that nothing was impossible for God in His
absolute power; and in removing the bar of impossibility, it
opened t e way to neutrality and indeterminacy. Neutrality
was ex ressed in the refusal to limit God so that any course
was as ikely as another in his inﬁnite freedom; accordin ly, the
sceptics refused to limit themselves in what could be saig about
Him; it enabled them to join the blasphemous to the
devotional, to make black art of white, to consider the
impossible as possible, all in t e name of His freedom. . . . As
a result, God was as he willed; His attributes dissolved before
the blaze of His omnipotence, making him unknowable not
only in the wider and accepted sense, but in those traits which
were virtually the precondition of belief. His goodness,
perfection, mer , justice and wisdom all faded from man’s
vision as beyon his ken. He could be known only by His
ability ever to do differently than He had done. God,
therefore, lost his certainty; He became identiﬁed with inﬁnite
plossibility rather than with any ﬁxed and ascertainable order.

ence an hing could be posited of Him, for {-95 patentia
absoluta su stituted speculation for understanding.

The implications of Ockham’s theory for explaining God’s relation to the created
world are so extreme, says Leff, that Bradwardine had no choice but to refute them.
The comparisons which have been made between Ockham and Bradwardine

in this dissertation have indicated that the view of Ockham advanced by Gilson and

Leff have somewhat exaggerated the extremity of Ockham’s philosophical and

215

theological views. We have seen that Ockham never advocated so rigorous a
skepticism that it rendered God and the natural order totally incomprehensible; he
merely pointed out that the human tools of propositional logic and philosophical
analysis can only partially explain how and why God exercises his absolute power as
he does. This reevaluation of Ockham’s thought obviously raises serious questions
about the interpretation of the work of his followers. If Ockham cannot be accused
of excessive or radical skepticism, how, then, do we evaluate the work of those
thinkers whose ideas have been associated with his? In other words, to what extent
did the "Ockhamists" deviate from Ockham’s essentially moderate position, and to
what extent did they advocate the view of God ascribed to them by Gilson and Leff?
More important in the context of this dissertation, did the ideas of the "Ockhamists"
inﬂuence Bradwardine’s arguments concerning time, contingency, grace and free
will? Although it would be inappropriate to attempt here a comprehensive analysis
of the entire group of scholars commonly referred to as the "Ockhamists," I shall try
to address some aspects of the question of Bradwardine’s relationship to his
contemporaries through two examples of academic interaction. Thomas
Buckingham and Robert Holcot are the two "Ockhamists" most often associated
with Bradwardine. Not only did all three move in the same circles, but there is good
evidence of mutual inﬂuence in both philosophical and theological matters. By
brieﬂy comparing their opinions about God’s absolute power, natural justice and
grace, I hope both to show the complexity of academic interaction in the mid-
fourteenth century and to emphasize the role of cosmological differences,
particularly those involving time, in late medieval scholarly debate.

Bradwardine’s interactions with Thomas Buckingham indicate that
Buckingham moderated his somewhat extreme skepticism after considering
Bradwardine’s complaints against the modem Pelagians, although he remained

convinced that Bradwardine’s approach to contingency was too deterministic. A

216

slightly younger contemporary of Bradwardine’s, Buckingham was born at the turn
of the fourteenth century and was a fellow at Merton from 1324 to 1340. Gifted
both as a natural philosopher and as a theologian, Buckingham would certainly have
had direct contact with so prominent a Mertonian as Bradwardine. In his sentence
commentary, completed in the mid 1330s, Buckingham took a great interest in
contemporary speculation about the importance of grace in determining the merit of
an act. Buckingham’s Opinion that God, in his absolute power, could create a sinless
individual without having to provide him with justifying grace, led him into conﬂict
with both Bradwardine and F itzRalph. Buckingham’s assertions about grace
corroborated the conventional teaching that unbaptized infants are unjustiﬁed even
though they are too young to act meritoriously or without grace; nevertheless, the
assumptions about God’s absolute power, which he used to support this thesis,
raised doubts about Buckingham’s overall orthodoxy. 13 In probing the question of
God’s capacity to contravene the natural order established by his ordained powers,
Buckingham took the potentially dangerous step of undermining the importance of
grace.

According to Leff, in fact, Buckingham pushed the "Ockhamist" approach to
God’s absolute power so far that his theology was only barely orthodox. The
doctrine of God’s absolute power enabled him to challenge the orthodox position on
contingency in two dangerous ways: ﬁrst, by denying the necessity of grace for a
meritorious act; and second, by describing God’s knowledge of the future as fully
contingent. Instead of stressing God’s constant involvement in the world and
participation in human acts, Buckingham contended that God has provided human
beings with a kind of "natural justice" which allows them to perform good acts
without grace. Since one could therefore do good without the constant intervention

of God, one could postulate that salvation might be attained without the beneﬁt of

217

created grace. Buckingham even went so far as to suggest that this natural justice
empowers the human will to reject sin of its own accord.14

Buckingham claimed that he placed such a strong emphasis on human
freedom only in order to ensure the absolute freedom of God. Leff has suggested,
however, that Buckingham’s real concern was to safeguard the freedom of the
human will and to disguise the radical nature of his views by maintaining the widely
accepted view that human freedom depends on and resembles divine freedom. It is
perhaps more likely that Buckingham over-emphasized the analogy between human
and divine freedom on account of his legitimate concern about the restrictions
which God’s ordained powers might have on his absolute power. Therefore,
although Buckingham did not wish to deny the reality of God’s ordained power, he
struggled with the question of how God could be truly free if he must participate in
the world according to his ordained powers. Nevertheless, in his early thought at
least, Buckingham expressed views about grace and necessity which appeared to his
contemporaries to stress too much the correspondence between human and divine
freedom. Bradwardine, in particular, criticized Buckingham’s underestimation of
the importance of created grace, although his regard for God’s absolute freedom
equalled or even surpassed Buckingham’s.

Buckingham’s view of contingency suggests that his cosmology prevented him
from accepting Bradwardine’s solution to the problem of free will. Leff claims that
Buckingham’s radical view of contingency reﬂects better than any other issue
Buckingham’s extreme skepticism:

In essence the problem is how to reconcile God’s eternal
knowledge of eve hing with man’s freedom to act
contingently; that is, if God knows all from eternity how can
men act freely without either making His knowledge mutable
or their actions determined? It is a problem which arises only
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in the circumstances, be onl two alternatives, if freedom for
the future 18 to be preserve : either God, while knowing the

218

general shape of things to come, foregoes,.in the interests of

effii’e‘é'é’p‘é‘ﬁiiﬁifr’éné’i’if‘ége’eﬁlﬁ‘fg‘éSfﬁliaéiee’l‘foké’ii’a‘llgﬁi

they themselves are. . . . Buckingham . . . chooses the second

way. and makes God’s foreknowledgg of the future as

contingent as the contingents He knows.
In following this line of argument, says Leff, Buckingham willingly sacriﬁced two
attributes of God, omniscience and immutability, in order to preserve both God’s
absolute power and the freedom of the human will. Although Buckingham did not
deny that God has complete knowledge of all future contingents, he stated much
more openly than Ockham ever had the implication of this contingency for creation:
God knows all of the possibilities of the future but he waits to see which possibilities
will be realized. To ensure that the future remained contingent, therefore,
Buckingham qualiﬁed God’s foreknowledge, making it a knowledge of potentiality,
not of actuality. By emphasizing these themes, Leff is able to portray Buckingham
as a theologian for whom conventional explanations of God’s powers and ways of
acting in his creation are unnecessarily deterministic and so are inadequate.

Robson argues that Buckingham responded decisively to the unfavorable
reaction that his sentence commentary received in the academic community.
According to Robson, Bradwardine had an especially strong inﬂuence on
Buckingham, not only because Bradwardine was a highly respected ﬁgure in
Buckingham’s own circle but because they were both interested in the same kinds of
philosophical and theological problems.16 Although Buckingham continued to
maintain that the future is in an absolute sense more contingent than the past,
because the future still holds the possibility of change, he tried in his later works to
ﬁnd a middle ground between determinism and skepticism. In his Quaestianes, for

example, Buckingham reevaluated Bradwardine’s criticism of his view of antecedent

necessity:

219

In a necessary consequence, if the antecedent is not in the free
control of the person concerned, then neither is the
consequence; and if the consequence is under his control so is
the antecedent; and the rules brou ht with authorities and
arguments against my second, ird, ninth and tenth
conclusions have (I hope) been fully refuted to the
understanding of those who uttered them. But to what has
been said here a certain doctor objects, by roving that
whoever has free control over a consequence is ago in control
of whatever follows from it and whatever is necessarily
antecedent. And he says that he understands this only of any
antecedent which is not absolutely impossible: and it is his
13th conclusion.

This passage indicates that Bradwardine and Buckingham had a fundamental
disagreement about the temporal nature of created acts. Whereas Bradwardine
continually afﬁrmed both the past and the future as equally necessary because they
exist simultaneously in God’s mind, Buckingham insisted on temporal variations in
necessity. Even for God, he argued, the past is more necessary than the future
because it has lost its contingency.

Although Buckingham conceded that his earlier opinions about grace might
have been too extreme, he was not prepared to give up his temporal approach to
contingency.18 Nevertheless, Robson points out, Buckingham denied in his
Quaestiones that the past and future are so contingent that God would arbitrarily
change or destroy conditions which are necessary for faith and so gently chastised
Bradwardine for misrepresenting his position:

Likewise the Reverend Doctor, arguing in opposition to this
conclusion, says that unless we admit antecedent necessity, we
must admit it possible for the whole of God’s church to fall,
collapse and perish, for the whole vessel of Peter to suffer
shi wreck and drowning, for all Christ’s faith before the Day of
Ju gement to be defective and shattered (and even that all the
articles of faith concerning the future should be, and should
always have been, false and erroneous); that Christ should

have lied and all the Saints, Apostles, Martyrs and Confe rs
who formerly lived in this faith should have been deceived.

220

Robson, calling this passage a "caricature of the alternative to rigid determinism,"20

depicts Buckingham as a moderate theologian trying to ﬁnd a compromise between
restrictive determinism and arbitrary contingency. Buckingham afﬁrmed his
orthodoxy by refusing to go too far in either direction. To this extent, be followed
Ockham in balancing the necessary truth of God’s revelation with seemingly
irrefutable sensory evidence that the future contains many possibilities while the
past can no longer be changed. Buckingham and Bradwardine were in conﬂict over
this issue because they had fundamentally different conceptions of time.
Buckingham was unwilling to accord to God an eternity and simultaneity which
completely remove him from the human experience of time; consequently, his view
of necessity was ambiguous. Bradwardine, as we have already seen, sacriﬁced some
of the full range of human freedom to avoid this very ambiguity.

Buckingham’s and Bradwardine’s disagreement concerning God’s experience
of time manifested itself in different interpretations of God’s essential attributes.
While they both gave the highest afﬁrmation to God’s absolute power, Buckingham
stressed God’s freedom to change his mind in a temporal way, whereas Bradwardine
viewed God’s freedom, unlike human freedom, as an entirely atemporal reality.
Though wishing to remain orthodox Buckingham could not relinquish his conviction
that divine and human freedom share certain characteristics:

To the argument alleged by the Master and Reverend Doctor,
that unless we admit antecedent necessity in all acts of the will,
we must admit the possibili of the whole church being
destroyed, and so forth: in rep y, I wish to know whether God
is free to chan e his ordinances; and if he is, whether he cannot
2y his free wil effect and fulﬁl all those things here named. . . .

or I think that the created will has liberty of contradiction,
and no man has the ower to destroy Holy Church. . . . And I
know that, as logic emands, [I must affirm] the co-operation,
grace, predestination, and prescience of God, which I shall not
deny. Nor like the Fool shall I deny his existence, nor like
Pela ius do I wish to exalt my will as master and God’s as mere
han maid. But I wish to attribute to God, as ﬁrst agent, every

ood. we have and to declare that we are in many things his
ree instruments, not coerced, and also ﬁt to be rewarded out

221

of his abundqqt mercy for which, as I am bound, I return all the

thanks I can.
Nothing in this statement contradicted Bradwardine’s positions about God as ﬁrst
cause or the freedom of the human will to respond to the inﬁnitely divine will. In
fact, Buckingham’s language clearly indicates that he was responding directly to
complaints which Bradwardine had levied against him in the De causa Dei.
Buckingham openly acknowledged that God is the ﬁrst cause of created acts. His
differences from Bradwardine arose mostly from the question of how God "changes
his mind": for Buckingham, the change could occur temporally, so that the future
could be seen as at least somewhat contingent; for Bradwardine, any change in the
divine plan would be atemporal and entirely independent of human perceptions of
change in time.

Buckingham’s disagreement with Bradwardine over the temporal basis of
necessity should not be exaggerated, however. There is little doubt that
Buckingham was sensitive to the charge of "Pelagianism" and adjusted his opinions
accordingly, although he continued to distinguish between the necessity of the past
and the contingency of the future. Leff would have us believe that Buckingham and
Bradwardine stood so far apart on this issue that they both strayed perilously close
to heresy: that Buckingham, in his extreme interpretation of "Ockhamist" principles,
provoked Bradwardine into an equally extreme form of determinism. What Leff
fails to take into account in his analysis of Buckingham is the positive inﬂuence of
academic dialogue. While it is true that Buckingham’s temporal approach to
contingency resembled Ockham’s, he neither slavishly followed Ockham nor altered
his cosmology in favor of Bradwardine’s when he was alerted to some of his
errors.22 Robson has shown that communication between Buckingham and
Bradwardine led to reconsideration and reﬁnement on Buckingham’s part, just as,

we may suppose, Buckingham’s immature expression of his early opinions provided

222

a useful target for Bradwardine’s analysis of the problem of contingency. The fact
that they did not ultimately agree on every issue does not diminish the value of their
attempts to work out their views in an environment of debate and criticism.
Bradwardine’s exchange with Buckingham, far from suggesting bitterness, radicalism
and despair over the collapse of an old way of thinking, reﬂects the capacity of mid-
fourteenth-century thinkers to collaborate on new solutions to difficult problems.23

Another contemporary of Bradwardine who has been regularly included in
the list of "Ockhamists" was Robert Holcot. Holcot was a Dominican who combined
study and lecturing at Oxford with an active career of public preaching. In addition,
he wrote on a variety of topics of contemporary interest. Indeed, Oberman has
called Holcot a "proto-humanist" on account of his intense interests in classics and
moral theology.24 Although he was a friar, Holcot’s career paralleled
Bradwardine’s remarkably closely. Both arrived at Oxford in the 13205, taught and
wrote in the 13305 and early 13405 and spent the last years of their lives away from
the universities, though Holcot entered a quiet retirement at the same time that
Bradwardine was enjoying his most active period of public service. Both died in
1349. More important than these coincidental comparisons, both Bradwardine and
Holcot belonged for a time to Richard de Bury’s household, which ensures that they
were at least reasonably well known to each other. Unlike the Mertonians in
Bishop Bury’s circle, Holcot did not specialize in natural philosophy. He shared
with Bradwardine the distinction, however, of publishing several books which were
immediately popular and widely read.25 Given his Dominican training, Holcot
showed an unusual enthusiasm for many of Ockham’s ideas, particularly in the
sphere of logic. Like Ockham, Holcot was fascinated by the problem of reconciling
matters of faith with the philosophical constraints of Aristotelian logic.26 Holcot
was also involved in discussions about contingency and necessity. He has generally

been considered an opponent of Bradwardine’s determinism, although historians

223

have disagreed as to the nature and extent of his criticism. Gilson and Leff have
portrayed Holcot primarily as an "Ockhamist" whereas Oberman has stressed the
more original features of his attack on determinism.

Those historians who emphasize Holcot’s ties to Ockham point to Holcot’s
nominalistic tendency to separate faith and reason. According to Gilson, for
example, Holcot tried to prove in his sentence commentary that faith and natural
philosophy require two separate logical systems, because Aristotelian logic is
ineffective for examining a theological mystery such as the Trinity. Holcot’s reliance
on the concept of God’s absolute power to prove that one cannot apply the same
analytical methods both to natural philosophy and theology indicates to Gilson that
Holcot was deeply inﬂuenced by Ockham’s teaching about contingency, prediction,
natural order and sin.27 Leff goes even farther than Gilson in identifying Holcot as
a follower of Ockham and an inevitable opponent of Bradwardine. Indeed, says
Leff, Holcot made himself the main target of Bradwardine’s attack on Pelagianism
by fully exploring the implications of Ockham’s extreme skepticism. For Leff,
Holcot is the quintessential "Ockhamist":

Robert Holcot well illustrates how fruitfully Ockham provided
for his followers along the path of scepticism. He takes up
many of the same positions that Ockham held; and he also
extends them. Despite his fulsome qualiﬁcation to everything,
it is not hard to discern the same trait of doubt that moulded
Ockham’s views. With some room for everything, there is
hardly room for God; possibility once again dissolves the stable
order that Bradwardine proclaims; and men can do all that
men can will. Thus, on the one hand, there is divine causality;
on the other divine indeterminacy. Holcot’s view represents
the application to which the latter outlook can be put. As the
almost exact contem orary of Bradwardine, he indicates the
attitude against whic Bradwardine had to contend, the
effect of Ockham’s teaching on thinkers of his generation.
Thus Leff sees Holcot as a leading participant in a well-deﬁned and well-integrated

school of thought against which Bradwardine desperately battled.

224

Like Gilson, moreover, Leff stresses Holcot’s use of the principle of God’s
absolute power, the favored "Ockhamist" method for deferring the charge of heresy.
As with Buckingham, Leff underlines Holcot’s belief in the inherent goodness of
natural human powers, . which permits the will to recognize and sometimes even
perform good acts without the necessity of created grace. All of these concepts, says
Leff, come more or less directly from Ockham. Holcot deviates from Ockham only
in the direction of even greater skepticism, as when he denies that the human will
need do anything to attain merit, because merit depends on God’s will alone.29

According to Leff, Holcot’s approach to contingency also reﬂects his
tendency towards further skepticism. Holcot accepts Ockham’s logical explanation
of contingency and his assumption that the future is mutable in order to prove that
God cannot know future contingents. Since revelation must be true, God’s
knowledge of revealed truths must be necessary and complete. Therefore, since
God cannot have both complete and incomplete knowledge, it must be the case that
he knows revealed truth with certainty and has no certain knowledge of contingent
truths. In Left’s view, Holcot uses revelation as "the sign that God cannot know
future contingents: in his desire to prevent God’s word from being fallible he has
chosen the other alternative of limiting his knowledge. . . . As a result, revelation
has been transformed: it is now no longer the eternal sign of God’s foreknowledge,
but of its limitations."30

Although Oberman also considers Holcot sympathetic to many of Ockham’s
positions, he portrays Holcot as a more complex ﬁgure. Oberman admits that
Holcot and Bradwardine disagreed on certain fundamental theological issues, but
he does not think "Ockhamist" doctrines were the only source of the conﬂict. In fact,
Oberman maintains, Holcot supported several of Bradwardine’s ideas and

sometimes departed signiﬁcantly from Ockham: he did not simply intensify

"Ockhamist" views.31 By comparing Holcot’s and Bradwardine’s positions on grace

225

and will, Oberman is able to demonstrate, as Robson demonstrated for
Buckingham, both Holcot’s independence from "Ockhamism" and his positive
contributions to a process of fruitful academic discussion.

Oberman cites Holcot’s popular Commentary on the Wisdom of Solomon to
indicate precisely where Holcot deviated from Bradwardine on the issue of grace.
Whereas Bradwardine risks the charges of determinism and unnecessary restriction
of the innate human capacity for. good in order to assure God’s primacy, Holcot tries
very hard to preserve the integrity of the human will in the process of justiﬁcation.
Holcot wishes to deﬁne merit in such a way that intrinsic human worth is not
ignored. Thus he distinguishes between the natural value of an action and its
contracted value:

Now if we understand man’s merit according to the ﬁrst
interpretation, the natural goodness of our works does not earn
eternal life fully (de candigna) but only partially (de confrua),
since it is appropriate (cangruens) that if man has done a 1 that
he can with his ﬁnite resources God should reward him with
His inﬁnite resources. But according to the second
understanding of merit we can say that our works are fully
worthy of eternal life, not because of any merit inherent in the
acts themselves but because of grace, since our Lord has
established that he who3goes good works in a state of grace
shall receive eternal life.
At this level Holcot appears to be in agreement with Bradwardine. Both accept the
necessity of grace for transforming a human act, which is neither good nor bad in
itself, into a meritorious one. They agree, moreover, that it is the direct activity of
God which ensures a meritorious act.

Their differences become more apparent, however, when Holcot begins to

discuss the precise way in which grace is received. Not only does Holcot claim that

"whoever prepares himself to accept grace necessarily receives it," but he implies

that God’s capacity to give grace can be limited by circumstances:

226

it may be said that there is a distinction between compulso

necessity and unfailing necessity [that is, consistency]. Wit

God compulsory necessity has no place, but an unfailing

necessity is appropriate to God because of His promise, that is,

His Covenant, or established law. This is not an absolute, but

rather a conditional necessity. According to God’s established

law the pilgrim who does whatever he can to dispose himself

for ace always receives grace. However, if He should choose

to, ad could deviate from His law for someone other than the

pilgiim or the devil. Then, however much a person [with

whom God has not made His Covenant] might dispose himself

for grace, he would not receive it. Man’s disposition does not

require the giving of grace except by congruen , because grace

surpasses every natural act; it is impossiblf3 or man to fully

merit (de candigno) through any natural act.
Bradwardine would agree with the ﬁnal sentiments of this passage but would take
exception to the limiting language Holcot use to deﬁne God’s scope in giving grace.
In Bradwardine’s opinion grace and act are inseparable because God causes and
sanctiﬁes the act all at once; Holcot, who has a different view of God’s experience of
time, sees the process of act and grace as sequential and temporal.

Although Oberman focuses on grace, not the problem of time and eternity,
he argues convincingly that the disagreement between Bradwardine and Holcot
cannot be conceived simply along the traditional lines of "Ockhamism" versus
Augustinian determinism. Holcot shared some of Ockham’s views about the nature
of God’s absolute power and future contingency but he produced his own views
about grace and justiﬁcation. Oberman’s account of the exchange between Holcot
and Bradwardine emphasizes themes which were of common interest to a large
number of scholars. Instead of searching for the "Ockhamist" source of all Holcot’s
opinions, Oberman acknowledges the originality of both theologians as well as their
dependence on the work of predecessors and contemporaries from various
philosophical and theological traditions.

More recent interpretations of Holcot bear out this notion of subtlety and
complexity of scholarly interaction in the mid-fourteenth century. Historians

observe, for example, that Holcot accepted Ockham’s logical approach to

227

contingency and note Holcot’s ability to adjust Ockham’s views to support his own
particular interests. Although they do not describe it in such terms, most historians
recognize that the conﬂict between Holcot and Bradwardine had to do with a basic
difference in their conception of God’s activity in the world. While Bradwardine
and Holcot arrived at similar conclusions about grace and God’s absolute power,
they disagreed about the essential characteristics of the God who dispenses that
grace and wields that power.

Furthermore, as Ockham’s views increasingly come to be regarded as
conventional, it becomes more difficult to distinguish fourteenth-century theologians -
on the basis of their skepticism.34 Since Ockham, Bradwardine, Buckingham and
Holcot identiﬁed many of the same problems and applied to them the analytical
methods of their common education, they perhaps had more in common than the
standard interpretation of late medieval philosophical trends recognized.35
Although Holcot’s place in the scholarly debates of the mid-fourteenth century has
not yet been fully worked out, it is safe to assume that he, like Buckingham and
Ockham, possessed the ability to respond to the ideas of others and to incorporate
many perspectives into new ones.

The examples of Thomas Buckingham and Robert Holcot indicate that it is
no simple matter to explain the complexities of late fourteenth-century intellectual
life in terms of a clear-cut division between either conservatives and radicals or
Augustinians and Ockhamists. Much more work remains to be done on the less
well-known participants in fourteenth-century academic discussions at Oxford and at
Paris, who also contributed to the rich and varied intellectual life of this period.
Although fourteenth-century thinkers considered the same problems and looked to
the same authorities as their predecessors, their innovations in logic and natural
philosophy helped to push theological speculation, the most revered subject for

human reason, in new directions and into new controversies. The closeness of the

228

academic community in training, patronage and belief made lively intercourse
inevitable, particularly at Oxford, where the absence of any serious complaints of
heresy stimulated a relatively uninhibited exchange of ideas. The multi-disciplinary
skills of many of scholars signiﬁcantly enriched debates about both traditional and
novel tapics.

As a highly respected member of late medieval academic circles both as a
natural philosopher and as a theologian, Bradwardine epitomizes the vibrancy and
multi-disciplinary extent of scholarly debates in that period. His mastery of many
types of learning and his productive interaction with colleagues and students reﬂect
the eagerness with which fourteenth-century scholars approached long-standing
philosophical and theological problems in new ways. If the thirteenth century was
the age of synthesis of Aristotelian natural philosophy and Christian doctrine, the
fourteenth century represents an age of exploration of the implications of that
synthesis. Occasionally, studies culminated in expressions of uncertainty about the
propriety of using traditional methods to solve complex cosmological and
theological questions: hence the charge of skepticism. If we look beyond the
obvious lines of debate, however, we can also discern their optimism and conﬁdence
about the relationship between God and his creation which characterized the
’speculation of this period. Bradwardine’s treatments of time and eternity and his
critical responses to his contemporaries clearly indicate that skepticism in the mid-
fourteenth century was not the consequence of anxiety about God’s sovereignty or
the rationality of the created world; rather, its source was dissatisfaction with
traditional analytical methods which were inadequate to the needs of increasingly
sophisticated scientiﬁc and theological investigations.

This examination of Bradwardine’s view of time concurs with other recent
studies which suggest that fourteenth-century thought cannot be accurately

portrayed by emphasizing individual personalities, well-organized intellectual

229

alliances, pervasive skepticism or the breakdown of thirteenth-century syntheses.
Instead, the complex interaction of scholars is the most striking feature of the
period. William Courtenay describes the fourteenth century as a time when
"methods and topics were generally more important than individual thinkers."36
Bradwardine’s scholarly achievements, seen in this context of criticism and debate,
reﬂect his skill in correcting others’ methods, contributing original perceptions
based on his special knowledge of mathematics and natural philosophy and
redeﬁning cosmological problems in a way which combined the traditional authority
of Aristotle, Augustine and Boethius with fresh perspectives.

The problem of time is an ancient one which still has not been resolved.
Bradwardine’s elegant solution was so tied up with his cosmology that it could not
be accepted by those who proposed alternative cosmologies. Because he ignored
aspects of the problem which were paramount to others, he was unable to convince
all of his contemporaries that his approach was the correct one. Nevertheless, the
state of the debate about time in the mid-fourteenth century, with Bradwardine so
skillfully defending a view accepted from Plato through Aquinas while others built
on an equally long tradition of criticism of this view, provides a great insight into the
interests and abilities, the prejudices and limitations of the entire age. The
discussions about time were neither universally optimistic nor completely
pessimistic, but they exhibited an intense desire to understand God and how he
operates in the world. As a physical, metaphysical, logical and cosmological
concept, time afforded many different avenues for investigation. Bradwardine’s
training in both natural philosophy and theology put him in the position to
understand the various aspects of time as well as any of his contemporaries. Even
today many aspects of the problem of time remain unsolved, but the work of

Bradwardine and his colleagues show how much can be accomplished when such a

230

complex issue engages the interest of a varied and well-integrated academic

community.

NOTES

INTRODUCTION

1 For a good general discussion of late medieval attitudes to time see Jean
Leclercq, "The Experience of Time in the Late Middle Ages," Studies in Medieval
Culture, 8—9 (1976), pp. 137-50.

2 Full references to this and all subsequent texts by Bradwardine discussed
in this dissertation can be found under Thomas Bradwardine in the Bibliography.
Citations to the most frequently used texts are included in the List of Abbreviations.
Basic bibliographical works on Bradwardine are cited in this chapter. For a
comprehensive list of Bradwardine’s writings see J. A. Weisheipl, "Repertorium
Mertonense," Mediaeval Studies, 31 (1969), pp. 174-224.

3 Gordon Leff, Bradwardine and the Pelagians, Cambridge Studies in
Medieval Life and Thought, Series 2, Number 5 (Cambridge: Cambridge University
Press, 1957), pp. 18-19.

4 Katherine Walsh, A Fourteenth-Century Scholar and Primate: Richard
FitzRalph in Oxford, Avignon and Annagh (Oxford: Clarendon Press, 1981). Even
for F itzRalph, whose career is remarkably well-documented, it is impossible to ﬁx
the details of his birth, early life and death (ibid., pp. 1-15, 445-50).

5 Leff, p. 2.

6 Walsh, p. 28.

7 James A. Weisheipl and Heiko A. Oberman, "The Senna Epinicius
Ascribed to Thomas Bradwardine (1346)," AHDL, 26 (1958), p. 295. For some

231

232

useful remarks on Bradwardine’s contribution to fourteenth-century mathematics
and logic see J. M. Thijssen, "Burdian on Mathematics," Vivarium, 23 (1985), pp. 55-
78 and Paul Vincent Spade, "Insalubilia and Bradwardine’s Theory of Signiﬁcation,"
Annuaire de l’école pratique des hautes e’tudes, 85 (1977-78), pp. 391-93.

8 Anneliese Maier, "Zwei Recensionen," in Ausgehendes Mittelalter:
Gesammelte Aufsdtze zur Geistesgeschichte des 14. Jahrhunderts, 2 vols. (Rome:
Storia e letteratura, 1967), II: 458.

9 William Abel Pantin, The English Church in the Fourteenth Century
(Cambridge: Cambridge University Press, 1959), p. 159; Walsh, p. 28.

10 Weisheipl and Oberman, p. 299.

11 Ibid., p. 300.

12 left, p. 3.

13 J. A. Robson, Wyclif and the Oxford Schools (Cambridge: Cambridge
University Press, 1961), p. 39.

14 Quoted in Gotthard Lechler, John Wycliffe and his English Precursors,
trans. P. Lorimer (London: The Religious Tract Society, 1878), p. 66. See De causa
Dei, Book 1, Chapter 35, p. 308, C-E.

15 Ibid.

16 William J. Courtenay, "Recent Work on Fourteenth Century Oxford
Thought," History afEducatian Quarterly, Spring-Summer, 1985, pp. 227-32.

17 Sebastian Hahn, Thomas Bradwardine und seine Lehre van der
menschlichen Willemfreiheit (Miinster: Aschendorff, 1904); Herbert Workman, John
erclif: A Study of the English Medieval Church (Oxford: Clarendon Press, 1926);
Justin Ferdinand Laun, "Die Pridestination bei Wyclif und Bradwardin," in Imago
Dei, ed. H. Bomkamm (Giessen: Alfred Topelmann, 1923), pp. 63-84; and Justin
Ferdinand Laun, "Thomas Bradwardin, der Schiller Augustins und Lehrer Wyclifs,"
Zeitschnﬂ ﬁt'r Kirchengeschichte, 47 (New Series 10) (1928), pp. 333-56. See also

233

Laun, "Recherches sur Thomas Bradwardin, précurseur de Wyclif," Revue d ’histaire
et de philosophic religieuse, 9 (1929), pp. 217-33, which brieﬂy summarizes the
contents of the previous article and provides a useful appendix on texts.

18 See also Oberman’s "Thomas Bradwardine: un précurseur de Luther?"
‘Revue d’histoire et de philosophie religieuse, 40 (1968), pp. 146-51 for a brief analysis
of Bradwardine’s place in the Reformation tradition. For a critical appraisal of
Oberman’s view see Alistair E. McGrath, "Forerunners of the Reformation,"
Harvard Theological Report, 7 (1982), pp. 219-42.

19 The editions produced by Nielsen and Genest will be discussed extensively
in later chapters of this dissertation. Hiiner Gillmeister has edited a very short
treatise by Bradwardine on mnemonic devices in "An Intriguing Fourteenth-Century
Document: Thomas Bradwardine’s De arte memorativa," Archiv ﬁir das Studium des
neueren Sprachen und Literaturen, 220 (1983), pp. 111-14. See also Beryl Rowland,
"Bishop Bradwardine on the Artiﬁcial Memory," Journal of the Warburg and
Courtauld Institutes, 41 (1978), pp. 307-12. Niels Jorgen Green-Pedersen discusses
an anonymous text which has been attributed to Bradwardine in "Bradwardine (?)
on Ockham’s Doctrine of Consequences: An Edition, "Cahiers de l’Institute du
mayen dge grec et latin, 42 (1982), pp. 8-20. Since evidence for the identiﬁcation of
the text is inconclusive and the subject of the treatise is unrelated to the issue of
time, this text will not be examined in this dissertation.

20 For some examples of recent work connecting Bradwardine with his
contemporaries on issues not directly related to the subject of this dissertation see
Kaluza, "La prétendu discussion parisienne de Thomas de Bradwardine avec
Thomas de Buckingham: témoinage de Thomas de Cracovie," RTAM, 43 (1976),
pp. 209-36; Kaluza, "Le probleme du ‘Deum non esse’ chez Etienne du Chaumont,
Nicolas Aston et Thomas Bradwardine," Mediaevalia Philasaphia Palanarum, 24

(1979), pp. 3-19; Kaluza, "L’oeuvre théologique de Nicolas Aston," AHDL, 45

234

(1978), pp. 4-82; Leonard Kennedy, "Oxford Philosophers and the Existence of
God," RTAM, 2 (198), pp. 194-208; and M. L. Rouré, "La problématique des
proportions insolubles au XIIIe siecle - William Shyreswood, Walter Burleigh et
Thomas Bradwardine,"ADHL, 37 (1970-71), pp. 205-36.

235

CHAPTER TWO

1 P. E. Ariotti, "The Concept of Time in Western Antiquity," in The Study of
Time, ed. J. T. Fraser and N. Lawrence (New York: Springer-Verlag, 1975), II: 69-
70. Ariotti points out, however, that the earliest Greek writers also conceived of
time as the accumulation of "multiple times," (e. g. astronomical and seasonal
cycles), rather than as a single entity. The poet Hesiod, for example, referred to
several of these cycles in Works and Days. Says Ariotti, (p. 69): "Natural events
were used for timing important activities. The arrival of cranes in ancient Greece,
Hesiod noted, marks the time for planting, the return of the swallows the end of
preening. . . . Hesiod noted the setting of the Pleiades as marking the time for
hauling the fragile ships of the Greeks up on dry land, and the summer solstice for
safe seafaring."

2 Ibid. Ariotti suggests that these artists (e. g. Pherecydes, Aeschylus,
Sophocles, Solon) might have been inﬂuenced by Iranian sources. In Studies in
Icanology (New York: Harper and Row, 1959), pp. 70-75, Erwin Panofsky discusses
the mythological tradition of the god Chronos. Although there was no god of time
in the earliest Greek pantheon, the similarity between the Greek word for time,
chranas, and the name of the oldest Greek Titan, Kranas, (Saturn in Roman
mythology), caused poets and philosophers to begin to associate the symbols of
Kronos with concepts of time. Thus by the fourth century B. C. Kronas’ name had
been changed to Chronos and he was widely considered to be both a Titan and the
god of time. Panofsky suggests, moreover, that the deiﬁcation of time, though based
on a linguistic coincidence, reﬂects a signiﬁcant change in ancient Greek cosmology:
"When religious worship gradually disintegrated and was ﬁnally supplanted by
philasaphical speculation, the fortuitous similarity between the words Chronos and
Kronos was adduced as proof of the actual identity of the two concepts which really

had some features in common (p. 73)." The association of Chronos with Kronos has

236

had considerable inﬂuence an artistic expressions of time in Western Art. Panofsky
observes that Father Time is usually depicted as an old man with a scythe because
Kronos, originally a god of agriculture, had those characteristics.

3 D. Corish, "rhe Beginning of the Beginning in Western Thought," in The
Study of Time, IV: 36. Nevertheless, classical philosophers could not escape the
cosmological implications of their speculations about time. For a good brief
introduction to the cosmological aspects of classical temporal theory see William
Calvert Kneale, "Time and Eternity in Theology," Proceeding of the Aristotelian
Society, 60 (1960-61), pp. 87-108.

4 Ariotti, p. 72.

5 J. Alexander Gunn, The Problem of Time: An Historical and Critical Study
(London: Allen and Unwin, 1929), p. 18.

6 Simplicus, In Aristotelis Categorias Cammentarii, ed. Carolus Kalbﬂeish
(Berlin: G. Reimeri, 1907), p. 350. Trans. Ariotti, p. 72. See note 53 below for
additional information on the N eoplatonists.

7 Zygmunt Zawirski, L ’Evalutian de la nation du temps (Cracow: Libraire
Gebethner et Wolff, 1936), pp. 8-10.

8 Ariotti, p. 72.

9 Gunn, p. 18.

10 Ariotti, p. 72.

11 Zawirski, pp. 11-12.

12 Gunn, p. 22.

13 lbid, pp. 21-22.

14 Timaeus, 388, trans. Alfred Edward Taylor in Plato: Timaeus and his
Critics (London: Methuen, 1929), p. 34.

15 John F. Callahan, Four Vtews of Time in Ancient Philosophy (Cambridge,

Massachusetts: Harvard University Press, 1948), p. 6.

237

16 Iota, pp. 6-7.

17 Ibi'd., p. 16.

13 Ibid., p. 17.

19 Robert E. Cushman, "Greek and Christian Views of Time," Journal of
Religion, 33 (1953), p. 256.

20 Ibid., p. 257.

21 Callahan, p. 189.

22 Corish, p. 37.

23 Ibid.

24 Republic, 528E-530C, trans. Francis MacDonald Cornford in The Republic
of Plato (Oxford: Clarendon Press, 1961), p. 243.

25 Cushman, p. 258.

26 G. E. L. Owen, "Aristotle on Time," in MTSM, p. 3

27 See for example, Physics, IV 11.221b3, in Barnes, pp. 374-75; or Physics,
IV 14.223a33,in Barnes, p. 377.

28 Cushman, pp. 258-59.

29 Physics, IV 11.218b21, in Barnes, p. 371.

30 Ariotti, p. 75.

31 Physics, IV 11.219b3-5, in Barnes, p. 372.

32 Physics, VIII 1.252b5, in Barnes, p. 421.

33 Callahan, pp. 70-71.

34 Cushman, p. 260.

35 Callahan. pp. 72-73.

36 Qishman, p. 260.

37 Callahan, p. 22. "On Eternity and Time" is the seventh treatise of the
third book of Plotinus’ Enneads. For a standard edition and English translation of

this text see Plotinus, Volume HI, ed. and trans. Arthur Hilary Armstrong (London:

238

Heinemann, 1967), pp. 293-355. In the following discussion I quote from excerpts of
this treatise which have been translated by Callahan in his chapter on Plotinus, pp.
88-148.

38 Gordon H. Clark, "The Theory of Time in Plotinus," Philosophical Review,
53 (1944), p. 337.

39 "On Eternity and Time," trans. Callahan, pp. 88-89.

40 Ibid., p. 89.

41Ibid., pp. 90-91.

42 Ibid., p. 93.

43 Callahan, p. 98.

44 Ibid., p. 101.

45 Ibid., p. 102. Whereas Aristotle based his rejection of this second theory
on an argument from natural philosophy (time is the measure of heavenly bodies so
it cannot be equated with them), Plotinus used a more metaphysical approach by
placing time in a different coeval from the material sphere of heavenly bodies.

46 Ibid.

47 Ibid., p. 107.

48 Ibid., p. 111.

49 Ibid., p. 122.

50 Ibid., p. 123.

51 Ibid., pp. 197-98.

52 Samuel Sambursky and Shlomo Pines, The Concept of Time in Late Nea-
Platanism (Jerusalem: The Israel Academy of Sciences and Humanities, 1971), pp.
12-13.

53 Richard Sorabji thoroughly discusses the temporal theory of the late
Neoplatonists in Time, Creation and the Continuum: Theories in Antiquity and the
Early Middle Ages (London: Duckworth, 1983). For a good general introduction to

239

the late Neoplatonists see A. C. Lloyd, ”The Later Neoplatonists," in The Cambridge
History of Later Greek and Early Christian Philosophy, ed. Arthur Hilary Armstrong
(Cambridge: Cambridge University Press, 1967), pp. 272-32; see also R. T. Wallis,
Nea-Platanism (London: Duckworth, 1972); and Philip Merlan, From Platonism ta
Neoplatonism (The Hague: Martinus Nijhoff, 1975).

54 The Confessions of Augustine, xi.2, ed. John Gill and William Montgomery
(Cambridge: Cambridge University Press, 1927), pp. 333-34: ". . . et olim in
ardesco meditari in lege tua et in ca tibi conﬁteri scientiam et inperitiam meam."
Quoted in Callahan, p. 149. .

55 Clark, p. 358. See also Hugh M. Lacey, "Empiricism and Augustine’s
Problems about Time," in Augustine: A Collection of Critical Essays, ed. Robert
Austin Markus (New York: Doubleday, 1972), pp. 280-308.

56 Herman Hausheer, "St. Augustine’s Conception of Time," Philosophical
Review, 46 (1937), p. 512.

57 Ibid., p. 503.

58 Confessions, ix.10, trans. Richard Sidney Pine-Cofﬁn (Harmondsworth,
Middlesex, England: Penguin, 1961), pp. 197-98. See Sorabji, p. 164.

59 Sorabji, pp. 164-165.

50 Ibid., pp. 304-305.

61and, p.304.

62 Confessions, xi.17.9-10, ed. Gibb and Montgomery, p. 345: "[Qluid est
ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare uelim, nescio."

63 In response to people who asked what God was doing before creation,
Augustine said that God was creating Hell for those impertinent enough to ask such
a question. See Confessions, xi.12.13-16: "Ecce respondeo dicenti: ‘quid faciebat

Deus antequam faceret‘ caelum et terram?’ respondeo non illud, quod quidam

240

respondisse perhibetur ioculariter eludens quaestionis uiolentiam: ‘alta,’ inquit,
‘scrutantibus gehennas parabat.’" See also Sorabji, p. 233.

64 Etienne Gilson, The Christian Philosophy of Saint Augustine, trans. L E.
M. Lynch (London: Victor Gallancz, 1961), pp. 190-91.

65 J. de Blic, "Les arguments de saint Augustin contre l’éternité du monde,"
Mélanges de science religieuse, 2 ( 1945), pp. 43-44.

66 Jules Chaix-Ruy, "Le probleme du temps dans les ‘Confessions’ et dans
‘Ia cite de Dieu,’" Giamiale di Metaﬁsica, 9 (1954), pp. 468-69.

67 Rudolph Berlinger, "Le temps et l’homme chez saint Augustin," L’année
théalagique augustinienne, 13 (1953), pp. 278-79.

68 James McEvoy, "St. Augustine’s Account of Time and Wittgenstein’s
Criticisms," Review of Metaphysics, 37 (1984), p. 555.

69 Confessions, xi.15, from S. Aurelii Augustini Canfessianem Libri XIII, ed.
Martinus Skutella (Stuttgart: Teubner, 1969). Translated by McEvoy, pp. 555-56.

70 Confessions, xi.20-26. Translated by McEvoy, p. 557.

71 Jules Chaix-Ruy, Saint Augustin: temps et histoire (Paris: Etudes
augustiniennes, 1956), p. 15.

72 M. Moreau, "Mémoire et durée," Revue des études augustiniennes, 1
(1955), p. 244.

73 Confessions, xi.28. Translated by McEvoy, p. 562.

74 Joseph Maréchal, "Lettres sur le probleme du temps chez saint Augustin
et sur le probleme de la philosophic catholique," Mélanges Joseph Maréchal 2 Vols.
(Paris: Desclée, de Brouwer et Cie, 1950), I, 263.

75 Robert Jordan, "Time and Contingency in St. Augustine," Review of
Metaphysics, 8 (1955), p. 395.

76 Ibid., p. 394.

241

77 City of God, V, 10, trans. Bettensen, p. 195. For a complete discussion of
this topic see William L. Rowe, "Augustine on Foreknowledge and Free Will," and
John M. Rist, "Augustine on Free Will and Predestination," in Augustine: A
Collection of Critical Essays, ed. Robert Austin Markus (New York: Doubleday,
1972), pp. 209-217, 218-252.

73 Etienne Gilson, History of Christian Philosophy in the Middle Ages
(London: Sheed and Ward, 1955), p. 97. Additional information on Boethius is
available in Henry Chadwick, The Cansalatians of Music, Logic, Theology and
Philosophy (Oxford: Clarendon Press, 1981) and in a collection of scholarly articles
entitled Boethius: His Life, Thought and Inﬂuence, ed. Margaret Gibson (Oxford:
Basil Blackwell, 1981). There is no consensus among historians as to whether
Boethius was a professed Christian. Because Bradwardine considered BoethiuS’
phi1050phy to be Christian and relied so heavily on Boethius’ view of eternity in his
natural philosophy and theology, the language of this dissertation assumes that
Boethius consciously sought a philosophical explanation of God which would not
contradict Christian doctrines.

79 Sorabji, p. 256. Unlike Augustine, who applied philosophical techniques
to theology, Boethius was a trained, practicing philosopher. Moreover, his
translations of Plato and Aristotle gave Boethius greater mastery of these materials
than Augustine had.

30 Consolation afPhilasaphy, 5:6, ed. Edward Kennard Rand, in Hugh Fraser
Stewart, Edward Kennard Rand and S. J. Tester ed., Boethius: The Theological
Tractatus and the Consolation of Philosophy (London: Heinemann, 1973).
Translated by Eleonore Stump and Norman Kretzmann, in "Eternity," Journal of
Philosophy, 78 (1981), p. 430.

81 Stump and Kretzmann, p. 430.

242

32 De trinitate, 20.64-22.77, ed. Rand. Translated by Stump and Kretzmann,
pp. 430-431. For a Standard edition of this work see Philosophiae cansalatia, ed.
Ludwig Beiler, in Corpus Christianorum Series Latina, XCIV (Turnholti:
Typographic Brepols, 1957). ‘

83 Anthony Kenny, The God of the Philosophers (Oxford: Clarendon Press,
1979), p. 107.

34 Consolation afPhilasaphy, 5:6. Translated by Sorabji, pp. 119-20.

35 De Blic, p. 42.

86 Sorabji, p. 256.

87 Consolation of Philosophy, 5:6. Translated by Sorabji, p. 256. See below,
Chapter 6.

33 Gillian R. Evans, "Time and Eternity: Boethian and Augustinian Sources
of Thought in the Late Eleventh and Early Twelfth Centuries," Classical Folia, 31
(1979), p. 105.

39 Ibid., pp. 107-8.

90 De Pracessione Spiritu Sancti, 52.200.1-2, from Sancti Anselmi Opera
Omnia, ed. Franciscus Salesius Schmitt (Rome: 1938), quoted and translated by
Evans p. 108.

91 Evans, pp. 109-10, cites and translates a passage from Garlandus
Compotista’s Dialecta, ed. Lambertus Maria De Rijk (Assen: Van Gorcum, 1959),
pp. 25-27.

92 Evans, p. 111.

93 Evans, p. 112 cites and translates a passage from Abelard’s Dialectica in
Peter Abaelards philasaphische Schnften, ed. Bernhard Geyer (Miinster:
Aschendorff, 1933), p. 184.34-6.

243

CHAPTER THREE

1 Gilson, History of Christian Philosophy, pp. 235-36. For additional
information about the introduction of Aristotelian philosophy into the medieval
West see especially "The Entry of the ‘New’ Aristotle," Part IV of A History of
Twelfth-Century Western Philosophy, ed. Peter Dronke (Cambridge: Cambridge
University Press, 1988); and "Aristotle in the Middle Ages," Part II of CHLMP. For
an account of and bibliography for the reception of Aristotelian and Muslim
learning in the twelfth through fourteenth centuries see John Marenbon, Later
Medieval Philosophy (1150-1350): An Introduction (New York: Routledge and
Kegan Paul, 1987).

2 Gilson, p. 238.

3 Gilson, p. 217. For Averroes see also René Antonin Gauthier, "Notes sur
les débuts (1225-1240) du premier ‘averroisme,’" Revue des sciences philosophiques et
théologiques, 66 ( 1982), pp. 321-74; Gauthier, Ibn Rachd (Averroes) (Paris: Presses
Universitaires de France, 1948); Majid F akhry, A History of Islamic Philosophy (New
York: Columbia University Press, 1970), pp. 302-25; and Oliver Leaman, An
Introduction to Medieval Islamic Philosophy (Cambridge: Cambridge University
Press, 1985), pp. 42-57, 92-104.

4 Gilson, p. 218. Faith debases theology because it allows a person to
accept probable truth without rigorous analysis of necessary principles.

5 "Aristotelis doctrina est summa veritas, quoniam eius intellectus fuit ﬁnis
humani intellectus. Quare bene dicitur quod fuit creatus et datus nobis divina
providentia, ut sciremus quidquid potest scire." Quoted and translated by Gilson,
my translation adapted, p. 220. See also Gilson, p. 642, note 17, for additional

references to Averroes’ praise of Aristotle.

244

6 Augustin Mansion, "Ia théorie aristotélicienne du temps chez les
péripateticiens médiévaux: Averroes, Albert le Grand, Thomas d’Aquin," Revue
néo-schalastique, 32 (1934), p. 280.

7 Averroes, Commentary 98 on Aristotle’s Physics, quoted from Volume IV
of Aristotelis Opera cum Averrais Commentarius (Venice: J untas, 1562-74) by
Mansion, p. 281: "Si tempus non sequitur aliquem motum existentem extra animam,
. . . quomodo igitur dicit Aristoteles post, ipsum sequi motum corporis caelestis . . . ?
Et etiam si sequitur motum corporis caelestis, continget ut caecus non percipiat
tempus, quia numquam percepit motum caeli. Et etiam, si sequitur omnem motum,
continget etiam ut tempus multipliciter per multiplicationem motuum. Aut
sequetur unum motum, et sic qui non sentit illum motum non sentit tempus, quod
est impossible."

8 Ibid., quoted by Mansion, p. 282: "Et manifestum est quod nos non
sentimus nos esse in esse transmutatabili, nisi transmutatione caeli. Et, Si esse
possible ipsum quiescere, esset possible nos esse in esse non transmutabili. Sed hoc
est impossible. Ergo necesse est ut sentiat hunc motum qui non sentit motum
corporis caelestis, scilicet per visum."

9 Mansion. pp. 282-83.

10 Mansion, p. 284.

11 Averroes, Commentary 98, quoted by Mansion, p. 284: " . . . quarum una
est, quad nos non percipimus tempus, nisi quando fuerimus moti in anima nostra; et
hoc existimavit Galenus, et est corrupta per se. Secunda autem est, quad nos non
percipimus tempus, nisi cum perceperimus aliquem motum quicumque sit, et hoc est
percipere per accidens. Tertia vero est, quod nos non percipimus motum neque
tempus, nisi cum percipimus nos transmutari, quia sumus in esse transmutabili; et
ista perceptio est perceptio quam sequitur tempus essentialiter, et non accidet ei

aliqua quaestio. Et verba Aristotelis manifesta sunt secundum hanc intentionem . . .

245

et secundum hunc modum possumus ponere tempus sequi motum corporis caelestis,
et quod sentiet tempus qui numquam sensit corpus caeleste. Et ideo omnes
conveniunt in hoc quod tempus sequitur motum caeli."

12 Ibid., quoted by Mansion, p. 288: ". . . quia unaquaeque rerum numeratur
per aliquod suae speciei, . . . necesse est ut tempus etiam numeretur per aliquod
tempus notum et terminatum naturaliter. Et dixit (scil. Aristoteles) in praecedenti
quod hic est motus translationis et circularis; quoniam, cum fuerit positum quod
tempus est numerus cuiuslibet motus, et fuerit positum quod hic est prior motus
caeteris motibus, sequitur ut tempus istius motus sit prius caeteris temporibus, et
numerans illa."

13 Gilson, History of Christian Philosophy, pp. 218-19.

14 Ibid., p.229. See Moses Maimonides, The Guide of the Perplexed, trans.
Shlomo Pines (Chicago: University of Chicago Press, 1963). Good secondary
accounts of Maimonides include Georges Vajda, "Mo‘i'se ben Ma‘i'mon," in
Introduction a la pensée juive du mayen dge (Paris: J. Vrin, 1974), pp. 129-51; Essays
on Maimonides: An Octocentennial Volume, ed. Salo Wittmayer Baron (New York:
Columbia University Press, 1941); and Abraham Joshua Heschel, Maimonides: A
Biography, trans. Joachim N eugroschel (New York: F arrar, Strauss, Giroux, 1982).

15 Gilson, pp. 230-31.

16 Gilson, p. 230.

17 From "Die Opuscula De summo bono sive de vita philosophi und De
sompniis des Boetius von Dacien," ed. M. Grabmann, AHDL, 6 (1931), pp. 287-317;
translated by Gilson, p. 401.

18 Gilson, p. 401.

19 Richard C Dales, "Maimonides and Boethius of Dacia on the Eternity of
the World," The New Schalasticism, 56 (1982), p. 306.

20 Ibid., pp. 309-312.

246

21 Ibid., p. 315

22 Ibid., p. 319.

23 Gilson, p. 278. For a full discussion of Albertus’ broad scientiﬁc and
philosophical interests see Albertus Magnus and the Sciences: Commemorative
Essays 1980, ed. James A. Weisheipl (Toronto: Pontiﬁcal Institute of Mediaeval
Studies, 1980).

24 In his discussion of Albertus, Gilson, pp. 279-81, makes several references
to Albertus’ Summa de creaturis in Volume XXXIV of Alberti Magni Opera Omnia,
ed. A. Borgnet (Paris: L. Vives, 1890-99), pp. 319-84 (hereafter cited as Borgnet).

25 Gilson, pp. 279-80, citing Borgnet, pp. 323-25.

26 Gilson, p. 280, citing Borgnet, pp. 339-52.

27 Gilson, p. 281, citing Borgnet. pp. 369-70.

23 Gilson, p. 281, citing Borgnet, pp. 373-74.

29 Gilson, p. 281, citing Borgnet, p. 384.

30 Mansion, pp. 289-90.

311bid., p. 296.

32 From Albertus’ commentary on Aristotle’s Physics in Borgnet, Volume III,
p. 341; quoted by Mansion, p. 295: "Cum autem diciinus suum (scil. circulationis
primae) tempus esse mensuram aliorum temporum, non intelligimus plura esse
tempora, sed unum diversimode referri ad multa. Refertur enim tempus ad primam
mobile et ad motum ejus sicut ad subjectum et numeratum, ad alios autem motus
sicut numerus extrinsecus ad numerata solum et in illis non est sicut in subjecto: et
ideo non multiplicatur multiplicatione comm."

33 James A. Weisheipl, Friar Thomas d’Aquina: His Life, Thought and Works
(Oxford: Basil Blackwell, 1975), pp. 46-47. For additional information about
Aquinas’ education and philosophical and theological interests see especially Marie

Dominique Chenu, St. Thomas d’Aquin et la théologie (Bourges: L’imprimerie

247

Tardy, 1959) and Frederick Charles Copelston, Aquinas (Hammondsworth,
Middlesex, England: Penguin, 1965).

34 Summa Theologica, Ia.ix.l-2, quoted in St. Thomas Aquinas: Philosophical
Texts, trans. Thomas Gilby (London: Oxford University Press, 1951), p. 82.

35 Summa Theologica, Ia.x.4, trans. Gilby, p. 83.

36 Summa Theologica, Ia.lrorix.9, trans. Gilby, p. 26.

37 Summa Theologica, Ia.lixxix.6, trans. Gilby, pp. 250-51.

38 Commentary, IPerihennenias, lect. 14, trans. Gilby, pp. 84-45.

39 See Anthony Kenny, "Divine Foreknowledge and Human Freedom," in
Aquinas: A Collection of Critical Essays, ed. Anthony Kenny (London: Macmillan,
1969), pp. 255-70.

40 Summa Theologica, Ia.xiii.7, trans. Gilby, p. 95.

41 Etienne Gilson, The Christian Philosophy of Saint Thomas Aquinas, trans.
L. K. Shook (London: Victor Gallancz, 1961), pp. 149-50.

42 John M. Quinn, The Doctrine of Time in St. Thomas: Same Aspects and
Applications. An Abstract of a Dissertation (Washington, D. C.: The Catholic
University of America Press, 1960), pp. 17-23.

43 Commentary, 111 Physics, lect. 2, trans. Gilby, p. 51.

44 Commentary, XII Metaphysics, lect. 5, trans. Gilby, p. 53.

45 Disputations, III de Potentia, 17, trans. Gilby, p. 138.

46 Disputations, III de Potentia, 17 ad 5, trans. Gilby, p. 138.

47 For a discusison of Aquinas’ Opinions about the eternity of the world see
James F. Anderson, "Time and Possibility of an Eternal World," Thomist, 15 1932),
pp. 137-144.

48 Summa Theologica, Ia.vii.3, trans. Gilby, p. 140.

49 Vincent Edward Smith, St. Thomas on the Object of Geometry (Milwaukee,

Wisconsin: Marquette University Press, 1954), pp. 54-55.

248

50 "Ohne Dinge, ohne Qualitiit, ohne Kontinuum ist keine Zahl mOglich."
See Ewald Bodewig, "Zahl und Kontinuum in der Philosophie des hl. Thomas,"
Divus Thomas, 13 (1935), p. 63.

51 Anderson, p. 144; Mansion, pp. 297-98.

52 Copelston, Aquinas, p. 79.

53 Daniel A. Callus, "Robert Grosseteste as Scholar," in Robert Grosseteste,
Scholar and Bishop, ed. D. A. Callus (Oxford: Clarendon Press, 1955), pp. 6-9.

54 Ibid., pp. 12-13. For additional information on Grosseteste see Richard
William Southern, Robert Grosseteste: The Growth of an English Mind in Medieval
Europe (Oxford: Clarendon Press, 1986).

55 Alistair Cameron Crombie, Robert Grosseteste and the Origins of
Experimental Science (Oxford: Clarendon Press, 1953), pp. 52-53.

56 Commentary on the Posterior Analytics, i.2, f. 2”, quoted in Crombie, pp.
58-59. For a standard edition of this work see Commentarius in Posterior-um
analyticarum libras, ed. Pietro Rossi, Unione Accademica N azionale Corpus
Philosophorum Medii Aevi, Testi e Studi, 11 (Florence: L. S. Olschki, 1981)..

57 "Robert Grosseteste on Induction and Demonstrative Science," Synthese,
40 (1979), p. 97.

53 Ibid., p. 113.

59 The Philosophy of Robert Grosseteste (Oxford: Clarendon Press, 1982), p.
168.

60 Translated by McEvoy, p. 168, from Die philasaphischen Werke des Robert
Grosseteste, Bischap van Lincoln, ed. Ludwig Baur, Volume XV of Beitrc'ige zur
Geschichte der Philosophie und Thealogie des Mittelalters (Miinster: Aschendorff,
1912), pp. 59-60..

61 McEvoy, pp. 175-76.

249

67' Translated by McEvoy, p. 176, from Annaliese Maier’s transcription of the
Venice Bibl. Marciana MS Lat. VI, 222, printed in her Zwischen Philosophie und
Mechanik: Studien zur Naturphilasaphie der Spiitschalastik (Rome: Storia e
letteratura, 1958), pp. 24n.-25n.

63 McEvoy, p. 176..

64 Quoted by McEvoy, p. 177, from Maier’s transcription: "Sicut enim que
vere in se ﬁnita sunt, nobis sunt inﬁnita, sic que vere se sunt inﬁnita, illi sunt ﬁnita.
Iste autem omnia creavit in numero, pondere et mensura, et isti est mensurator
primus et certissimus. Isti numeris inﬁnitis, sibi ﬁnitis, mensuravit lineas quas
creavit. Numero aliquo inﬁnito sibi certo et ﬁnito mensuravit et numeravit lineam
cubilem, et numero inﬁnito duplo lineam bicubilem et numero inﬁnito subduplo
lineam sernicubilem."

65 Efrem Bettoni, Duns Scotus: The Basic Principles of his Philosophy, ed.
and trans. by Bemardine Bonansea (Westport, Connecticut: Greenwood, 1978), p.
10. For additional information on Duns Scotus see Hermann Schwamm, Das
gOttliche Varherwissen bei Duns Scotus und seiner ersten Anhl‘ingem, Volume V of
Philosophie und Grenzwissenschaften (Insbruck: Felizan Rauch, 1934) and Etienne
Gilson, Jean Duns Scat (Paris: J. Vrin, 1952).

66 Bettoni, pp. 13-14. Bettoni points out that, in spite of his interesting ideas,
Duns’ writing style is so awkward that modern readers tend to avoid his works
altogether. In Bettoni’s opinion, the lack of current studies on Duns can give the
wrong impression that he was a minor ﬁgure in the medieval universities; in fact, the
numerous references to Duns in works Of his contemporaries indicate that his views
were quite inﬂuential.

57 Ibid., p. 15

63 Ibid., pp. 16-17.

69 Ibid., p. 21.

250

70 De rerum principia, q. xviii, art. 1, n. 4, quoted by Charles Reginald Schiller
Harris in Duns Scotus, 2 vols. (New York: Humanities Press, 1959), 11.129-30: ". . .
motus et tempus non dicunt diversas res absolutas sicut quantitas et qualitas
inhaerens, sed omnino dicunt eandem secundum diversas rationes denominatam
aliquando tempus, aliquando motus." For a standard edition of this work see John
Duns Scotus, Opera Omnia, ed. Luke Wadding (Paris: L. Vives, 1891-95).

71 De rerum principia, q. xviii, n. 6 (Commentary on Aristotle’s Physics, Book
IV, Cap. xi), quoted by Harris, p. 131: "Aristoteles videtur suadere tempus extra
animam nihil esse . . . . Si ergo ipsum est aliquid, est ab actione animae . . . . Hanc
autem rationem videtur Philosophus deducere ‘quia cum nihil ipsi mutamur
secundum intellegentiam aut latet nos mutari, non videtur nobis ﬁeri tempus sicut
neque his qui in Sardo fabulantur dormire apud Heroas, cum expergis cuntur.
Copulant enim primum nunc posteriori nunc, et unum faciunt removentis proper
insensibilitatem medium.’ Putabant enim esse numero tempus quo dormire
coeperant et in quO evigilabant . . . . Unde etiam dorrnientes in obscuro loco, non
perpendentis aliquid se motu coeli per lucem solis, quando evigilant quaerunt
tempus, nec scimus quae hora sit certitudinaliter, nisi referemus nos ad alia signa."

72 Harris, pp. 131-32.

73 De rerum principia, q. xviii, n. 13, quoted and translated by Harris, p. 134:
"Patet ergo quod haec fuit ejus Opinio, tempus habere esse in conceptu animae non
extra."

74 Harris, pp. 136.

75 De rerum principia, q. xviii, n. 16, quoted by Harris, p. 136: "Alii dicunt
magis realiter, ut credo quod tempus sit idem in re quod motus, differens formali
ratione, per quam rationem vocatur vere tempus: secundum suum esse materiale
est in rebus extra, secundum suam vero rationem formalem est ab anima et est in

ea.

251

76 De rerum principia, q. xviii, n. 16, quoted by Harris, p. 136: "Et huius
Opinionis videtur fuisse Commentator . . . . Et ista est doctrina Aristotelis . . . ubi
vult quod tempus inest omnibus rebus per motum in terra, in mare et in coelo, cum
sit passio et mensura motus, nec possint ab invicem separari. Motus autem est
aliquid reale praeter actionem et conceptum animae. Quod autem habet aliquem
motum essendi habeat ab anima immediate concedit, arguens quod tempus est
numerans; ergo numerans; hoc autem est anima."

77 De rerum principia, q. xviii, n. 32, translated by Harris, pp. 139-40.

78 Harris, pp. 141-45.

79 Ibid., p. 145

252

CHAPTER FOUR

1 For a concise account of the development of the natural philosophy
curriculum in the medieval universities see Edward Grant, "Science and the
Medieval University," in Rebirth Reform and Resilience: Universities in Transition,
1300-1700, ed. James M. Kittelson and Pamela J. Transue (Columbus, Ohio: Ohio
University Press, 1984), pp. 68-102. In the same collection of essays William J.
Courtenay traces the inﬂuence of Oxford on continental universities, especially
Paris, in "The Role of English Thought in the Transformation of University
Education in the Late Middle Ages," pp. 103-62.

2 William J. Courtenay, Schools and Scholars in Fourteenth-Century England
(Princeton, New Jersey: Princeton University Press, 1987), pp. 262-63. Courtenay’s
book presents a thorough study of fourteenth-century academic life in England. For
a good brief review of the theological trends in fourteenth-century universities see
Paul Vignaux, "La philosophic médiévalc dans ‘Le temps dc l’églisc,’" in his De saint
Anselm d Luther (Paris: J. Vrin, 1976), pp. 69-75.

3 For an illustration of Bradwardine’s method of argumentation see John
Emery Murdoch, "Atomism and Motion in the Fourteenth Century," in
Transformation and Tradition in the Sciences: Essays in Honor of I. Bernard Cohen,
ed. Everett Mendelsohn (Cambridge: Cambridge University Press, 1984), pp. 45-66.

4 Some notes on the name of this work are found in James A. Weisheipl,
"Ockham and Some Mertonians," Mediaeval Studies, 30 (1968), p. 191. Marshall
Clagett has published and discussed sections from an abbreviated version of the De
prapartianibus entitled Tractatus brevis prapartianum in Chapter 7 Of The Science of
Mechanics in the Middle Ages (Madison, Wisconsin: University of Wisconsin Press,
_ 1959), pp. 421-44, 465-84. The edition of the De prapartianibus which will be used in
this dissertation is Thomas Bradwardine, His Tractatus de Prapartianibus: Its

Signiﬁcance for the Development of Mathematical Physics, ed. H. Lamar Crosby

253

(Madison, Wisconsin: University of Wisconsin Press, 1961). Hereafter citations to
Bradwardinc’s text will appear in the notes as De prapartianibus and references to
Crosby’s introduction will be noted as "Crosby."

5 Weisheipl, "Ockham and Some Mertonians," p. 189. Some studies of
medieval commentaries on the De prapartianibus include Anne Harrison, "Blasius of
Parma’s Critique of Bradwardine’s ‘Tractatus dc prapartianibus,” Scienza e ﬁlasaﬁa
all ’Universita di Padava nel Quattracento, Centro per storia dell’Universita di Padova
I (Trieste: Edizionc Lint 1985), pp. 19-69; Michael McVaugh, "Arnold of Villanova
and Bradwardine’s Law," Isis, 50 (1967), pp. 56-64; and Graziella Frederice
Viscovini, "Due conunenti anonimi a] ‘T ractatus proportionum’ di Tommaso
Bradwardine," Rinascimenta, Series 2, 19 (11979), pp. 231-33.

6 Die Vonaufer Galileis irn 14. Jahrhundert, 2nd edition (Rome: Storia c
letteratura, 1966), p. 86, note 10. See also Edward Grant, "Bradwardine and
Galileo: Equality of Velocities in the Void," Archive for the History of Exact
Sciences, 2 (1965), pp. 344-64; and Edith Sylla, "Compounding Ratios: Bradwardine,
Oresmc, and the First Edition of Newton’s Principia," in Transformation and
Tradition in the Sciences, pp. 11-43.

7 Weisheipl, p. 198. See also Crosby, p. 4.

8 De prapartianibus, pp. 64-65.

9 For the following discussion I am dependent on David C. Lindberg, "On
the Applicability of Mathematics to Nature: Roger Bacon and his Predecessors,"
British Journal for the History of Science, 15 (1982), pp. 3-25. For additional material
on late medieval applications Of mathematics to natural philosophy see MTSM;
Ernest Moody, "Laws of Motion in Medieval Physics," SMPSL, pp. 189-201; and
James A. Weisheipl, "Matter in Fourteenthh-Century Science," in The Concept of
Matter in Greek and Medieval Philosophy, ed. Eman McMullan (Notre Dame,
Indiana: University of Notre Dame Press, 1965), pp. 147-69. I

254

10 Metaphysics, xi.3.1061a30-35, trans. Hugh Trcdennik (London, 1935),
quoted by Lindberg, p. 7.

11PosteriorAnalytics, i.l3. 78b34-79a3, quoted by Lindberg, p. 7.

12 Lindberg, pp. 7-8.

13 J eromc Taylor, ed. and trans., The Didascalican of Hugh of Saint Victor: A
Medieval Guide to the Arts (New York: Columbia University Press, 1961), p. 72,
quoted by Lindberg, p. 9.

14 Taylor, p. 64, quoted by Lindberg, p. 9.

15 Crombie, Grosseteste, pp. 105-6.

16 Commentarius in VIII Libras Physicarum Aristotelis, trans. Crombie, p. 94.

17 See Lindberg’s edition and translation of the text Concerning Lines,
Angles, and Figures, in Saurcebaak in Medieval Science, ed. Edward Grant
(Cambridge, Massachusetts: Harvard University Press, 1974), p. 385 ; also quoted by
Lindbcrg in "Applicability," p. 12.

18 De natura lacarum in Die philasaphischen Werke des Robert Grosseteste, ed.
Ludwig Baur (Beitrage zur Geschichte dcr Philosophie des Mittelaltcrs, ix)
(Miinster: Aschendorff, 1912), pp. 59-60; translated and quoted by Lindberg, p. 12.

19 The Opus Major of Roger Bacon, Volume 1, ed. John Henry Bridges
(Oxford: Clarendon Press, 1897-1900), pp. 168-69; translated by Lindberg, p. 18.

20 Bridges, p. 107; translated by Lindberg, p. 18.

21 Bridges, p. 175; translated by Lindberg, p. 19. For an edition of the
Geometria speculativa see A. G. Molland, ed., "The Geometria Speculativa of
Thomas Bradwardine: Text with Critical Edition," Dissertation, University Of
Cambridge, 1967.

22 Molland discusses the dating and authenticity Of this treatise in "An
Examination of Bradwardine’s Geometry," Archive for the History of Exact Sciences,

19 (1978), pp. 115-20.

255

23 Ibid., p. 121.

24 Molland provides an informative synopsis of the contents, pp. 122-31.

25 Ibid., p. 131.

26 Pedro Sanchez Cirvclo, ﬁrst editor of the Geometria speculativa, on the
title page (Paris: 1495); quoted in A. G. Molland, "The Geometrical Background to
the ‘Merton School’: An Exploration into the Application of Mathematics to
Natural Philosophy," British Jaumalfar the History of Science, 4 (1968), p. 112.

27 Molland, "Examination," pp. 17072.

23 Ibid., p. 174.

29 Geometria speculativa, translated by Molland in "Examination," pp. 150-51.

30 Ibid., p. 151.

31 Molland, "Examination," p. 154.

32 Geometria speculativa, translated by Molland in "Examination," pp. 154-55.
"Double ratio" in this context means a squared ratio. Fourteenth-century
mathematicians did not have two separate expressions to distinguish 2x from x2.

33 Ibid., p. 157.

34 John Emery Murdoch, "The Medieval Language of Proportions:
Elements of the Interaction with Greek Foundations and the Development of New
Mathematical Techniques," in Scientiﬁc Change, ed. A. C. Crombie (London:
Heinemann, 1961), p. 265. See also Murdoch, "From Social to Intellectual Factors:
An Aspect Of the Unitary Character of Late Medieval Learning," in The Cultural
Context of Medieval Learning, ed. Murdoch and Edith Dudley Sylla (Boston,
Massachusetts: D. Reidel, 1975), pp. 280-89, in which Murdoch describes the
application of proportion theory to a wide variety of logical problems in the early
fourteenth century.

35 Crosby, p. 13.

36 Ibid., p. 14.

256

37 Ibid., p. 15.

33 Ibid., p. 14.

39 Ibid., p. 15.

40 opera Aristotelis cum Averrais cammentariis, Volume IV, fol 132v (Venice: .
1560), translated by Ernest A. Moody in "Galileo and Avempace," Journal of the
History of Ideas, 12 (1951), p. 191..

41 De prapartianibus, pp. 86-87.

42 Ibid., pp. 86-89.

43 Ibid., pp. 88-89.

44 Ibid., pp. 110-11.

45 James A. Weisheipl, The Development of Physical Theory in the Middle
Ages (London: Sheed and Ward, 1959), p. 75.

46 Stillman Drake, "Medieval Ratio Theory vs. Compound Medicines in the
Origins of Bradwardine’s Rule," Isis, 64 (1973), pp. 72-73.

47 De prapartianibus, pp. 13031.

48 Ibid., pp. 94-95. The meaning of "proportio" in this context is slightly
different from Bradwardinc’s use Of this term in his treatment of velocity. Here
Bradwardine uses the word "proportio" to mean a simple ratio or comparison Of two
times or two distances.

49 "Aristotle’s Physics and the Science of Motion," CHLMP, p. 535.

50 Ibid., p. 534.

51 De prapartianibus, pp. 92-93.

52 Crosby, p. 31.

53 Augustine ta Galileo, II, p. 79.

54 Ibid.

55 Weisheipl, Development, pp. 68-69.

56 "Empiricism and Metaphysics in Medieval Philosophy," SMPSL, p. 301.

257

57 Ibid., p. 302.

58 "The Analytical Character of Late Medieval Learning: Natural
Philosophy Without Nature," in Approaches to Nature in the Middle Ages, ed.
Lawrence D. Roberts (Binghampton, New York: Center for Medieval and Early
Renaissance Studies, 1982), pp. 174-75.

59 Crosby, p. 17.

60 See Anneliese Maier, "Die Subjectivierung dcr Zeit in dcr scholastichen
Philosophie," Philosophia Naturalis, 1 (1951), pp. 361-98.

61 De prapartianibus, pp. 140-41.

258

CHAPTER FIVE

1 De incipit. For a full discussion of this text, see Chapter Six.

2 References to the De continua in this thesis are from John Emery
Murdoch’s edition of the text which also includes a good introduction to the
philosophical aspects of continuity in late medieval academic debates.

3 "The Interpretation of Aristotle’s Physics and the Science of Motion,"
CHLMP, p. 523. Grossetestc’s atomism came not from a rejection of Aristotelian
physics but from his particular interpretation of Aristotle to support his metaphysics
Of light. Although Bradwardine was inﬂuenced by Grosseteste’s use of mathematics,
he did not consider atomism in the De continua from the perspective Of
Grosseteste’s metaphysical system. Therefore, Grosseteste’s views will not be
treated in this chapter. See McEvoy, The Philosophy of Robert Grosseteste, pp. 153-
54.

4 Murdoch, "Inﬁnity and Continuity," CHLMP, p. 564. For an introduction
to the classical origins of the problems of inﬁnity and continuity see Leo Sweeney,
Inﬁnity in the Presacratics: A Bibliographical and Philosophical Study (The Hague:
Martinus Nijhoff, 1972); for discussions of various aspects of these problems from
the classical period to the late Middle Ages see Norman Kretzmann, Inﬁnity and
Continuity in Ancient and Medieval Thought (London: Cornell University Press,
1982).

5 Murdoch, "Inﬁnity and Continuity," p. 565.

6 Edwin SchrOdingcr, Nature and the Greeks (Cambridge: Cambridge
University Press, 1954), pp. 74-77.

7 Sorabji, p, 321.

3 an Generation and Corruption, 1, 2.3l6b19-317a2, in Barnes, pp. 517-18.
For an analysis of Aristotle’s method of refuting Zeno see Sorabji, pp. 336-38.

9 On Generation and Corruption, VIII, 325a13-22, in Barnes, p. 531.

259

10 Physics, v, 3, 226b34-227a16, in Barnes, pp. 383-84.

11Ibid.,227a3033, in Barnes, p. 383..

12 Ibid., V, 2, 231a24-231b9, in Barnes, p. 391.

13 Jbid, V, 2, 232b20-233a12; 233a18-21, in Barnes, p. 393.

14 Ibid., IV, 219a4-14, in Barnes, p. 371.

15 F. D. Miller, "Aristotle against the Atomists," in Inﬁnity and Continuity in
Ancient and Medieval Thought, pp. 106-7.

16 Ibid., p. 109.

17 Sorabji, p. 401.

13 Murdoch, "Inﬁnity," p. 566.

19 Physics, 111, 7, 207a32-207b1; 207b16-21, in Barnes, p. 353.

20 Murdoch, "Inﬁnity," p. 569.

21 Ibid., pp. $69-70.

22 Murdoch, "Medieval Language," p. 520.

23 See Murdoch, "Superposition, Congruence and Continuity in the Middle
Ages," in L’Aventure de la science: Mélanges Alexandre Koyré, I (Histoire dc la
pensée, XII) (Paris: Ecole pratiquc des hautcs études, 1964), p. 424. Here
Murdoch quotes from commentary twenty-two of Averroes’ Commentary on the
Physics, Volume IV of Aristotelis Opera cum Averrais Commentarius (Venice: Juntas,
1562-74): "Dcinde dixit: Et dica contingua et cetera, id est, et contigua sunt corpora
quorum ultima, scilicet superﬁcics, sunt simul ita quod inter illas non est corpus
cxtrancum; et hec est contiguatio naturalis. Contiguatio vero mathematica est in
magnitudinibus quorum ultima superponuntur. Si igitur fuerint corpora,
superponuntur superﬁcies eorum contigue; et si superﬁcies, superponentur linee; et
si lince, superponentur puncta, sicut dicitur punctus superponitur puncto. Set hic

non intendit mathematica, quoniam in mathematicis duo ultima revertuntur in

260

unum, ct sic assimilantur continua. In naturalibus vero duo ultima remancnt duo
dcmonstrata."

24 Murdoch, "Superposition," pp. 428-29.

25 Murdoch examines Albertus’ approach to Euclid in "Superposition," pp.
428-29.

26 Henry of Harclay, Quaestia de inﬁnita et continua (MS Tortosa Catcd. 88,
83v; MS Firenze Naz. 11.11. 281, 95r), quoted and translated by Murdoch in "Inﬁnity,"
p. 571: "Illud quad continet aliud et aliquid ultra illud vcl praeter illud est totum
respectu illius."

27 Murdoch, "Inﬁnity," p. 572. For further information on Gregory of
Rimini’s philosophical outlook see Gordon Leff, Gregory of Rimini. Tradition and
Innovation in Fourteenth-Century Thought (Manchester: Manchester University
Press, 1961).

23 Murdoch, "Inﬁnity," p. 572.

29 Aquinas’ position on continuity is thoroughly discussed by Bodewig in
"Zahl und Kontinuum." According to Bodewig, Thomas’ view of continuity was
essentially Aristotelian except for a somewhat Platonic tendency to consider
continuity in terms of being, that is, as a metaphysical problem not a physical or
mathematical problem, and to emphasize the symbolic importance of number in his
analysis.

30 Ernest Moody, "William of Ockham," SMPSL, p. 409.

31 For a discussion of this problem see William J. Courtenay, "The
Reception of Ockham’s Thought in Fourteenth-Century England," in From Ockham
to Wyclif, Studies in Church History, 5 (Oxford: Basil Blackwell, 1987), pp. 89-107.

32 Weisheipl, "Ockham and the Mertonians," in The History of the University
of Oxford, I, ed. Jeremy I. Catto (Oxford: Clarendon Press, 1984), pp. 609-10.

33 SMPSL, pp. 412-13.

261

34 Ibid, p. 413.

35 Weisheipl, "Ockham and the Mertonians," p. 611.

36 Ibid., p. 610.

37 Ibid.

33 Ibid., p. 612.

39 Moody, "William of Ockham," p. 429.

40 Ibid., p. 430.

41 André Goddu, The Physics of William of Ockham (Leiden: E. J. Brill,
1984), p. 83.

42 Ibid., p. 84. By "imagination experiment" Goddu simply means that
Aristotle, Ockham and, as we shall see, Bradwardine used a method for
investigating physical problems which somewhat resembles modern scientiﬁc
methods, in that it involved proposing hypotheses and devising speciﬁc procedures
for testing their validity. Since these enquiries were conducted according to a
precise methodology but were nevertheless conﬁned to purely mental speculation
and did not involve laboratory experimentation, Goddu calls them thought or
"imagination" experiments.

43 Ibid., p. 110.

44 Ibid., p. 236.

45 In "Inﬁnity," p. 573, Murdoch quotes the following from Thomas Bruce
Birch’s edition of The De Sacramento Altaris of William of Ockham (Burlington,
Iowa: The Lutheran Literacy Board, 1930), pp. 36-38: "Et si queratur quid est
punctus, aut est res divisibilis, dicendum est quod, si sic dicendo ‘punctus est aliquid’
vel ‘punctus est res’ vel huiusmodi 1i ‘punctus’ supponat pro aliqua ita quod habeat
precise vim nominis et non includat equivalentcr unum complexum ex nomine et
verba vel aliquid consimile quod secundum proprietatem vocis potest rcddere

suppositum verbo, debet concedi quod punctus est aliquid et quod punctus est res;

262

et hoc quia debet concedi quod punctus est linea ct punctus est quantitas, quia tunc
hoc nomcn ‘punctus’ equivalct toti isti: ‘linea tante vel tante longitudinis’ sive ‘linea
non ulterius protensa vel extensa’ vel alicui toti composito ex adiectivo et
substantivo vel alicui toti composito ex nomine et verbo mediante coniunctione vel
adverbio vel hoc pronomine ‘qui,’ secundum quod placet dare diversas difﬁnitiones
exprimentes quid nominis illius ‘punctus.’

46 Murdoch, "Inﬁnity," p. 574.

47 Herman Shapiro, Motion, Time and Place According to William Ockham
(St. Bonaventure, New York: The Franciscan Institute, 1957), p. 36, n. 75. Also
discussed in Gordon Leff, William of Ockham: The Metamorphosis of Scholastic
Discourse (Manchester: Manchester University Press, 1975), p. 585.

48 Leff, p. 585.

49 Philosophia Naturalis Guilielmi Ockham, Book HI, p. 1, ed. Bonaventura
Theulo (Rome: Typis B. I. Robletti, 1637); quoted in Leff, William of Ockham, p.
585: ". . . quamvis hoc probari non possit tamen est notum per cxperientia, propter
quod contra negantem motum non habet philosophia naturalis disputare sicut nec
aliquis habet disputare contra negantem sua principia per se nota."

50 Ibid. Translated by Leff, p. 591.

51 Leff, pp. 592-93.

52 In his introduction to his edition to The Tractatus de Successivis Attributed
to William of Ockham (St. Bonaventure, New York: The Franciscan Institute, 1944),
p. 30, Philotheus Boehner refers the reader to the following passage from Part 1,
chapter 44 Of Ockham’s Summa Lagica: "Ideo est alia opinio de quantitate, quae
mihi videtur esse de mente Aristotelis, sive sit haeretica sive catholica, quam volo
nunc recitare, quamvis nolirn cam asserere. Et ideo quando illam opinionem posui
et scripsi super Philosophiam [vz., the Expositia aurea and the Expositia super libras

Physicarum], non scripsi cam tamquam meam, sed tamquam Aristotelis, quam

263

exposui ut mihi vidcbatur; et eodem modo nunc sine assertione recitabo cam. Est
autem ista opinio, quam etiam multi theologi tenent et tenuerunt, quod scilicet nulla
quantitas est realiter distincta a substantia et qualitate, sive tales propositiones:
substantia est quantitas, qualitas est quantitas, sin concedendae, sive non." For the
entire chapter see Venerabilis Inceptan's Guillelmi de Ockham Summa Lagicae, ed.
Philotheus Boehner, Gedeon G1 and Stephanus Brown (St. Bonaventure, New
York: The Franciscan Institute, 1974), pp. 132-39.

53 Boehner, ed., Tractatus de Successivis, p. 96: " . . . tempus non est aliquid
secundum se totum distincta a rebus permanentibus."

54 T ractatus de Successivis, p. 97: "Dum motus durat, Oportet necessario
quod aliquid sit futurum, quod non habet esse extra animam, quamvis possit
cognosci ab anima; et praeter illud est aliquid importatum realiter per hoc nomen
motus, quod est est realiter extra animam; ct ita si accipiatur quasi unum
aggregatum ex omnibus, quae importantur per hoc nomen motus, Oportet quod sit
aliquid extra animam et aliquid quod non est extra animam, quamvis possit cognosci
ab anima."

55 Ibid., pp. 98-99: "Verumtamen sciendum, quod aliqua modo magis
dependet tempus ab anima quam motus, quia sicut declarabitur, tempus non est
aliqua res distincta a motu. . . . Servando talem modum loquendi, isti aequivalent:
motus est tempus, et: motus est motus, quo anima cognoscit, quantus est alius
motus. Et ita cum illud praedicatum motus, quo aliquis cognoscit, quantus est
motus alius, non possit competere alicui sine anima, ideo impossibile est, quod
motus sit tempus nisi per animam; sicut impossibile, est quod motus sit illud, quo
mensurat anima motum sine anima. Et ita patet, quod in deﬁnitione exprimente
quid nominis temporis necessario ponitur operatio animae. Et propter hic dicit
Commentator commento 88°, quod ‘tempus est de numero entium, quorum actus

completur per animam.”

264

56 Ibid., p. 99: ". . . unde tempus potest esse motus sine anima, sed nullo
modo tempus potest esse tempus sine anima."

57 Leff, William of Ockham, p. 593.

58 In The Logic of William of Ockham (New York: Russell and Russell,
1965), p. 147, Moody takes the following quotation from Ockham’s Expositia aurea
et admodum utilis super artem veterem edita . . . cum quaestionibus Alberti parvi de
Saxania Part 11, f. 55r (Bononiae: 1496): "Praeterea quad tempus non est aliqua res
talis alia ostendo, quia omnis res per se una habens partes distantes realiter, si sic
accidens, est in aliquo subiective tam secundum se quam secundum partes suas. Sed
tempus non est in aliquo subiective tanquam unum accidens ipsius, quia subiectum
non est subiectum alicuius nisi quod actualiter existit, sed partes temporibus non
existunt secundum istos. . . . Praeterea, nulla pars temporis est, quid nec praeterita
nec futura, igitur nec ipsum tempus est aliqua res distincta totaliter ab aliis rebus."

59 Ibid., II, 78v; quoted in Moody, p. 171: " . . . quando non dicat rem talem
aliam . . . quia sic necessario derelinquitur ex tempore in re, sed hoc est impossible,
nam tunc in illa re quae fuit inﬁnitis instantibus esset tales res inﬁnitate . . . ."

60 Goddu, p. 167.

61 Tractatus de Successivis, pp. 120-21: "Et quad instans non sit talis res
raptim transiens secundum sc totum distincta ab omni re permanente, sicut moderni
ponunt, ostendo breviter sic: Tum quia aut est substantia aut accidens; non
substantia, quia nec materia nec forma nec compositum. Nec accidens, quia quaero
de subiecto eius prima: Aut est divisibile aut individibile. Non primum, quia
quando subiectum primum est divisibile; ipsum accidens existens in ca est divisible.
Si detur secundum, scilicet quod subiectum primum est indivisibile tunc quaero dc
isto subiecto: Aut est substantia aut accidens. Non primum, quia nec substantia
corporca nec incorporea, sicut patet inductive. Nec accidens quia quaerendum est

de subiecto eius prima, et sic in infinitum. Tum quia in tempore ﬁnito esset res

265

inﬁnitae secundum se totaS distinctae pertransitae. Tum quia non possit dari,
quomodo talis res possit corrumpi, quia nec per corruptionem sui subiecti nec per
inductionem contrarii nec per subtractionem causae conservantis vel per eius
absentiam, sicut patet inductive."

62 Goddu develops this idea at length in his chapter on Ockham’s view of
place, pp. 112-36.

63 Goddu, p. 32.

64 Ibid., p. 144.

65 Ibid., p. 46.

66 Ibid., pp. 141-42.

67 Goddu, p. 139, cites Quaestianes in libras physicarum, MS Paris Bib. Nat.
Lat. 17841, quaestio 39; and also [quaestio 40, "tempus est motus quo anima
cognoscit quantus alius motus."

68 Goddu, p. 167, suggests, for example, a connection between Bradwardine’s
critique of atomism and his derivation of instantaneous velocities. Although
Bradwardine did not support the atomist position, he Often took advantage of
atomist reasoning when it suited his mathematical analysis.

69 De continua, p. 63, 11. 3-7: "Nullus enim physico certamine se spcret
gavisurum triumpho nisi mathematice utatur, consilio et auxilio confortetur. Ipsa
enim revelatrix omnis veritatis sincere, et novit omne secretum absconditum, ac
omnium literarum subtilium clavem gerit. Quicumque igitur ipsa neglecta physicari
presumpserit, sapientie ianuam se numquam ingressurum agnoscat." The last part
of this translation is based on Weisheipl’s translation in The Development of Physical
Theory in the Middle Ages, p. 73. See also Murdoch’s introduction to the De
continua, p. 59, hereafter cited as "Murdoch."

70 De continua, p. 121, l. 5: "Nullam continuum ex athomis integrari. "Here

Bradwardine uses the term "athomis" to mean an individual "now" or instant of time

266

which is itself inﬁnitely divisible, as opposed to a time segment which consists of a
series of consecutive instants. This use of the term "athomis" is consistent with
Aristotelian physics and does not imply that an atom of time is indivisible.

71 For a discussion of this problem see Murdoch, pp. 89-91.

72 Murdoch, p. 247.

73 De continua, p. 1, 11. 1-15.

74 Ibid., p. 2, l. 5 - p. 3 l. 2: "17 - Aliquod post aliud esse, fuisse, vel fore est
ipsum cum medio inter illa esse, fuisse, vel fore. 18 - Aliquod immediate past aliud
esse, fuisse, vel fore est ipsum Sine media esse, fuisse, vel fore. 19 - Incipere esse
per afﬁrmationem de presenti et negationem dc preterito est nunc esse et
immediate ante hoc non fuisse. 20 - Incipere esse per negationem dc presenti et
afﬁrmationem de futuro est nunc non esse et immediate post hoc fore. 21 -
Destinere esse per negationem dc presenti et afﬁrmationem de preterito est nunc
non esse et immediate ante hoc fuisse. 22 - Destinere esse per afﬁrmationem dc
presenti ct negationem de futuro est nunc esse immediate post hoc non fare." The
implications of these deﬁnitions will be discussed at length in Chapter Six of this
dissertation, which examines Bradwardine’s view Of contingency.

75 De continua, p. 4, l. 13: "Pro istis duabus difﬁnitionibus est sciendum,
quod secundum Philosophum tertio Physicarum, ratio inﬁniti quantitati congruit."

76 Ibid., p. 9, 1.6 - p. 10, l. 2: "Si autem dicatur quod est negativa, aut est
universalis, aut particularis, indeﬁnita, vel singularis. Singularis autem non est
propter rationem predictam; nec est indeﬁnita vel particularis, quia tunc ille essent
vere: ‘Inﬁnitum est mundus,’ ‘Inﬁnita puncta sunt duo puncta,’ ‘Inﬁnita chymere
currunt,’ qui universales afﬁrmative contradicentes eis sunt false, et alique illarum
habent aliquas singulare veras ut: ‘Hoc ﬁnitum non est mundus,’ ‘Hec puncta non
sunt duo puncta.’ Item, in sua exponente negation precedit totum, igitur est

universalis negativa. Ideo, forte dicitur quod est universalis negativa, sed tunc sunt

267

iste vere: ‘Inﬁnitum est mons aureus,’ ‘Inﬁnita chymere currunt,’ ‘Inﬁniti mundi
sunt,’ quia particulares afﬁrmative contradicientes eis sunt falsa. Et iste sunt false:
‘Inﬁnitum tempus est ﬁnitum,’ ct ‘Inﬁnita puncta sunt ﬁnita’; signiﬁcent enim quod
nullam tempus est ﬁnitum, ct quod nulla puncta sunt ﬁnita; que tamen solent
concedi et debent."

77 Ibid., p. 11, l. 13 - p. 12,1. 6: "6 - Omne corpus, superﬁciem, lineam, acque
punctum, uniformiter et continue posse moveri. 7 - Omnium duorum motuum
localium eodem tempore vel equalibus temporibus continuatorum velocitates et
spacia illis pertransita eodem tempore proportionales existere. Id est, sicud una
velocitatum ad aliam, ita spaciam per unam velocitatem pertransitum ad spacium
per aliam pertransitum. 8 - Omnium duorum motuum localium super idem spacium
vel equalia deditorum, velocitates et tempora proportionales econtrario semper
esse. Id est sicud velocitas prima ad secundam, ita tempus secunde velocitatis ad
tempus prime. 9 - Quacumque velocitate veltarditate potest unum mobile moveri,
vel unum spacium quodcumque pertransiri potest quocumque. 10 - Esse vel non
esse ﬁnitum certo tempore mensuratur." Suppositions 6-8, trans. Clagett, pp. 230-
31. Suppositions 9 and 10 my translation.

78 Murdoch, pp. 96-97. In proposition 121 Bradwardine applies the same
arguemnt to the physical continuum Of temperature (De continua, p. 106, l. 15 - p.
107,1. 1).

79 De continua, p. 38, 11. 8-12: In a slightly different context, in proposition
124, Bradwardine makes a similar observation about the importance of time in
other physical continua, again using temperature as an illustration.

3° Murdoch, pp. 166-67.

81 De continua, p. 52, 11. 7-11: "Si sic, motus uniforrnis per unum gradum

velocior alio equali sibi in tempore acquirit plus illo, et per nullam divisibile sed per

268

indivisibile tantum. Postquam reprobavit opiniones Pytagori ct Henrici in quo
conveniunt per rationes geometricas, hic incipit faccre idem per rationes naturales."

82 De continua, p. 94, 11. 10-12: "Si Sic de substantia, velocitatem in motibus
proportionem motorum ad sua mota non sequi. Quare manifestum est:
substantiam naturalem compositam ex ﬁnitis athomis non componi."

33 De continua, p. 94, l. 12 - p. 95, l. 14.

84 De continua, p. 97, l. 19 - p. 98, l. 6: "Si sic, omnis motus similis speciei in
velocitatibus adequari. Quia per quemlibet, in quolibet instanti temporibus
mensurantis motum, acquiritur unum indivisibile tantum, ut patet per 26am et eius
corollarium manifeste; igitur omnia illa indivisibilia acquisita sunt equalia illis
instantibus tempori, igitur sunt equalis inter se, igitur per secundam, continua
composita ex illis sunt equalia, ex quo patet propositum."

85 De continua, p. 116, 11. 3-10: "Si sic, omnes velocitates ct tarditates
motuum equale esse. Hcc sequitur ex proxima. Ad item: per 26am et eius
corollarium, per omnem motum semper in uno instanti acquiritur unum indivisibile
tantum; igitur indivisibilia acquisita per quemcumque motum in aliquo tempore
sunt equalia numero instantibus illius temporis, et per consequens quibuscumque
indivisibilius acquisitis per motum in eodem tempore. Igitur, per 263‘“, continua
composita ex illis sunt equala. Igitur motus sunt cqueveloces."

86 De continua, p. 132, l. 20: "Superﬁciem, lineam, sive punctum omnio non
esse."

87 Murdoch, p. 196.

33 Murdoch, p. 173.

269

CHAPTER SIX

1 See Norman Kretzmann, "Incipit/ Destinit," M TSM, p. 102.

2 237a17-28, in Barnes, p. 400.

3 Ibid., 237b10-22, in Barnes, p.401.

. 4 Ibid., 263a9-31, in Barnes, p. 440.

5 See Nielsen’s discussion of Aristotle in the introduction to his "Thomas
Bradwardinc’s Treatise on ‘incipit’ and ‘destinit’: Edition and Introduction," pp. 8-9,
hereafter cited as "Nielsen." References to Bradwardine’s text will be cited as De
incipit.

6 Nielsen, PP. 10-11.

7 In "Incipit/ Destinit," pp. 104-5, Kretzmann suggests that early medieval
interest in these words was primarily grammatical and based on the rediscovery Of
Aristotle’s De saphisticis elenchis. This is in contrast to Curtis Wilson’s thesis,
developed in William Heytesbury: Medieval Logic and the Rise of Mathematical
Physics (Madison, Wisconsin: University of Wisconsin Press, 1960), that medieval
logicians were inspired mostly by the passage from Aristotle’s Physics quoted above.

8 For discussions Of syncategorematic words, see especially Wilson, pp. 11-
12, and Nielsen, PP. 10-11.

9 Nielsen, pp. 10-11.

10 William Sherwood was an English master at the University of Paris in the
first half of the thirteenth century who wrote extensively on syllogisms and dialectics.
Peter of Spain (d. 1277), also a logician at Paris, wrote a number of very inﬂuential
treatises on logic and physics. For details Of their work see Gilson, History of
Christian Philosophy, pp. 317-23. Walter Burley (ca. 1275-1345), a contemporary Of
Ockham, was a master Of arts at Oxford and, like Bradwardine, was both a fellow at

Merton and a member of Richard de Bury’s household. Like William Of Sherwood

270

and Peter of Spain, Burley specialized in logical studies. For additional information
on Burley see CHLMP, pp. 888-89.

11 Nielsen, pp. 11-15. For an edition of Sherwood’s treatise on
syncategorematic words see "Syncategoremata," ed. J. Reginald O’Donnell,
Mediaeval Studies, 3 (1941), pp. 46-93. For a translation and analysis of this text see
Norman Kretzmann, William Sherwood: Treatise on Syncategarematic Words
(Minneapolis, Minnesota: University Of Minnesota Press, 1968).

12 Nielsen, p. 16. See also Wilson, pp. 32-33. For an edition of Burley’s text
see "‘De Primo et Ultimo Instanti’ des Walter Burley," ed. Herman and Charlotte
Shapiro, Archiv ﬁir Geschichte der Philosophie, 47 (1966), pp. 157-73.

13 Kretzmann, "Incipit/ Destinit," pp. 108-9.

14 Ibid.

15 From an excerpt from Tractatus syncategorematum, translated by
Kretzmann, "Incipit/ Destinit," in Appendix A, pp. 122-23.

16 Ibid., p. 123.

17 Ibid., pp. 123-24.

18 See Kretzmann, "Incipit/ Destinit," p. 121 and Wilson, p.31.

19 Nielsen, p. 6. The De incipit is a fragment and has no speciﬁc title. The
ﬁrst sentence of the fragment (De incipit, 1.1, p. 47) reads as follows: "Ad clariorem
igitur notitiam istarum duarum dictionum ‘incipit’ et ‘destinit’ habendam in primis
taliter procedimus."

20 Nielsen, pp. 5-6. Because their disagreement concerned an aspect of
proportional logic and has no bearing on either man’s view of time, it will not be
considered here.

21Ibid., pp. 3-4.

22 Ibid. Nielsen also suggests that Bradwardine might have written the De

incipit before his conversion experience, when he was immersed in the study Of

271

natural philosophy and convinced of Aristotle’s authority. Certainly the narrow
scope of the treatise and its relatively unsophisticated style indicate Bradwardine’s
youth. Yet Since Bradwardine never says precisely when his conversion experience
occurred, it is difﬁcult to use this event for dating a text. As Nielsen points out,
however, Bradwardine could have written the De incipit either before or after his
conversion experience since he left theological questions out Of consideration.

23 De incipit, 2.3, p. 50: "Quad hec est necessaria ‘omnia motus est,’ probo
sic physice loquendo." See also Nielsen, pp. 24-25. In spite of Bradwardine’s
remark, his approach in this text was mostly logical. See Murdoch, "Proportional
Analysis in Medieval Philosophy: A Case Study," Synthese, 40 (1979), 125-26.

24 De incipit, 2.3, p. 51: "Istis prehabitis TERTIA CONCLUSIO est, quod
hec propositio est impossibilis ‘motus incipit esse.’ Istam conclusio probo sic: ista
propositio est necessaria ‘omnis motus est’ igitur sua opposita simpliciter est
impossibilis, videlicet ‘aliquis motus non est,’ ct per consequens ista est impossibilis
‘motus non est.’ Consequentia est bona, ergo ista copulativa est impossibilis ‘motus
nunc non est et immediate post hoc erit.’ Sed ista copulativa - ut prehabitum est -
convertitur cum ista propositione ‘motus incipere esse,’ igitur ista propositio ‘motus
incipt esse’ est impossibilis." Nielsen, p. 24, refers the reader to Aristotle’s assertion
in Book V of the Physics (236b.34, in Barnes, p. 400) that " . . . it is evident that
everything in motion must have been in motion before."

25 Sec Nielsen’s discussion of instantaneous being, p. 23 and pp. 29-30.

26 De incipit, 2.3.1.1, pp. 55-56: ". . . pro cuius solutione notandum est quod
futurum contingens dupex est, quia quoddam est futurum contingens quod pro illo
pro quo est verum nullo modo potest esse falsum, et tale futurum contingens est
‘nunc futurum contingens,’ quod sequitur necessario ex propositione vere et mere de
presenti. . . . Per hoc dico ad argumentum concedendo quod de primis futuris

cantingentibus potest esse determinata veritas et determinata et distincta scientia

272

sicut de propositionibus mere dc presenti ex quibus talia contingentia sequuntur.
De futuris secundis cantingentibus nulla est veritas determinata nec certa scientia et
de talibus loquitur Aristoteles in loco sepius allegato."

27 Nielsen, pp. 24-25.

28 De incipit, 2.3.1.2.1.1, pp. 57-58: ". . . si ista consequentia sit bona ‘Sortes
movetur localiter, ergo Sortes movebitur localiter,’ cum illud consequens sit de
futuro contingenti de qua non est aliqua determinata veritas, sequitur etiam quod
de iStO antecedente ‘Sortes movetur localiter’ non erit aliqua determinata veritas,
quia in omni bona consequentia si consequens sit alicui dubium et antecedens erit
eidem dubium. Et Si consequens sit indeterminate verum vel falsum, et antecedens
erit indeterminate verum vel falsum. Et per consequens sequitur quod aliqua
propositio mere de presenti non erit determinate vera vel falsa."

29 Ibid., p. 60: "Ad aliud quod dicitur de Aristotele qui ponit motum esse
sensibile commune, hoc ideo dicit non quia sentimus aliquid moveri, sed quia
pluribus sensibus percepimus quod aliquid movebatur. Quia sicut nos non
possumus percipere per sensum vel per intellectum quod aliquid movebitur, ita
etiam non possumus percipere per sensum vel per intellectum quod aliquid
movetur."

30 De incipit, 23.1.2.1.2, p. 62: "Ista enim - ut videtur - non stant simul
‘nullam spatium immediate post hoc erit pertransitum’ quia ista sunt contradictoria,
ut patet de se. Sed ista videntur equivalere ‘aliquod spatium erit pertransitum
immediate post hoc’ et ‘immediate post hoc aliquod spatium erit pertransitum.’
Antecedens prime consequentie patet inductive, videlicet quod nullum spatium erit
pertransitum immediate post hoc, quia quocumque spatio dato tempus erit
antequam illud spatium erit pertransitum, ut de se patet. Item, immediate post hoc
aliquod spatium erit pertransitum, igitur sine media aliquod spatium erit

pertransitum. Et ultra, in nullo tempore aliquod spatium erit pertransitum, ergo in

273

non-tempore aliquod spatium erit pertransitum, igitur motus erit sine tempore.
Consequens est impossible, igitur illud ex quo sequitur."

31 Of course Bradwardine is speaking here only about predicting the future
Of real beings using incipit and destinit propositions. He is not concerned with
whether time and space are theoretically inﬁnite. _

32 De continua, p. 2, 11. 5-8; translated by Murdoch in his introduction of the
text, p. 176.

33 De continua, p. 40, 11. 1-2: "Omnis incepto vel destino non mensuratur
tempore sed instanti."

34 See Murdoch, pp. 178-80.

35 Ibid., pp. 185-86.

36 Ibid. See also Wilson, pp. 51-56. As a mathematician like Bradwardine,
William Heytesbury approached the problem of beginning and ceasing by analyzing
instantaneous motion, a concept which Burley had suggested and Bradwardine
almost completely ignored. In the process, Heytesbury derived several important
theories regarding motion, continuity and inﬁnity. The work of Heytesbury and
Bradwardine illustrates the strong connection which existed between logic and
natural philosophy in early fourteenth-century Oxford.

37 Jaakko Hintikka, "The Once and Future Sea Fight: Aristotle’s Discussion
of Future Contingents in De interpretatiane 9," in Time and Necessity: Studies in
An'statle’s Theory of Modality (Oxford: Clarendon Press, 1973), p. 147. In this essay
Hintikka thoroughly explores Aristotle’s extensive but rather confusing treatment Of
the logical implications of contingency. Although it is not possible to cover all of
this material in this dissertation, relevant aspects of Aristotle’s view of contingency
will be treated below.

33 Hintikka, p. 152.

39 17b8-22; 19b1-3, in Barnes, p. 30.

274

40 Hintikka, pp. 164-65.

41 See M. Jean-Francois Genest’s discussion in "Le De ﬁlturis cantingentibus
de Thomas Bradwardine," Recherches augustiniennes, 14 (1979), p. 253.

42 Concerning the City of God against the Pagan, trans. Henry Bettensen
(Harmondsworth, Middlesex: Penguin, 1972), p. 191. Quotation from Cicero, De
Fata, 17.40.

43 City of God, p. 194.

44 See Jordan, "Time and Contingency," pp. 268-69.

45 Chadwick, Consolations, pp. 157-59.

46 The Consolation of Philosophy, trans. H. R. James (London: Elliot Stock,
1897), p. 260-61.

47 Ibid., p. 228.

43 Ibid., pp. 231-32.

49 The material for the following summary is taken from Calvin Normore,
"Future Contingents," CHLMP, pp. 359-69.

50 Normore, pp. 359-61, notes that Anselm discussed aspects Of antecedent
and subsequent necessity in several works, including Cur Deus Homo, II, 17; De
cancordia praescientiae et praedestinatianis et gratiae Dei cum libero arbitria, Quaestio
1; De cancordia, I, 3; and in his Incomplete Works, sometimes called the Philasaphical
Fragments. The standard edition for all of these texts is Sancti Anselmi Opera
Omnia, ed. Franciscus Salesius Schmitt (Rome: 1938).

51 Normore, pp. 361-63, cites the following texts in which Abelard discussed
aspects of future contingency: Editia super Aristotelem De Interpretatione, ed. Mario
dal Pra, in Pietra Abelardo: Scritti di lagica (Florence: La nuova Italia Editricc,
1969), p. 103; Logica ‘Ingredientibus,’ ed. Bernhard Geyer, in Peter Abaelards
philasaphischen Schn'ften (Miinster: Aschendorff, 1919-27), pp. 427 ff.; and

275

Dialectica, ed. Lambertus Maris De Rijk, Wijsgerigc teksten en studies, I (Assen:
Van Gorcum, 1970), p. 212.

52 Normore, p. 363, cites Lombard’s Sentences, Book I, Distinctions 38-40.
For a Standard edition Of this text see Libri IV Sententiarum, ed. Albanus Heysse
(Florence: Editiones Collegii S. Bonaventura ad Claras Aquas, Grottaferrata,
1916).

53 Normore, pp. 364-66, cites Grosseteste’s De liber arbitria, Chapter 6, ed.
Ludwig Baur, in Die philasaphischen Werke des Robert Grosseteste, Bischaf van
Lincoln (Miinster: Aschendorff, 1912).

54 Normore, pp. 366-67, cites especially Aquinas’ Summa Theologica, Book I,
Questions 14, 25 and 62. For a standard edition Of this work see Opera Omnia, ed.
S. E. Fretté and P. Mare (Paris: L. Vives, 1874-89).

55 Normore, pp. 367-69, cites Duns Scotus’ Lectura on Lombard’s Sentences,
Book I, Distinctions 39 and 40. For an edition of Scams’ Lectura see Opera Omnia,
ed. Luke Wadding (Paris: L. Vives, 1891-95).

56 Normore, pp. 369-70.

57 Ibid., p. 370.

53 See Philotheus Boehner, "Ockham’s Tractatus de praedestinatiane et de
praescientia Dei et de futuris cantingentibus and its Main Problems," in Collected
Articles on Ockham, ed Eligius M. Buytaert (St. Bonaventure, New York: The
Franciscan Institute, 1958), p. 423.

59 Boehner, The Tractatus praedestinatiane et de praescientia Dei et de ﬁtturis
cantingentibus (St. Bonaventure, New York: The Franciscan Institute, 1945), pp. 49-
50.

60 William Ockham: Predestinatian, God’s Foreknowledge and Future
Contingents, trans. Marilyn McCord Adams and Norman Kretzmann (New York:

Appelton-Century-Crofts, 1969), pp. 48-50.

276

61 Question 11, article III, trans. Adams and Kretzmann, pp. 61-62.

62 From Book I, Distinction 38 of Ockham’s commentary on Lombard’s
Sentences, also called his Ordinatia, ed. and trans. Adams and Kretzmann in
Appendix I of William Ockham, Predestination, p. 90: "This conclusion [concerning
God’s complete knowledge of future contingents], although it cannot be proved a
priori by means of the natural reason available to us, nevertheless can be proved by
means of the authorities of the Bible and the Saints, which are sufﬁciently known."

63 The issue of Ockham’s view of time and Bradwardine’s reaction to it will
be discussed at length below in Chapter Seven. Bradwardine’s reaction tO some of
Ockham’s followers will be explored in Chapter Eight.

64 Genest, p. 253. See also De futuris, Opinion 7, 20, p. 293, which simply
states: "Septirna opinio est que ponit quod nihil est in futurum contingens ad
utrumlibet, sed omnia que eveniunt necessario eveniunt. Sed ista opinio est tam
contra philosophiam quam theologiam, ideo hic illa non reprobantur."

65 De ﬁtturis, Opinion 6, 17-18b; 18c; 18h-19; p. 292: "Respondetur pro
intencione Anselmi et aliorum diciencum quod omnia sunt Deo presencia: verum
est in esse cognito, et consimiliter dicet Philosophus quod anima est quodammodo
omnia, scilicet sensibilia omnia comprehendit per sensum ct omnia intelligibilia per
intellectum, et non excluditur quin aliqua sint futura et quod illa Deus prescit. Nec
similiter vult Anselmus dicere quod omnia sunt Deo presencia, scilicet futura. Sed
verum est quod hec consequencia non valet: ‘Omnia sunt sibi presencia in esse
cognito, igitur non habet prescienciam’; sed verum est quod bene sequitur ‘igitur
non habent prescienciam excludendo dc illis scienciam.’"

66 Ibid., p. 294: ". . . si Deus habet prescienciam futurorum contingencium ad
utrumlibet, sequitur quod Deus potest velle et promittere Oppositum nunc sciti,
promissi ct voliti ab eO. Consequens est falsum, quia sic Deus potest mutari de

scitis, volitis et promissis, quad est contra illud Malachie 30 [Malachi 3:6]: ‘Ego

277

Dominus et non mutor’; et ita sequitur quod non erit si sicut Deus promisit vel
voluit fore, igitur Deus mutatur. . . . Sed contra: quia sic sequitur quod contingenter
potest scire aliquid fore futurum postquam non fuit futurum ct e converso.
Consequens est falsum, quia sciencia sua est necessaria preteritorum, ut hujus:
‘diluvium fuit,’ et idem est apud Deum scire diluvium fuisse et scire ipse fore
quando non fuit. Igitur sequitur quod sciencia sua est necessaria futurorum."

67 See especially De futuris, Opinion 8, 24a-25p, pp. 295-98; also Genest’s
introduction, pp. 263-64.

68 Ibid., 35j, p. 303: "Conﬁrmatur, quia si Deus velit illum actum stare in
voluntate ejus per diem continue et voluntas illius potest tunc illum actum ante
ﬁnem diei dimittcre, sequitur quod Deus non foret omnipotens, quia non potest uti
creatura sua ut nunc vult ea uti. Consequens est falsum. Et quod Deus possit velle
hominis voluntatem immutabiliter stare per diem vel in etemum, consequencia
patet per Augustinum in Enchiridian et 5° De civitate Dei, c. 10°, ubi arguit conta
Stoycos, qui maluerunt negare prescienciam in Deo quam libertatem arbitrii in
hominibus. Contra quos dicit Augustinus ibidem quad necessitas et libertas non
repugnant in aliqua, quia necesse est Deum velle se esse in vivere in tamen libere,
et sic de beatis, et sic potest esse in nobis; dicit quod necessitas ex natura, ut est illa
qua moriemur, repugant libertati arbitrii, sed non illa qua dicitur necesse est hoe
esse vel fore universaliter. Et sic concedit quOd necessitas aliqua est in voluntate,
que non repugnat libertati arbitrii, ut predictum est, igitur merito dc demerito." For
a standard edition of the Enchiridian see Enchiridian ad Laurentium de F ide et Spe et
Caritate, ed. Ernest Evans, in Aurelii Augustini Opera, Part XIII, 2, Volume XLVI of
Corpus Christianorum Series Latina (Turnholti: Typographi Brepols, 1969), pp. 21-
114.

69 See for example De futuris, Opinion 8, 35p, p. 304: "Et sic potest Deus

facere, et movere ad faciendum illud quod bonum est ﬁeri omnia instrumenta, et

278

tamen credimus nos facere nostra voluntate et contra voluntatem Dei, et Sic
peccamus necessario. Et hoc patet in illo processu: ‘Ve Assur’ (Is., 10:15), ubi
dicitur virga et baculus Jude rex Assur; et simul habetur Enchiridian c. 25°" (See
Enchiridian, 25:99 and 26:100-1)." Also 44c, p. 313: "Item hoc patet per
Augustinium per super Genesim [Cantra Gaudentium 1:30:35], ubi dicitur quod non
potuit in superversione Sodome perdere justos cum impiis, quia foret contra
justiciam et ideo hoc non potest velle facere, et per consequens non potest hoc
facere; sed tamen de potencia absoluta potuit hoc fecisse si voluisset." Also 45g, pp.
314-15: "Sirniliter Boecius in De consolacione, prosa ultima (5:6:36), dicit quod
necesse est futura evenire referendo illa ad cognicionem divinam, sed propria
natura libera sunt et a nexibus necessitatis absoluta." And again, 47h, p. 316: "Item
Anselmus [De cancordia, 1:2] et Boecius [Philosophiae cansalatia, 5:6:27-36], ubi
supra, distinguunt dc necessitate, que est duplex, quedam antecedens et quedam
consequens, et dicunt quod in futuro est necessitas consequens et non antecedens."
70 De futuris, Responsio propria ad questionem, 54a, p. 323: "Sed accipiendo
contingens ad utrumlibet simpliciter, sic conceditur consequencia et consequens,
scilicet quod nihil est vel erit contingens ad utrumlibet, eO quod nihil est vel erit in
etemum nisi quod determinatum ad volitum et prescitum a Deo fore, quia nihil ﬁet
in etemum nisi a potencia ordinata cause superioris vel inferioris. Sed secundum
quid ﬁent plura contingencia, quia illa potencia non est plus ordinata ad unam
partem contradictionis quam ad aliam, ut est potencia absoluta in utraque causa. Et
sic dico de casu et fortuna, quia nihil eveniet in etemum immediate a Deo, vel a
Deo creatura mediante, quin ﬁet a proposito saltem cause superioris, licet plura in
istis inferioribus a casu ct fortuna secundum quid ﬁant, ct non a proposito cause
inferioris; et hoc intendit Philosophus de contingenti equaliter vel utrumlibet, vel de

casu et fortuna."

2 7 9
CHAPTER SEVEN

1 Bradwardine and the Pelagians, p. 16.

2Archbishop Thomas Bradwardine, p. 1.

3 A History of Medieval Philosophy (London: Methuen, 1972), pp. 259-60.

4 Ibid., p. 258.

5 These points are developed at greater length in the Introduction.

6 From a conversation with Dr. Jeremy I. Catto, Oriel College, Oxford,
January, 1987. Dr. Catto has suggested that the comforting tone of some passages
of the De causa Dei might have been prompted by Bradwardine’s desire to reassure
people in the court of Edward III (among others) who did not fully understand
contemporary theological debates and were disturbed by them. .

7 See J. A. Weisheipl, "Ockham and the Mertonians," in The Early Oxford
SchaaLs, ed. J. I. Catto, Volume I of The History of the University of Oxford, ed. T. H.
Aston (Oxford: Clarendon Press, 1984), p. 652.

8 De causa Dei, 1, 40, p. 364, A: "Quod gratia, quae est habitus gratis datus
a Deo una cum voluntate humana est causa efﬁciens proprie cuiuslibet boni ct
meritorij actus sui."

9 Ibid., 1, 41, p. 371, A: "Quod gratia prius naturaliter quam voluntas
humana efﬁciat actus bonos."

10 Ibid., 11, p. 540, B: "Quod cuiuslibet actus voluntatis creatae Deus est
necessarius coeffector." See also chapter 29, p. 577, B: "Quod voluntas increata et
creata in coefﬁciendo actum voluntatis creatae, non sunt coaequales, nec
coaequaeuae in ordine naturali."

11 See Weisheipl, "Mertonians," p. 652.

12 Leff, pp. 56-57.

280

13 De causa Dei, I, 26, p. 251, A: "Quad tota vniuersitas rerurn est bona, et
nulla res per se mala"; and I, 30, p. 271, E: "Quod res voluntariae diuinae
prouidentiae legibus gubemantur."

14 Ibid., 1, 4, p. 174, B: "Prima, quod nihil potest quicquam mouere sine Deo
idem per se et proprie comouente. Secunda, quOd nihil potest quicquam mouere
sine Deo immediate idem mouente. Tertia, quod nihil potest quicquam mouere
Sine Deo idem mouente irnmediatius alio motore quocunque."

15 Ibid., E: "Pro secundo dicendum quod Philosophus in talibus loquitur,
sicut Philosophus naturalis, scilicet de irnmediatione causae secundae, causae
scilicet naturalis; et haec est immediatio secundum quid, quia tantum in genere
creatorum; non autem de immediatione simpliciter, quae simpliciter omnem
mediam causam priuat."

1° For example, Bradwardine states as a corollary to his ﬁrst proposition that
the created world has to be limited, temporally and spacially, in order to distinguish
the mutability of created being from the perfect, inﬁnite simplicity of God. See De
causa Dei, 1, 1, 6, p. 5, A: "Mvtentur credentes Deum non necessario, sed
contingenter esse summe perfectum ct Deum, ipsumque esse mutabliem [nouiter]
irascibilem, placibilem, tristabilem, laetabilem, atque possibilem, nouiter quacunque
alia passione: Opinantes quoque quod Deus sit nomen accidentale, et non essentiale
siinplicter. Quod autem Deus sit necessario summe perfectus et Deus, ex prima
suppositione consequitur euidentcr; cum perfectus et melius sit sic esse; quam
contingenter, sicut patet ex premisses in ostensione suppositionis illius."

17 Bradwardine devotes Book 1, chapter 1, corollaries 33, 34, 37 and 40 to
various aspects of creation in time. See especially De causa Dei, 1, 1, 34, p. 66, B-C:
"Constat autem Philosophis quod prius, ct ante accipitur dupliciter ad propositum,
scilicet secundum naturam et secundum tempus. Pono igitur contrate Aristoteles et

Averroes quod mundus incepit et motus in A instanti, et quod nullum fuit tempus,

281

mutatio, neque successio temporalis, aut aliqua duratio vera mutalibis, aut partibilis,
magna, vel parua ante illium primum motum qui sit B. Pono igitur consequenter
quod nihil omnino praecessit A prioriate aliqua temporali, sicut nihil praecedit
caelum exterius prioriate vel superioritate locali, et quod hoc sit consequens, patet
per teipsum 10. ilius 8i dicentem; Prius et posterius quomodo erunt, tempore non
existente, aut tempus, si non sit motus? et ex alia parte pono, quad Deus aetemus,
euisque aetema sapientia ac voluntas praecessit A prioritate naturae, sicut causa
causarum. Cum ergo tu Aristoteles per totum illum processum supponis quod
cuiuslibet rei factae non esse praecedit necessario suum esse, et hoc loquendo de
praecessione temporali, vt innuis 10. et tu Averroes hoe idem dicis expresse in
comment. decimaoctavo quoque decimoquinto ac alijs hoc supponis."

13 Ibid., 1, 1, p. 1, C.

19 Ibid., 1, 1, parts 33-34, pp. 65-71.

20 Ibid., 1, 1, corollary 40, pp. 119-45.

21 Ibid., I, 40, p. 125, D: "Puto autem quad Democritus prima istam
sententiam adinuenit, et Epicurus postea conﬁrmauit, sicut dc sententia afﬁrmante
cuncta geri fortuito, Lactantius primi institutionum diuinarum aduersus Gentes
prima, recitat manifeste, sicut 27. huius primi plenius recitatur. Et haec videtur
opinio, quam Aristoteles I. de Coelo et Mundo 76. et post, nitium reprobare.
Singula namque minima corpora, qualis videtur minimus puluis terrae, de singulis
mundis assumpta, et modo praedicto ad inuicem cumulata, vuniuersum locum,
situm, spacium, seu vacuum verum vel irnaginarium totaliter occuparent. Vbi ergo
hospitarentur alia corpora plura incomparabiliter et maiora? quomodo
contenarentur illa situ minori, et non totale spatium vniuersum totaliter occuparent?
Quomodo etiam cubi illi, partes ﬁli, seu corpora minima de mundis singulis nunc
collecta, et sphaerice cumulata non prius occurabunt tantum spaciurn, quantum

modo spacium vniuersum? et quomodo nunc occupant spacium amplius, quam tune

282

fecerunt? praesertim cum secundum doctrinam Geometrarum certissimam, sphaera
sit capacissima ﬁgurarum."

22 Ibid., p. 126, E: "Inﬁnito namque simpliciter maius esse non potest, sed
secundum‘quid tantum, et secundum quid ﬁnite."

23 Ibid., p. 130, D: "Nee potest quis vlterius ﬁngere cauillando, quad tam B
quam C secundum quid est inﬁnitum, et secundum quid ﬁnitum, sicut secundum
' sententiam Aristotelis, partes praeterita et futura temporis simpliciter inﬁniti, quas
copulat praesens instans; quia inﬁnitum intensiue quantumlibet modicum
remittatur, est simpliciter et omniquaque ﬁnitum intensiue: vt patet de caliditate
posita inﬁnita intensiue, quae si quantumlibet remittatur, necessario est simpliciter
omniquaque ﬁnita; Finitur enim superius intrinsece ad certum gradum ﬁnitum, et
inferius extrinsece ad non esse caliditatis, sicut et quaelibet forma intensibilis
terminatur."

24 Ibid., p. 131, B: "Ideo fortassis dicetur quod Deus non potest facere
creataram, quae sit ex se necesse esse et aetema, quare nec Deum. Sed etsi non
possit facere creaturam istas virtutes seu proprietates habere, faciat ipsam habere
omnes alias virtutes possibiles creaturae, et quamlibet simpliciter inﬁnite."

25 Ibid., 1, 26, p. 251, A: "Hie autem in mediastino pro praecedentibus et
sequentibus ostendendum, totum vniuersitatem rerum omnium esse bonam, nec
esse in ca aliquid quod sit malum. Huius enim oppositum Empedocles, Pictagoras,
Manes, Manichaei haeretici dicere videbantur, sicut 18a pars Corollarij primir
docet. Omne sequidem per se volubile et amabile a bono sapiente, est aliqua modo
barium, vt tam Philosophi, quam Theologi partier contestantur: et quaelibet pars
mundi est per se volubilis et amabilis a Deo, sicut ct per se creabilis, et conseruabilis
est ab co, sicut ex capitulis 2.3.6.8.&9. poterit apparere."

2° In fact, says Bradwardine, the act of applying reason to the Observation Of

the natural world, as Aristotle had done, is one of the best ways of arriving at an

283

understanding of God’s inﬁnite goodness. See, for example, De causa Dei, I, 11, p.
198, C-D: "Dicit enim Philosophus 4. Metaph 9. quod hoc est primum principium
complexorum, Idem simul inesse, et non inesse eidem, et secundum idem est
impossibile; sed ne tanto Philosopho tantillus videar obgarrire, sciendum quod
duplex est principium, cognosccndi scilicet et essendi, vel, quoad nos et quoad
naturam; Ipse autem loquitur ibi de primo principia cognosccndi, et apud nos
tantum, per quod generaliter in omnibus scientijs regulamur, sicut processus textus
et comment. satis ostendit. Principium autem complexorum primum simpliciter est
de Deo vt puta Deus est, vel Deus scit omnia, vel Deus vult omnia, vel aliquid
quicquam tale."

27 Ibid., I, 1, part 13, pp. 8-10.

28 Ibid., p. 10, A: "Nulla ergo res temporalis, generabilis, corruptibilisue est
Deus."

29 Ibid. "0 miserabiliter miscrabilis, miser homo, si tamen homo, cur non
verecundaris naturam irrationalem naturaliter viliorem, ignobiliorem,
imperfectiorem ct tibi subiectam adorare et colere pro Domine Deo tuO? cuius
etenim animus non praeponit Deum suum sibi ipsi, et omnibus alijs in ordine
dignitatus. . . ."

3° Leff, pp. 48-49. Bradwardine compares God’s causality to that Of an
architect who transforms the idea Of a house into an actual physical Object in De
causa Dei, I, 2, p. 154, B: "Imaginare itaque in mente Architecti formam domus
fabricandae quam solummodo respicit, vt ad eius imitationem domum faciat, et
imaginare cum hoc per impossibile ipsius voluntatem ita potentem, quod se sola
applicct materiam formandam in domum; et imaginare cum his quod materia
domus esset ﬂuida, nec posset pcrmanere in forma recepta in se, si separatctur a
forma in mente Architecti, sicut aqua ﬁgurata sigillo argenteo, separato sigillo,

statim amitteret ﬁguram receptam. Imaginare itaque voluntatem artiﬁcis

284

applicantem materiam domus ad formam in mente sua, non solum vt sic formetur in
domum, sed quamdiu domus manet in esse domus, vt formaliter in esse seruetur.
EO itaque modo quo forma huiusmodi in mente Architecti esset forma domus, est
ars siue sapientia, siue verbum omnipotentis Dei, forma omnium creaturum; Ipsa
enim simul est examplar efﬁciens, Formans, et in forma data conseruans. Et infra
dicit aetemam Dei sapientiam sic esse formam omnium, velut si imagineris ﬁguram
sigilli argente vitam et intelligentiam, intelligentem se volentemque ﬁguare ad sui
imitationem simultudinem magis minusue expressam ceram ﬂuidam, non potentem
per se pcrmanere in aliqua ﬁguratione recepta, ipsaque hac sola 'voluntate
informem ct ﬂuidam ceram ad se moueret, sibique applicaret, ct sic suam
simultudenem aliquantam imprimeret, et impressam seruaret; sic aetema Patris
sapientia est forma omnium."

31 See, for example, De causa Dei, 1, 2, p. 147, B-C: "Quare et Chrysostomus
istud expondendo, homilia 2a sic ait; Ferens, inquit, omnia hoe est gubemans;
siquidem cadentia et ad nihilum tendentia contenit. Non enim minus est continere
mundum quam fecisse; sed si oportet aliquid audacius dicere, adhuc amplius est.
Nam in faciendo quidem ex nullis existentibus rerum essentiae productae sunt; In
continendo vero, ea quae facta sunt, ne ad nihilum redeant, continentur. Hic ergo
dum reguntur, et ad inuicem sibi repugnantia coaptantur, magnum et valde mirabile
plurimumaeque virtutis indicium declaratur. Dicitque Augustinus in De diuinitatus
Dei essentia, et de inuisibilitate, atque incommutabilitate, 1° sic de Deo; Procu
dubio nullus est locus ab eius praesentia absens: Super omnem quippe creaturam
praesidet regendo, subtus est omnia sustinendo atque portando, non pondere
laboris, sed infatigabili virtute; quoniam nulla creatura ab eO condita per se
subsistere valet, nisi ab eo sustinetur qui earn creauit; extra omnio est, sed non

exclusus, intra omnia est, sed non conclusus."

285

32 Ibid., p. 154, E: "An forte et hoc est quod Deus sciscitanti Moysi nomen
eius, velate respondit, Ego sum qui sum, sic dices ﬁlijs Israel, Qui est, misit me ad
vos. Exod. 3 quasi velit innuere se esse seipsum simpliciter per seipsum, et se etiam
esse quodammodo totum ens, essentiﬁcando videlicet alia vniuersa."

33 Ibid., I, 1, part 40, pp. 139-40, E-A: "Ex his omnibus potest cuilibet sobriO
non proteruo rationabiliter apparere, mundum nedum habuisse principium
temporale, verum et fuisse creatum ex nihilo. Ex qua namque materia ﬁeret
praecedente? qualis esset illa, simplex, vel composita; aetema vel nova? Quare et
tu, Aristoteles, multum rationabiliter saepe probas, mundum non fuisse factum ex
materia praeiacente? Quid ergo consequentius consequentia naturali, quam
concesso mundum habuisse principium temporale, concedere ipsum fuisse creatum
ex nihilo consequenter?" See Oberman, pp. 53-54.

34 Ibid., 1, 7, p. 189, C: "Deus enim scit omnia simul ct semper, non per vices
temporum; sicut ipsa scita incipiunt esse, vel desinunt more humana, quoniam apud
ipsum non est transmutatio, nec vicissitudinis Obumbratio." See Oberman, p. 54.

35 Ibid., 1, 6, p. 183, C: "Quare ct Auicenna 4. de Anima 2. dicit, Omnia quae
in mundo sunt praeterita, praesentia, et futura, habent esse in sapientia creatoris."

3° Ibid., E: "Et Si ipsi habuerunt scientiam huiusmodi saltem paruarn, vel
qualemcunque coniecturam tenuissimam, verum tamen, quis nesciens, seu potius
insaniens Deum audebit asserere nescium futurorum; cum per primam
Suppositionem, tertiam partem, et quartam Corollarij primi huius, necessario
consequatur ipsum ea cognoscere perfectius inﬁnite. Amplius autem Si Deus
secundum praemissa habet scientiam omnium praesentium, praeteritorum, ct
similiter futurorum, cum scire actualiter ct particulariter, distincte et certe sit
perfectius, quam scire tantum habitualiter, potentialiter ct vniuersaliter, confuse et

incerte."

286

37 Ibid., p. 184, A: "Quod Deus habet distinctam scientiam omnium, nedum
praesentium, praeteritorum et futurorum: verum et omnium possibilium et
impossibilium, imaginabilium et cognoscibilium quouismodo, unde et omnisciens,
sicut et omnipotens veraciter dici potest."

38 Ibid., III, 51, p. 826, B-C: "Constat siquidem secundum Philosophorum
sententiam, quod mensura debet esse vnigenita ct similis mensurato: homo autem
mutabilis est, ct actiones eius mutabile, quare et mensurantur mensura mutabili,
scilicet temporali, ipso videlicet tempore vel instanti: Deus vero, et quaelibet actio
eius intrinseca, puto cognito et volutio, immutabilis est omnino, sicut quintum et
vicesimum tertium primi docent; quare nee Deus, nec aliqua actio eius intrinseca
per se immediate et proprie mensuratur mensura mutabili, scilicet tempore vel
instanti, sed mensura immutabili, inuaribili, stabili, et aetema, seu potius ipsa
aeternitate immutabiliter penitus, insuccessibiliter, vniforrniter atque stabiliter
permanente. In ipsa namque nulla diuisibilitas, nulla maioritas, nulla minoritas,
nulla prioritas, nulla posterioritas, nulla mutabilitas, nulla accessio, nulla recessio,
nulla successio, nihil praeteritum, nihil futurum, nec vlla penitus differentia
successiua, sed indiuisibilis, simplex, vnica, eadem, insuccessibilis, ac instantanea
praesentialitas et simultas, sicut ostenditur primo primi, imo superindiuisibilis,
supersimplex, superunica, supereadem, superinsuccessibilis, ac superinstantanea
praesentialitas et simultas temporalis instantis."

39 Ibid., p. 827, A-B: "Vnde Plato 1. Timei 9. vtens aeuo pro aeternitate sic
ait, Dies et noctes ct menses et annos, qui ante coelestem exordinationem non
erant, tune nascente mundo iussit existere, quae omnia partes sunt temporis, nosque
haec cum aeuO assignamus eidem solitariae naturae, non recte partes indiuiduae rei
singimus. Dicimus enim fuit, est, erit; At illi solum esse competit iuxta veram sui

certamque rationem, fuisse vcro deinceps et fore non competit; haec quippe

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geniturae temporis propria. Motus enim sunt, vnus praeeuntis, alter imminentes
non aeui sed temporis."

4° Ibid., D: "Tempus ﬂuxibile sequitur ﬂuxibilem actionem, scilicet motum
coeli; sic aeternitas stabilis sequitur stabilem actionem, scilicet esse Dei, ct ab ipsa
quodammodo deriuatur, deﬂuit et emanat. Sicut enim punctus ﬂuens lineam, et
instans tempus; sic et Deus instans stabilissimus per actum suum veluti quendam
ﬂuxum videtur aeternitate causare, et hoc maxime apud cognitionem humanam,
quae secundum Philosophum in de memoria et reminiscentia, non sit sine continua,
nec sine ratione temporis atque motus, licet in Deo nullus sit ﬂuxus mutabiliter, aut
temporaliter successiuus."

41 Oberman, p. 54.

42 For a full discussion of the implications Of the notion of absolute power in
late medieval theology and natural philosophy see Edward Grant, "The
Condemnation of 1277, God’s Absolute Power, and Physical Thought in the Late
Middle Ages," Viator, 10 (1979), pp. 211-44. Grant attibutes the upsurge of
speculation on such topics as whether God can undo the past or create more than
one world to a response to the condemnations which claimed that Aristotelian
natural philosophy restricts the scope of God’s power.

43 See above, Chapter Six, note 62. Goddu, p. 8, argues that Ockham’s
tendency to separate natural philosophy and theology stemmed form his deeply held
convictions about the necessity Of protecting faith from over-zealous reasoning:
"For Ockham the issues concerning the relation of faith and reason, theology and
science were expressed typically with utter clarity, although the strength of the
analogy of science and theology was too strong for him to discard it altogether. But
Ockham’s characterization of theology as a science was an attempt to restrict
theology to a niche safe from questionable metaphysical entities and logical

criticisms. . . . By analytical inquiry Ockham demonstrated that philosophy was »

288

incompetent to deal with matters of theology, and freed philosophy even further for
the examination of the natural world."

44 Oberman, p. 52.

45 Copelston, p.258.

4° Ibid. Bradwardine’s opposition to certain younger contemporaries, such
as Robert Holcot, Thomas Buckinghan and Adam Wodeham, stems from their
tendency to go beyond Ockham’s rather moderate treatment Of the problem of
contingency to a much more radical contingency. All three Of these theologians
used logical and grammatical arguments to safeguard human freedom against rigid
determinism. Their main similiarity to Ockham was their use of the concept of
God’s absolute power to question the capacity of human reason to determine the
truth about God and the natural world. Unlike Bradwardine and Ockham, they did
not generally try to approach contingency from a cosmological perspective. Thus
their opinions shed little light on Bradwardine’s use of time as a factor in
contingency. Not being a logician and preferring a cosmological approach,
Bradwardine dismissed many of their arguments. J. A. Robson suggests, however, in
Wyclif and the Oxford Schools, pp. 48-49, that Bradwardine may have persuaded
Buckingham, a fellow Mertonian, to moderate his approach to contingency. For a
fuller treatment of this issue, see Chapter Eight below. For discussions of Holcot’s
view of contingency, see Normore, pp. 373-74; Paul A. Stretveler, "Robert Holkot’s
View of Contingency: A Preliminary Account," Studies in Medieval Culture, 8-9
(1976), pp. 163-71; Leff, pp. 216-227; and Oberman- PP- 43-46. For Wodeham, see
Leff, pp. 241-54, and Oberman, PP- 46-48.

47 Normore, p. 369.

48 Ibid., pp. 372-73.

49 Both Oberman (p. 54) and N ormore (p. 374) emphasize this point.

289

50 See De causa Dei, III, 50, p. 810, C-D, in which Bradwardine cites his
favorite authorities, including Aristotle, Grosseteste, Boethius and Anselm.

51Ibid, I, 14, p. 209, E: "Si Deus esse desineret, nihil esset praeteritum, nee
futurum, verum nec falsum, possibile vel impossibile, necessarium vel contingens,
nee etiam posset esse: ex quO et oppositum sequitur euidenter, scilicet ipsum Deum,
et Sic aliquid praefuisse, esse et fore, ct similiter alia posse esse per omnipotentiam
Dei magnam. O quam necessarium est hunc esse, quem tam impossibile est
desinere vnquam esse, et quod Deum qualitercunque non esse, contradictionem
necessarissime continet et importat; et quod necesse esse, videtur maxime proprium
nomen Dei." See Normore, pp. 374-75.

52 De causa Dei, III, 52, p. 857, B: "Respondebitur forsitan, quod ex
praeteritione rei praeteritae oritur quaedam relatio, qua necesse est simpliciter
illam fuisse, quare impossibile est simpliciter illam non fuisse. Sed hoc reprobatum
est prius, quando monstrabatur ‘A’ non fuisse, nullam contradictionem formaliter
implicate. Illam etiam relationem, non est necesse simpliciter esse vel fuisse;
Aliquando enim non fuit; quare nec repugnaret formaliter eam nunc non esse; ergo
nihil facit necessarium simpliciter. Illa quoque relatio vel est ad Deum, seu ad
voluntatem diuinam, vel rem aliquam naturalem seu res aliquas naturales. Primum
erat destructum per 30um huius; Secundum Stare non potest." Also III, 53,
proposition 23, p. 875, D: "Quad cum futura contingentia ﬁant praesentia, aut in
praeteritum dilabuntur, voluntas diuina respectu illarum non desinit esse libera
aliqua libertate, seu aliqua modo libertatis intrinsecus, qua vel quo prius fuerat
libera, nec incipit esse necessaria aliqua necessitate opposita respectu ipsorum."

See also William J. Courtenay, "John of Mirecourt and Gregory of Rimini on
Whether God Can Undo the Past," RTAM, Part II, 40 (1973), pp. 149-50. In taking
this position, Of course, Bradwardine found himself at odds with prevailing scholarly

opinion. Courtenay analyzes the debate over whether God can undo the past, which

290

reached its climax in Paris in the late 13405. Although Bradwardine was not directly
involved in the Paris condemnations of 1347, the theory that the past is no more
necessary than the future was criticized by some theologians as being too
deterministic. Courtenay describes Mirecourt’s attempt to reach a middle ground
between Bradwardine’s view that God can freely undo the past and Thomas
Buckingham, who insisted that the past cannot be changed even by God.
Mirecourt’s solution was to argue that God was initially free to make the past in any
way he wished, but he cannot change the past once it has occurred (see especially
Part II, pp. 147-54). Here again, the heart of the problem seems to be the difﬁculty
of relating God’s experience in his eternal present to the human experience of time.
In Bradwardine’s view, Mirecourt’s solution would afﬁrm his own idea that God can
freely act within his creation. When he says that God could alter a past event
without contradiction, Bradwardine is stressing that God’s will is not temporally
limited: even if God "changes his mind," he is not bound by the before-and-after
which is inherent in change in the created world. Mirecourt reﬂects sympathy with
the philosophical impulse of his age to think that God somehow is able to change
through time without impairing his fundamental attribute of immutability. For a
more thorough treatment of this particular issue, see also M. Jean-Francois Genest,
"La liberté de Dieu a l’égard du passe selon Pierre Damien et Thomas
Bradwardine," Annuaire de I ’écale pratiquc des hautcs études, 85 (1977-78), pp. 391-
93.

53 De causa Dei, I, 24, p. 243, D: "Deus autem ex sua inﬁnitissima claritate
comprehendit omnes res particulares, et omnes particulas temporis, sicuti sunt,
verissime per seipsum: Non enim indiget comparatione vel relatione praeteritorum
vel futurorum ad praesens instans, more inﬁrmitatis humanae, sed intelligit omnia
simul et praesentialiter acque clare; et hoc est, quia non scit per tales propositiones

verbalcs mutabiles, sed per suam essentiam, ct propriam voluntatem, quae semper

291

vniformiter, et inuariabiliter omnia repraesentant. Quemadmodum si poneretur
visus punctualis quiescens in centro coeli circumuoluti, et videret per extramissione
et actiue non passiue, sicut Deus res videt; videret semper vniformiter, sine omni
mutatione sui, circumgiratas continue singulas partes coeli, et eandempartem nunc
in oriente, nunc in meridie, nunc in occidentc: Sic et Deus omni eodem modo ex
parte sui intrinsece videt aliquid prima futurum, secundo praesens, tertio vero
praeteritum; et hoc est quia non videt patiendo quicquam a visis, seu passiue sed
agenda potius seu actiue, sicut superius est ostensum." See N ormore, p. 375.

54 De causa Dei, III, 1, p. 637, D-E: "In primis igitur ostendendum, Deum
posse necessitare quodammodo omnem voluntatem creatam ad liberum, imo ad
libcrrimum actum suum, sirnilemque cessationem et vacationem ab actu. Deus
enim potest velle voluntatem creatam produccre liberum actum suum, et hoc
antecedenter, et prius naturaliter voluntate creata; quare et per 10. primi, illa de
necessitate Obediret, et hoc, quamdiu Deus sic voluerit ipsam velle. . . . Quoniam
enim quod Deus vult, non potest non esse, cum vult hominis voluntatem nulla cogi
vel prohiberi necessitate ad volendum vel non volendum; et vult effectum sequi
voluntatem, tune necesse est voluntatem esse liberam, et esse quod vult." See Leff,
p. 98.

55 As creator and ﬁrst cause, God has an understanding of the universe too
perfect for created beings to comprehend. See De causa Dei, 1, 12, p. 201, B:
"Quamdiu igitur corpus quod corrumpitur, aggrauat animam, et terrena habitatio
deprimit sensum plurima cogitantem, non potest homo intelligere Deum perfecte
sicuti est, ipsom et dicente Mosi deprecanti. Non poteris videre faciem meam, non
enim videbit homo, et viuet, Exod. 33. Quare secundum Philosophum, 1. Physic. ct
alibi; Innata est nobis via a notioribus nobis ad notioria naturae, quae sunt
simpliciter notioria, a posterioribus siclicet ad prioria, et a causatis ad causas.

Nomina igitur quibus Deum cognoscimus, non Significant ipsum per se essentialiter,

292

et penitus absolute, quoniam a creaturis, et effectibus notioribus nobis transferuntur
ad ipsum ignotiorem nobis, licet simpliciter notiorem."

5° Bradwardine develops at considerable length the connection between
necessity and free will in De causa Dei, III, chapter 2, pp. 444-48. In a corollary to
this chapter Bradwardine makes the point that the human will is free to choose from
the possibilities which God makes available to it, p. 448, D-E: "Corollariuni, quod
non ideo dicitur liberum Arbitriurn, quia libere 'potest velle ct nolle quodcunque,
sed quia libere potest velle quodcunque obiectum suum volubile, et nolle
quodcunque obiectum suum nolubile; sicut si visus esset potentia libera, non ideo
tamem posset videre sonam, et visibilia sua tantum. . . . Nec ideo dicitur liberum
arbitrium quia libere potest in oppositum cuiuslibet actus sui, vt praemissa
demonstrant, sed quia ex rationali arbitrio siue iudicio spontance illum agit, Sicut
primum huius ostendit. Nec ideo dicitur liberum arbitrium quia libere potest
benefacere ct peccare, sicut ex praemissis consequitur euidenter, sed propter
causam proximo assignatam."

57 De causa Dei, 1, 27-29, pp. 261-271.

58 Ibid., 1, 28, p. 266, D: "Fatum vero inhaerens rebus mobilibus dispositio,
per quam prouidentia suis quaeque nectit ordinibus. Prouidentia namque cuncta
pariter quamuis diuersa, quamuis inﬁnita complectitur; Fatum vero Singula digerit,
in motu, locis, formis, ac temporibus distributa, vt haec temporalis ordinis explicatio
in diuinae mentis adunata prospectu, prouidentia sit; eadem vero adunatio digesta
atque explicata temporibus, Fatum vocetur, quae licet diuersa sint, alterum tamen
pendet ex altero."

59 I, 30, p. 271, E: "Quod res voluntariae diuinae prouidentiae legibus
gubemantur."

6° Leff, p. 104.

293

61 De causa Dei, III, p. 685, B-C: "Ponamus igitur simul esse praescientiam
Dei, quam sequi necessitas futurarum rerum videtur, et libertatem arbitrij, per
quam multa sine vlla necessitate ﬁeri creduntur. . . . Sed si aliquid est futurum sine
necessitate, hoc ipsum possit praescire Deus, qui praescit omnia futura; quad autem
praescit Deus necessitate futurum est sicut praescitur; necesse est igitur aliquid esse
futurum sine necessitate, vel praesciri sine veritate. Nequaquam ergo recte
intelligenti nomen, repugnare videntur praescientia, quam sequitur haec necessitas,
et libertas arbitrij, a qua remouetur necessitas, quoniam et necesse est, quae Deus
praescit, futura esse, et Deus praescit aliquid esse futurum sine omne necessitate."
See Leff, p. 104.

62 leff, pp. 104-5. Leff cites De causa Dei, III, 50, p. 823, A: "Corollarium,
quod omnem actum volutionis ct cognitionis diuinae praescntem necesse est,
necessitate sequente praedicta, semper fuisse, et similiter semper fore; quare et
quod omnia, quae pracsentialiter sunt, ﬁunt aut eueniunt, simili necessitate sunt,
ﬁunt ct eueniunt in praescnti; et quod omnia quae euenient, simili necessitate in
futuro; imo et quod omnia quae nunc ﬁunt, dc aliqua necessitate praecedente nunc
ﬁunt; et quod omnia, quae eueniunt, de aliqua necessitate precedente, euenient in
futuro." _

63 Leff, pp. 105—6.

64 Ibid., pp. 106-7.

65 De causa Dei, III, 52, p. 843, E: "Quod Deus vult, non potest non velle,
quia aliter sua voluntas esset mutabilis."

66 Leff, p. 108. Leff cites De causa Dei, III, 52, p. 841, A-B: "Sic forte in
Deo, vbi non est aliqua temporalis praecessio sed causalis, si respiciatur ipsa Dei
natura non in ratione agendi, et comparetur liberae voluntati hominis nudae ab actu
antequam velit, verum erit dicere, Deus potest non velle quod vult: Si verO

respiciatur ipsa diuina natura in ratione agendi, et comparetur liberae voluntati

 

294

hominis cum iam actu vult, verum erit dicere, Deum necesse est velle quod vult, et
non velle quod non vult: Impossibile est enim cum non velle quod vult, vel velle
quod non vult. Quam distinctionem facit in nostro posse et actu prioritas temporalis
hanc ibidem facit prioritas causalis et subiecti super quad redit praedicatio diuersa,
diuersa consideratione, sed manifestior est distinctio vbi cornitatur prioritas
temporalis."

67 Oberman, p. 65.

53 Ibid. Quoted from The Essentials of Thesz (London: Sheed and Ward,
1949), p. 123.

69 Oberman. pp. 66-67.

70 Ibid., p. 70.

71 Ibid., p. 71. The similarities between Anselm’s and Bradwardine’s
conception of God’s eternal knowledge are spelled out most explicitly in
Bradwardine’s analysis of eternity in De causa Dei, III, 51, pp. 826-31. See especially
the corollary to Book III, chapter 51, p. 830, D: "Huius autem transumptionis causa
est, quia non habemus verbum signiﬁcans proprie aeternitatis stabilem mansionem,
quare necessario cogimur transferre secundum similitudinem qualcmcunque verba
nostra temporalia secundum differentias quaslibet temporales ad aeternitatem ct
Deum aetemum, actusque suos intrinsecos coaetemos, quia omni tempori
coexistunt, nec vlli tempori defuerunt aut desunt, vel deerunt in futuro. Huic autem
testimonium perhibet Anselmus de Concord. 3. Propositium, inquicns, secundum
quod vocari sunt Sancti in aeternitate, in qua non est praeteritum vel futurum, sed
tantum pracsens, immutabile est in aeternitate: non enim fuit aliquid, aut erit
aliquid, sed tantum est."

72 In support of these points, Oberman cites De causa Dei, II, 30, pp. 578-97;
here Bradwardine explains at great length how God leads the human will without

forcing it consciously to follow a particular path.

 

 

 

295

73 Oberman, p. 72, says nevertheless that Bradwardine turned the ideas of
Anselm and Aquinas in new directions and Often away from the orthodox position..

74 Ibid., pp. 73-75.

75 Ibid., p. 76.

76 Ibid. ,

77 "Free Choice and Liberty According to Thomas Bradwardine,"
Dissertation, University of Toronto, 1965.

78 Ibid., p. 179.

79 Ibid., p. 71. See De causa Dei, 1, 19, p. 226, B: "Neque nonum procedit:
N on enim Deus arguitiue tantum, et non intuitiue scit futura, sicut Astrologus
calculator inclusus scit eclipsin futuram vel praesentem supra horizontem proprium,
vel sub illo, per certam demonstationem, non per claram intuitionem; Sed sicut
videns Solum, videt eum per specium eius receptam in oculo, priorem naturaliter
visione et causam illius, Sine quolibet argumento."

80 See above, note 50.

81 McCarthy, p. 3. See also p. 17 for a discussion of Augustine and p. 65 for
a discussion of Scotus.

82 For a recent comprehensive study of the problem of evil and sin in late
medieval thought see "Philosophy of Mind in Action" and "Ethics," Parts VIII and IX
of CHLMP, pp. 593-719.

83 De causa Dei, 1, 26, p. 251, B: "Omne siquidem per se volubile et amiabile
a bono et sapiente, est aliqua modo barium, vt tam Philosophi, quam Theologi
pariter contestantur. . . . Item omnis veritas est bona, quia recta, iusta, et sancta; et
omnis essentia est veritas. . . ." See Oberman, p. 124.

84 Ibid., p. 255, E: "Item si actus adulterij et homicidij per se sint mali, cum
actus secundum essentiam similis sit in coniugatis, et non coniugatis, in innocentibus

et reis mortis, erit et peccatum in istis." See Oberman, p. 125.

 

296

85 Ibid., 11, 2, p. 448, D: "Corollarium, quod non ideo dicitur liberum
arbitrium, quia libere potest velle et nolle quodcunque, sed quia libere potest velle
quodcunque obiectum suum volubile, et nolle quodcunque obiectum suum
nolubile." And ibid., p. 447, B-C: "Et credo quod posset saltem per accidens, si
videlicet nolendo et respuendo aliquod paruum bonum posset consequi aliquod
maius bonum, vel vitare aliquod maius malum, Sicut et potest velle malum. . . ." See
Leff, p. 92.

36 Leff, p. 58.

87 De causa Dei, 1, 12, p. 200, D: "Est etiam causa illius quia, enim bonum
est bonum, ideo non est malum, et non e contra; quia non esse malurn, penitus nihil
ponit, et per consequens nihil causat. Primum ergo principium complexorum
nullatenus negatiuum, sed afﬁrmatiuum ﬁrmiter arbitrandum." See also I, 34, p.
294, D: "Deus ergo est causa huius veritatis, et non nisi voluntarie. Vult ergo Deus
hanc esse veram, Peccatum est."

88 Ibid., 1, 34, pp. 295-96, E-A: "Sic igitur et omnium constitutionem, Coeli,
dico, et terrae vndiquc totius permixtarn, maxime contrariorum principiorum vna
decorauit harmonia, siccum humido, calidum frigido, graue leui, rectum circulato
decorauit: totam terram, et mare, aetherem, atque Solem et Lunam, et totum
caelum decorauit vna, quae per omnia transit virtus; ex immixtis et diuersis, ex acre,
terra, igne et aqua totum orbem creans et disposens vnius sphaerae superﬁcae; ac
maxime contrarias in ca naturas cogens adinuicem concordare, et ex hic ingenians
vniuerso salutem." See Leff, p. 60.

89 According to Oberman, p. 129, Bradwardine followed traditional
interpretations of the Old Testament, where, for example, God allowed the election
of King Nebuchadnezzar as a means for punishing sinners and vindicating the
righteous.

9° Oberman, p. 128.

297

91 De causa Dei, I, 47. Trans. Paul L. Nyhus in H. A. Oberman, Forerunners
of the Reformation: The Shape of Late Medieval Thought Illustrated by Key
Documents (London: Lutterworth Press, 1966), p. 158. See Saville edition, p. 438,
D.

92 Oberman-Nyhus, p. 154; see Saville edition, p. 437, B-C.

93 Ibid., p. 162; see Saville edition, p. 441, A.

94 Ibid., p. 161; see Saville edition, p. 440, E.

95 "The Senna Epinicius," pp. 295-306.

298

CONCLUSION

1 Of course Bradwardine admitted that one could have general knowledge
about the future but he denied that one could transform general knowledge Of the
future into certain knowledge through logic or any other means. For example,
Bradwardine acknowledged the usefulness of astronomical prediction but he did not
think that the prediction of astronomical events in the future constituted certain
knOwledge of the future since the prediction could only be veriﬁed by those events
taking place. Similarly he believed in the truth of divine revelation but he
considered it impossible for the human mind to determine how and when a given
prophesy might be fulﬁlled.

2 The essentially conservative nature Of Ockham’s thought is an underlying
theme in Marilyn McCord Adam’s extensive William Ockham (Notre Dame,
Indiana: University of N Otre Dame Press, 1987).

3 Leff, p. 18. See Introduction, note 3.

4 See Murdoch, "From Social to Intellectual Factors," pp. 271-72.

5 William J. Courtenay, "John of Mirecourt and Gregory of Rimini on
Whether God Can Undo the Past," Part I, RTAM, 39 (1972), p. 231.

6 History of Christian Philosophy, pp. 498-99.

7 Ibid., pp. 499-500.

8 Ibid., p. 498.

9 Ibid., p. 489.

10 Ibid., p. 501.

11 Bradwardine and the Pelagians, p. 131.
12 Ibid., pp. 131-32.

13 Robson, pp. 41-43.

14 Leff, pp. 228-30.

15 Ibid., p. 234.

299

1° Robson, p. 32.

17 Robson, p. 53, quotes and translates this passage from Buckingham’s
Quaestianes, New College, Oxford MS 134, F0. 327ra. See De causa Dei, III, 5,
corollary 13, p. 657, E.

18 Robson, p. 52.

19 F0. 335ra of Quaestianes, trans. Robson, pp. 57-58.

20 Robson, p. 58.

21 F0. 338rb-va of Quaestianes, trans. Robson, p. 58. See above, note 18.

22 For the subtle differences between Buckingham’s and Ockham’s views on
God’s capacity to undo the past, see, for example, Adams, William Ockham, pp.
1225-27.

23 In "Thomas Buckingham’s Ostensia Meriti Liberae Actionis, Conclusions 1-
15: ‘De Contingentia Futurorum er Arbitrii Libertate’: An Edition and Study"
(Dissertaion, University of Toronto, 1979), Bartholemew Ruben De La Torre
examines Bradwardine’s interaction with Buckingham on the issue of future
contingents. De La Torre suggests that parts of Buckingham’s sentence commentary
and the ﬁrst part of the Ostensia Meriti Liberae Actionis were direct replies to the De
causa Dei. Buckingham, who might have been Bradwardine’s student (see pp. 132,
note 19), rejected Bradwardine’s deﬁnition of antecedent necessity and tried to ﬁnd
a "Catholic middle way" between extreme determinism and the indeterminacy
advocated by Cicero and, to a lesser extent, by Pelagius (p. 89). Since De La Torre’s
analysis of the ‘De Contingentia Futurorum et Arbitrii Libertate’ supports Robson’s
conclusions about Buckingham’s relationship to Bradwardine without substantially
adding any new material relevant to Bradwardine’s view of time, De La Torre’s
study does not feature in the body of this dissertation.

De La Torre is not speciﬁc about the actual dating of Buckingham’s writing

as compared to the De causa Dei. He reports, however, (p. 185) a discovery made

 

300

by Zenon Kaluza that Bradwardine and Buckingham probably did not have a public
debate over contingency in Paris which Leff, Oberman and Robson believed had
taken place. In "La preténdu discussion parisienne de Thomas de Bradwardine avec
Thomas de Buckingham: témoinage de Thomas de Cracovie," RTAM, 43 (1976), pp.
209-36), Kaluza demonstrates that Thomas of Cracow, the supposed witness to the
debate, could not in fact have witnessed it since he was born eleven years after the
deaths of Bradwardine and Buckingham. Kaluza argues instead that Thomas of
Cracow was the owner of a manuscript (MS Paris Bib. Nat. Lat. 16409) written by
Stephen of Chaumont who had summarized Bradwardine’s and Buckingham’s
differences on future contingents. According to Kaluza, a misreading of the
manuscript in the early twentieth century gave historians the idea that a public
debate had taken place in Paris, when in fact the communication between
Bradwardine and Buckingham occurred in England over a period of several years.
Moreover, although this communication indicates disagreement on several points, it
does not suggest the personal antagonism which is usually associated with the Paris
debate.

24 Forerunners, p. 133.

25 Pantin, pp. 144-45.

2° History of Christian Philosophy, pp. 500-1.

27 Ibid.

23 Leff, pp. 216-17.

29 Ibid., pp. 218-19.

30 Ibid., p. 226.

31 Oberman, Archbishop Thomas Bradwardine, pp. 45-46.

32 Super Libras Sapientiae, Chapter III, Lecture 35, ed. Heinrich Gran
(Hagenau: 1494), trans. Paul L. Nyhus, in Forerunners, p. 143.

33 Chapter XII, Lecture 145, in Forerunners, p. 149. '

301

34 In "Philosophical Scepticism in England in the Mid-Fourteenth-Century,"
Vivarium, 21 (1983), pp. 56-7, Leonard Kennedy challenges the deﬁnitions of
skepticism commonly used by many historians of the late medieval period and
suggests that mid-fourteenth-century theologians in England were more skeptical
philosophically, if not theologically, than recent Studies of their work indicate.

35 In "Robert Holkot on Future Contingencies: A Preliminary Account," p.
168, Paul A. Stretveler contends that the Augustinian-Boethian solution was actually
very similar to the nominalist one, since the deﬁnition of an eternal idea in the
Augustinian-Boethian tradition corresponds very well to the late medieval deﬁnition
of a proposition as a statement which is always true. If Stretveler is correct, it might
be possible to identify points of agreement between late medieval thinkers on
matters which seem an the surface to be controversial. Again, the main distinction
between an eternal idea and a proposition depends not on the deﬁnition of a
proposition as such but on the different approaches medieval natural philosophers
and logicians took to the temporal factors which affect the truth of propositions.

3° William J. Courtenay, "Recent Work on Fourteenth-Century Oxford
Thought," p. 232.

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