A LOGICAL ANALYStS OF TOLMAN‘S
THEORY OF mm

M huh. Dam of Ph. D.

MICHCGAN STATE WW9“

Joseph Frederick Lambert
E956

THE-f3?“

This is to certify that the
thesis entitled
A Logical Analysis of Tolman's
Theory of Learning

presented by

Joseph Frederick Lambert

has been accepted towards fulfillment
of the requirements for

iii-i. degree in Mphy

fl/éMz/xflm‘z

Wajor professor

[hm September 14, 1956

 

LIBRARY

Michigan State
University

 

 

 

A LOUIQAL Al-~;ALIsIs or Ton-mus

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by

Joseph Frederick Lambert

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submitted to the School of Advanced Graduate
studies of michigan state University of
Agriculture and Applied Science in
partial fulfillment of the
requirements for the
degree of

DOCTOR OF PHILOSOPHY

Department of Philosophy

1956

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A LOGIUAL ANALYSIS CF TULL-LAIE'S

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I'm-Lulu or Lbhlinll-JU

by

Joseph Frederick Lambert

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Submitted to the School of Advanced Graduate
Studies of Michigan State University of
Agriculture and Applied Science in
partial fulfillment of the
requirements for the
degree of

DOCTOR OF PHILOSOPHY

Department of Philosophy

1956

Approved:£”

 

 

The purposes of this essay are two-fold. First, it
will present a legical, or formal construction of Tolman’s
theory of learning. The construction to be offered in this
essay is restricted, by and large, to that version of
Tolman’s theory as explained and illustrated in his book,

Purposive Behaviorism in Animals and Ivan.1 However, in

 

 

the formal develOpment of Tolman’s theory an attempt will
be made to derive certain versions of the so-called latent
learning principle. The latent learning issue has its be-
ginnings in the Blodgett experiment of 1929; the experiment

is discussed in Purposive Behaviorism.2 It is still a burn-

 

ine issue today. The importance of the latent learning ex-
periments for Tolman’s theory of learning cannot be under-
estimated. For they are generally taken to be the most
important of the many experiments which constitute the empi-
rical foundations of Tolman’s theory of learning. Investiga-
tors have questioned whether (in fact) they can be deduced
from Tolman’s theory and hence are in doubt as to whether
they constitute a test of Tolman’s theory of learning.3 The
system in this essay shows that at least some of them are de-

ducible from Tolman’s theory.
Secondly, it will present a critical appraisal of

Joseph Frederick Lambert

 

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Tolman’s theory of learning. This appraisal is initiated by
the problems which arise in the formal construction of
Tolman’s theory. The appraisal is largely methodological in
scepe; in general, it does not deal with empirical or experi-
mental issues. Nevertheless, to a certain extent, these
methodological points derive their plausibility from experi—

mental sources, for example, the latent learning issue.

Finally, it should be understood that the formal system
to be developed in this essay is not a complete construction
of Tolman’s theory. Time and space are invulnerable enemies;
especially when one is working in uncharted surroundings.

The present system though incomplete is more than programma-

tic. This, I trust, will become clear in the ensuing pages.

 

l. Tolman, E. C., Purposive Behavicrism in Animals and Men,
University of California Press, 1932 (Reprinted in 1951).

2. Ibid., pps. h8-50.

3. heehl, P. and NacCorquodale, K. "Edward C. Tolman", in
hodern Learning Theory, Appleton-Century-Crcfts, lQSh,
pps. 127-236.

 

 

 

Joseph Frederick Lambert

A LOGICAL AmALYsis or TCLhAR’S

ThEORY GE LEfithhG

BY

Joseph Frederick Lambert

Submitted to the School of Advanced Graduate
Studies of nichigan State University of
Agriculture and Applied Science in
partial fulfillment of the
requirements for the
degree of

DOCToH by P I‘csoiry

‘ Department of Philos0phy

1956

 

TABLE OF CONTENTS

 

 

Page
Preface iv
Chapter I -- Introduction 3
I
The Logically Organized System 3
Outline of the System of Principia Mathematics h
Definition of Formal Organization 7
II
The Rejection of the Argument from.Precision 9
The Utility of Formal Organization 13
Variables and Symbolization 13
The Argument from.Intuition and Calculation 15
The Argument from Prediction 16
The Argument from."Mathematization" 18
New Information 20
III

The Function of Intervening Variables 22

Chapter II -- Primitive Ideas and Definitions of
System TI 28
General Apparatus 28
Goal-Objects and States-of—Affairs 3h
The Primitive Idea of Demand hS
The Primitive Idea of Expectation #8
The Primitive Idea of Sensory Reception 57
The Peritive Idea of Response Tendency 65
Two Concepts of Docility 70
A List of Primitive Ideas 7h
The Definitions of TI 75
Chapter III -- Postulates and Theorems of System TI 81
A Replacement Rule in TI 95
Proof Procedures in TI 99
The Theorems of T1 103
Group A: Consequences of the Definitions 103
Group B: Consequences of the Postulates 108
Chapter IV -- System TII 123
Time Arguments in the Formulae of TII 123
Primitive Ideas of TII 129
Procedures and New Symbols in TII 132
The Definitions of TII 133
The Postulates of TII 139
The Theorems of TII 156
Chapter V -- Reexamination of the Present System 173

I

The "Core" System.and the "Courtesy" System. 173
Further Advantages of the Present System. 182
Extension of the Present System. 189

ii

Inadequacies of the Present Symbolism
Expectation Reexamined
The Nature of Natural Necessity

Bibliography

II

iii

Page

197
199
20a

211;

iv

PREFACE

The Purposes of the Essay

 

 

The purposes of this essay are two-fold. First, it will
present a logical construction of Tolman’s theory of learning.
The construction to be offered in this essay is restricted,
by and large, to that version of Tolman’s theory as explained

and illustrated in his book Purposive Behaviorism lg Animals

 

egg Eggpl however, in the formal deveIOpment of Tolman’s
theory an attempt will be made to derive certain versions of
the so-called latent learning principle. The latent learn-
ing issue has its beginnings in the Blodgett experiment of

1929; the experiment is discussed in Purposive Behaviorism?

 

The importance of the latent learning experiments for Tolman’s
theory of learning cannot be underestimated. They are gene-
rally taken to be the most important of the many experiments
which constitute the empirical foundations of Tolman’s theory
of learning. Investigators have questioned whether (in fact)
they can be deduced from Tolman’s theory and hence are in
doubt as to whether they constitute a test of Tolman’s theory
of learning.3 The system in this essay shows that at least

some of these experiments are deducible from Tolman’s theory.

 

l. Tolman, E. C., Purposive Behaviorism in Animals and Men,
University of California Press, 1932 Tfieprinted in 1951).
Hereafter, this source will be referred to in the body of
this essay as Purposive Behaviorism.

2. ,Ibid,, pp. h8-SO.

'heehl, P. and MacCorquodale, K., "Edward C. Tolman", in

hodern Learning Theory, Appleton-Century—Crofts, 195h,

pp. 127-266.

 

 

 

b.)
o

Secondly, this essay will present a critical appraisal
of Tolman’s theory of learning. This aspect of the essay
is a consequence of the problems which arise in the formal
construction of Tolman’s theory. The appraisal is largely
methodological in scope; in general, no attempt is made to
extend the scepe of this appraisal to empirical or experi-
mental issues. Nevertheless, to a certain extent these
methodological points derive their plausibility from experi-

mental sources, for example, from the latent learning issue.

The writer wishes to insist that the formal system to

be develOped in this essay is not to be taken as being a

p
complete construction of Tolman’s theory. Time and space

are invulnerable enemies; especially when one is working in
uncharted surroundings. The present system though incomplete

is more than pregrammatic. This, I trust, will become clear

in the ensuing pages.

A Logical Analysis of Tolman's

Theory of Learning

 

*7 .

‘ -._

O

I 1..

Eecause of type limitations the comma "’"

is used in place of the usual single quot-

ation mari.

 

CHAPTER I

 

INTRODUCTION

 

l. The introductory chapter deals with the following
points: (1) a general discussion of the technique of formal
organization, that is, the technique which will be used in the
construction of the system to be presented in this essay, (2)
a defense of the formal organization of scientific theories,
and (3) a general discussion of the crucial and fundamental
elements of Tolman’s "system", that is, a general discussion

of the function and character of the intervening variables.

 

In turn, the first of these points deals with (a) a brief
description of a logically organized system, (b) a brief

description of the apparatus of Principia Mathematica, and

 

(c) the definition of "formal organization"; and the second,
with (a) arguments in defense of logical organization to
hich the present author is Opposed and (b) arguments in

defense of logical organization to which the present author

)

 

subscribes.
I
The Logically Ogganized System
2. A system is a class of statements or prepositions.

A legically organized system is a system in which every pro-

position is either a postulate or is deducible from a postu-

 

late, that is, is a theorem. To illustrate, consider the

following class of prepositions.

 

(1) Some demanded goal-objects are means-objects.

(2) Where there are organisms which are docile
with respect to goal—objects, there are means-
objects.

(3) Some goal-objects are means-objects or they
are not demanded.

Call this class of prOpositions ’K’. Let us take (1) as a
postulate. Then (2) and (3) follow from (1) and, hence,
are theorems. Thus, every proposition in K is either a
postulate or a theorem; that is, K is a legically organized

system.

3. The above illustration made no use of either logical

or mathematical symbols. It is often convenient, however,

to translate statements in a natural language into statements
in a non-natural or symbolic language. Production of theorems
is often facilitated in the sense that symbolically translated
statements bring into bright relief those features of preposi-
tions which are essential to the deduction of theorems. Since
the system to be developed in this essay is not couched in
English it will be helpful to see how the logical organization
of a system is effected in terms of a symbolic language. For
purposes of illustration, K will be the system to be so organ-
ized. But first a general outline of the symbolic language to

be employed is in order.

Outline pf the System.g£,Principia Mathematica

 

 

h. The primary symbolic language to be used in this essay

 

is the system of Principia MathematicalL But the system to

 

be constructed in this essay also employs the apparatus and

symbolism in Tarski’s Second Axiom System for the Arithmetic

 

9f Real Numbers.5 However, for present purposes we may put

 

aside discussion of the apparatus of Real Fumbers until the

 

notion of a functor is discussed in Chapter II. Ho essential
distortion results from this omission in the ensuing account

of the logical organization of K by the symbolic apparatus of

 

Principia.

 

5. The system of Principia contains various signs which

 

are either formal constants, defined and undefined, or vari-
ables. Some of the constants are ’.’, ’~’, ’V’, ’3’,’§’,

’=’, and ’3’. Greek and English letters are the variables,
for example, ’x’, ’y’, ’o’, ’W’: ’p’, and ’q’. These con-
stants and variables, by different arrangements, form differ—
ent logical laws. For example, ’pnp’ is such a law. Within
this set of laws there are certain laws called postulates
which express certain prOperties of the basic constants, for
example, basic constants such as ’.’and ’~’. In addition,
Principia contains a set of rules for the deduction of certain

laws called theorems from the postulates; ’p3p’ is a theorem

in Principia.

 

 

u. Whitehead, A., and Russell, B., Principia Nathematica,
Cambridge U. Press, Second Edition, 1936. Hereafter,
this system will be called Principia.

5. Tarski, A. Introduction tg_Logic, Oxford Press, l9hl,
pp. 2.7-21é. Hereafter, this system will be referred
to as Real Numbers.

 

 

 

 

6. Since it is the logical laws in Principia which

 

guarantee the validity of the steps in a proof, the logical

organization of K may be construed as an application of

 

Principia to K. What I mean by "application" is what logi—

 

cians sometimes mean by "interpretation". Unfortunately

the word "interpretation" is‘often used ambiguously. It

has a narrow and broad sense. In its narrow sense "inter-
pretation" simply refers to the various meanings assigned

to the formal constants. In its broad sense, it refers both
to the various meanings assigned to the formal constants and
also to the kinds of things which are allowed to replace the
formal variables. for example, when ore says that the con-
stant ’3’ means "implies", one is giving an interpretation

of Principia in the narrow sense of the expression "inter-

 

pretation". But when one says that, for a given meaning of

 

’3’, the kinds of things which can replace the variables, say
’p’ and’q’, are prOpositions like "Organisms demand states-of-
affairs" and "There is a white card", one is proposing an

interpretation of Principia in the broad sense of the express-

 

ion "interpretation". In this essay, the word "application"
will be used for the broad sense of "interpretation" and the
word "interpretation" is confined to its narrow sense. So
defined, it follows that if a logical system has been applied,
then it has been interpreted. In this essay, the interpretation

of Principia is what Carnap calls the "normal interpretation of

 

a logical calculus". That is, the constants ’.’, ’~’, ’V’,

H H

’3’, ’5’, ’=’, ’3’, mean, respectively, "and", "not", or ,

"implies", "if and only if", "identical" and "There is at least

one".

Definition pf Formal Organization

 

 

7. The first step in logically organizing K in terms of

Principia consists in translating the prOpositions of K

 

into symbolic statements which include formal constants in

Principia "normally" interpreted. For example, consider (I)

 

in K. Let ’xDp’ mean ’x demands a state-of-affairs p’ and

 

’phx’ mean’p is a means-object of x’. Then (1) may be written
as
(1’) (3p)(xDp . pHX).
Again, if ’pr’ means ’x is teachable (docile) with respect
to p’, then (2) may be written
(2’) (3p)(pr) 3 (3p)(pRX).
Finally, (3) may be written as
(3’) (3p)(pr V ~ xDp).
If (1’) is taken to be a postulate, then (2’) and (3’) will
follow as consequences of (l’) where the laws which permit

these deductions are those found in Principia. That is, when

 

’xDp’, ’pr’, and ’pr’ are allowed to replace the variables

’

’p , ’q’, and ’r’ in the laws of Principia,—-when an application

 

of Principia is made to K--, (2’) and (3’) are seen to be theo-

 

rems following from (f) in accordance with the laws of Principia.

 

For example, from (1’), by distribution of the existential
quantifier over p, that is, ’(3p): there follows
(3p)(xDp) . (3p)(pNX);

then, by the Principia law "(p.q) 3 p",

 

(3p)(pHX)

from which, by the Principia law "p 3 (q 3 p)",

 

(3p)(pr) D (3p)(pMX)
follows. This is (2’).

Again, from (1’), with the aid of the Principia law

 

"(p.q) D (p 3 q)", there follows

(3p)( xDp 3 pm);
then, with the aid of the Principia law "(p 3 q) E (~q3~p)"

 

(3p)(~(pMX) 3 ~ xDp)

from which, in accordance with the Principia "(~p V q) =

 

Df (p 3 q)":
(3p)(phx V ~ xDp)

follows. This is (3’).

8. The account in Paragraph 7. thus provides an illustra-
tion of the logical organization of K by means of an applica-

tion of the symbolic language of Principia. K will thus be

 

said to be formally organized. It should be noted that in
this illustration, taking (1’) as a postulate results in a
certain economical reduction of the system K. For it can
easily be shown that neither (1’) nor (2’) follow from (3’)
and that neither (1’) nor (3’) follow from (2’). The "core"

of the system K is the prOposition expressed in (1’).

9. Two benefits to be derived from the formal organiza-
tion of a scientific theory or system have already been hinted
at in the preceding paragraphs. It has been suggested that

there results a certain facilitation in deduction and also a

 

certain economy in fundamental principles. The next section
of the chapter will be devoted to a discussion of the advan-
tages which are to be derived from formal organzation of a
scientific theory. The ensuing section is thus a defense of
the endeavor undertaken in this essay. The present author
feels compelled to discuss this matter for two reasons.
First, in contemporary psychology, there are some misunder-
standings and some misgivings about the advantages to be

obtained from such an endeavor for the experimental investi-

 

ggtgg. Secondly, there are certain claims which have been
made by lOgicians about formal organization which the present
author feels have perhaps led to the above mentioned misunder-
standings and misgivings on the part of the experimental in-
vestigator. The next section will attempt to resolve these

problems.

II

The Rejection 9£_the Argument from Precision

 

 

 

10. In this section some arguments concerning the utility
of formal organization will be examined. One of these sug-
gestions is unwarranted; the others are not. Let us first

consider the unwarranted argument.

 

10

b and Woodger7,

11. Some investigators, notably Carnap
believe that formal organization is a useful tool to the

experimental investigator because it is requisite to the

 

construction of rigorous, comprehensible theories. They
argue as follows: Eatural languages like English and German
are replete with obstructions to precise scientific express-
ion; for example, excessive ambiguity of expression, vague-

ness of expression, tendency to contradiction, and so on.

 

These obstructions are the result of the"unsystematic and
logically imperfect structure(s)" of the natural languages.8
In other words "the richness of their vocabularies and the
arbitrariness of their syntactical rules militate against
their suitability for scientific purposes by rendering them
difficult of control".9 Again, they possess moral and
religious overtones which make them scientifically suspect.lO
To borrow a Woodgerism, they are "not precise enough" for

scientific use.11

As a result both the lack of rigor and
the incomprehensibility that we find in so many scientific
theories is not so much due to the theorizer himself as it

is to the imprecise language with which he expresses his

theory. For, we are assured, "[The scientists] know what

 

6. Carnap, R., Logical Syntax.2£ Language, harcourt, Brace
and Co., l937.

7. Woodger, J. H., The Technique of Theorpronstruction,
International EncyclOpedia of Unified Science, Vol. II,
No. 5, l9u7. See also Woodger, J. H., Biology and Languagg,
Cambridge, l95u.

 

 

 

 

 

 

 

 

8. QB, gi£., LOgical Syntax of Language, p. 2.

9. QB. cit., The Technique of Theory Construction, p. 2.
10. lb d., p. 2.

ll. Op. 313., Biology and Language, p. 9.

 

1""-

11

they mean, but the current linguistic apparatus [natural
language] makes it very difficult for them to say what they

mean".12

In short, the incomprehensibility of many scienti-
fic theories is due to the contradictions, ambiguities and
deceptions, that is, to the "dangers", in the natural lan—
guages used to express them.13' Therefore, these investi-

gators recommend, --indeed, they insist, -- that formal

systems like Principia, which though perhaps not devoid of

 

like dangers at least reduce these dangers to a minimum,
must be used in order to organize scientific theories into

rigorous, comprehensible scientific instruments.

12. The preceding argument is unwarranted. It fails for
this reason: Woodger, Carnap, gt 31, have taken the wrong
kind of entities as arguments to the predicates "precise",

"ambiguous", and "deceptive". In other words, it is not a

 

language which is precise or imprecise, ambiguous or unambi-
guous, deceptive or not deceptive. Rather it is the use

which §_theorizer makes of §_1anguage which has these prep-

 

 

erties. Therefore, the rigor and comprehensibility of a
scientific theory i§_relative to the theorizer’s EEE of a
language and not merely to the language. Hence, we conclude
that formal organization is not requisite to the construction

of rigorous, comprehensible scientific theories.

 

12. Ibid., p. 95.
13. £3. cit., Logical Syntax pf Language, pp. 311-312.

 

 

13. To illustrate this point one need only consider the

fact that certain terms in the so-called "precise" languages

1h

are often used imprecisely. Thus, Carnap, when concerned

with Russell’s ambiguous use of "implication" writes:15

Russell’s choice of the designation ’implication’
for the sentential junction with the characteristic
TETT has turned out to be a very unfortunate one.

The words ’to imply’ in the English language mean the
same as ’to contain’ or ’to involve’. Whether the
choice of the name was due to a confusion of implica—
tion with the consequence—relation, I do not know;

but, in any case, this nomenclature has been the cause
of much confusion in the minds of many, and it is even
possible that it is to blame for the fact that a number
of peOple, though aware of the difference between impli-
cation and the consequence-relation, still think that
the symbol of implication ought really to express the
consequence-relation, and count it as a failure on the
part of this symbol that it does not do so. If we have
retained the term’implication’ in our system, it is,

of course, in a sense entirely divorced from its ori-
ginal meaning; it serves in the syntax merely as the
designation of sentential junctions of a particular
kind.

In summation, the View that a scientific theory needs to be
formally organized in order to be "rigorous and comprehens-
ible" must be rejected. Again, the view that loose and in-
comprehensible theories are not due so much to tke theorizer
as to the imprecise instrument he is using is also at fault.
For if the belief that it is the theorizer’s 232 of language
whichis precise or imprecise, and so on, is justified, then
the rigor and comprehensitility of his theory depend not so
much upon the language he uses to express his theory as it

does upon him, that is, upon the use which he makes of that

 

lu. See Eennett, A. A., and anlis, C.A., Formal ngic,
pp. 269-2710
15. 92, cit., Logical Syntax gf_Langu§ge, p. 255.

 

 

 

13
language.

The Utility_2£ Formal Organization

 

 

14. Let us turn now to the arguments in favor of formal
organization which the writer considers to be warranted.

There are five such suggestions.

15. Variables and gymbolization. Here the concern is

 

with the notion of a variable insofar as that notion con-
tributes (l) to the rigor of a given analysis -that is, to
the intended logical representation of the structure of a
prOposition or set of prOpositions and (2) to the avoidance
of difficult circumlocutions often required in order to ex-
press a given preposition or set of prepositions in an un-
standardized natural language. The point to be made here
is that a certain rigor and simplicity results from the
employment of a symbolic language in order to express the
logical relations holding between prOpositions in a given

empirical system. Hence, in this sense, it is expedient to

 

formally organize an empirical theory or system. To illus-
trate, let us examine the following passage from J. H.

Woodger’s, Technique gil’l‘heoryConstruction.16

 

 

The use of variables is a special instance of symboli-
zation which deserves a little further consideration.
It will be noticed that in the English translations of
some of the statements of Part II of T we were able to
avoid the use of variables without loss of precision.

 

16. Cf. pp. 67-68.

11;.

In other cases this was not done, because without
taking advantage of this convenient device an ac-
curate English translation would have been poss-
ible only at the cost of intolerable circumlocut-
ion and prolixity. In further illustration of these
facts we may consider the following examples.

Suppose we wish to state that the relation of being
earlier than or before in time (in the sense we have
denoted by ’T’) is transitive, but without using the
technical logical predicate ’transitive’. In a word
language this can be done as follows:

If any thing is earlier than another thing,

(a) and the latter is earlier than a third thing,
then the first is also earlier than the third
thing .

By the use of individual variables this becomes:

For every g, y, and E, if x is earlier than
(b) ‘y, and y,is earlier than a, then x'is earlier
than 2.

Thus the use of variables enables us to eliminate
such words as ’another’, ’the latter’, ’the first’,
’a third’, etc., without ambiguity, and reduces the
length of the statement by about one—half. The use
of a single relation—sign ’T’ in the place of ’is
earlier than’ prepares the way for the use of the
calculus of relations and reduces the statement to
a single line:

(c) For every g, y, and g, if xTy and ETEJ then ng.
In the notation of the theory T this was expressed by

(d) (All x) ((All 1) (All g) ((xTy and yTE) implies
512))7.

In the notation of Principia Mathematics ’All’ is
omitted from the quantifiers, and the logical con-
stants ’and’ and ’implies’ are symbolized by ’.’
and ’3’, respectively, so that we reach a complete
symbolization:

 

(e) (as. 1, a) = $1 - ITP. . 3 . ETE-
(here also some of the parentheses are replaced by dots.)
Finally, we reach the highest degree of brevity by formu-
lating the statement by means of ’T’ and signs belonging
to the calculus of relations:

(f) TITCT.

15

This last formulation owes its brevity to the fact
that, by the use of constants belonging to the cal-
culus of relations, we are able to eliminate indi-
vidual variables.

16. The argument from intuition and calculation. It

 

is a common observation that the results of insights are
often wrong. It is precisely because we do not always

trust the results of our intuitions that we require certain
checks on this sometimes wayward process. Calculation (or
deduction) may be regarded as one such check. On the inter-
dependence of intuition and calculation, Moodger writes:l7

Although it is by intuition or common sense that we
ordinarily think and discover new hypotheses, the
use of a logical technique can help intuition in
two ways: (i) by providing a check which enables
us to determine whether a theorem arrived at by
intuition is in fact a consequence of our assump-
tions or not and (ii) by providing intuition with

a guide rOpe in complicated and unfamiliar regions
where, without some such aid, it could not pene-
trate or would easily go astray. Intuition and
calculation are both necessary for science. Neither
is infallible. Together they compensate for each
other’s defects.

Formal languages like Principia are in part created and

 

conventionalized for the purpose of determining when it is
possible to calculate that certain prOpositions follow from
certain other prOpositions. Certain investigators who have
been hypnotized by the relatively concise and well organ-
ized set of rules for calculation found in formal languages,
have concluded that "calculation in a natural language is

not possible".18 This attitude, I believe, stems from the

 

17. Ibido , pp. 71-720
18. Ibid., p. 2.

lo

artifiCial distinction between "precise" formal languages

and "imprecise"

natural languages. Rather it is the case
that calculation is facilitated in a symbolic language like

Principia. bymbolic languages like Princinia arise from

-. p-

 

the desire to abstract away from the plethora of diversified
rules which guide the use of signs in natural languages just
those rules which apply to calculation. A symbolic language

like Principia then is a very simplified segment of natural

 

language. In short, the reason why we do not normally cal-

culate in natueal languages is because we find it unnecessary
to do so. For if we were to calculate in natural languages
we would first have to separate out, that is, abstract away,
at least implicitly, just those rules which apply to calcu-
lation. But this ha already been done, to some extent, by

peOple who have "constructed' symbolic languages like

Principia. here again, we are guided by the principle of

 

expediency.

17. The argument from prediction. Among the problems

 

well calculated to start a violent debate in psychological

“

circles is the problem of prediction. The ssue does not

He

turn about the nature of prediction, but rather is con-

cerned with whether a given statement is or is not a pre-

3
S

diction in accord .ce with some theoretical point of View.

0
F

The problem of deciding whether or not a given prOposition
is a prediction from a given theory is quite important. For
the adequacy of a theory is tested by what it predicts. Hence

if there is no means by which one is able to determine with

17

reasonable certainty that a given theory allows a certain
prediction, then experimental test of that theory is rather

difficult.

18. As above, the present author does not maintain that
decisions as to whether or not a certain state-of—affairs

is predictable from certain theoretical grounds are imposs-
ible in natural languages. But, again, decisions of this
sort are facilitated by formal organization. Again, as in
the preceding section, the claim here is that such decisions
when made in a natural language are usually circuitous and
prolix where the decision is at all complex. In short,
decisions of this sort in a natural language are often in-

expedient.

19. To illustrate the relationship between calculation
(deduction) and prediction (and also the relationship between
calculation and the converse of prediction, that is, explana-
tion), consider the following statement by Carnap.19

Of greater practical importance is the deduction of
a singular sentence from premisses which include
both singular and universal sentences. We are in-
volved in this kind of a deduction if we explain a
known fact or if we predict an unknown fact. The
form of the deduction is the same for these two
cases. ...we find it again in the following example,
which contains, besides signs of the logical calculus,
some descriptive signs. In an.application of the
logical calculus, some descriptive signs have to be
introduced as primitive; others may then be defined

 

19. Carnap, R., Foundations pf Logic and Eathematics,
International incyclOpedia of bnified Science,
Vol. II, No. 7, 1952, p. 36.

 

 

18

on their basis. (L ,neta-for-oescription—sians)-
rules must then be 1,8 id down in order to establish
the interpretation intended by the scientist. Ere-
miss (3) is the law of thermic expansion in quali-
tative formulation. in later eia.pl. we shall apply
the same law in quantitative forinulation.

 

l. g is an iron rod.
:remis ses: 2. c is now heated.

3. for every x, if x_is an iron rod and

x'is :me ted, x expands.

Conclusion: ’.'3 now expands.
A deduction of this fo can occur in two practically
quite different icinds oi si uations. 1n the first case
we may have found (ii) by observation and ask Lhe p(;si-
cist to explain the fact observed. re aives the expla-
nation by referring to other facts (1) and (2) and a“—

law (3). In the second case we may have found by ob—
servation the facts (1) and (2) but not (H). lere the
deduction Iith he 1elp of the law (3) supplies the
prediction (4), which may then be tested by furthe
observations.

ihe ean ’ole given shows only a very short deduction,
still more abbreviated oy t1e ozniss ion oi the inter-
mediate steps between re:isses and conclusion. But
a less trivial deduction consistin“ of many steps of
inference has fundamentally t1e sale nature.

H

20. ihe argument from mathematizationfl. Generally when

 

 

one sieaks of a naU ematicized part of a theory, he is

’1

thought to b

"'\

a referring to that ”art of a theory which has
been expressed in arithmetical or al ebraic formulas, that

-F

is, the quantifiable aspects of the theory. in fact, however,
the theory as a whole may be mathematicized if the deductive
procedure is used. that is, not only those parts of a theory
which are expressed in "quantitative" terms may be mathemati-
cized by the technique of fornal organization, but also both
tne quantitative and non-qua ntitativo aspects of a theory can

be "mathematically" arra n3ed :32 the technique of iormal orien-

ization. “hat is intended by mattematization of a theory in

19
this more genera sense is aptly expressed by Koodger.2o

Kodern logic has now been so far developed that it
enables us to mathematicize the whole of a scienti-
fic theory and not only the numerical or quantita-
tive part. It furnishes us with calculuses which
enable us to perform complicated transformations
with precision upon statements which contain no
signs belonging to traditional mathematics.

21. This consequence of formal organization is quite
valuable. Thus, for example, in the case of Tolman’s
theory, it permits one to mathematicize that theory in
which quantitative techniques are either not worked out

or are completely lacking. This is important because among
many scientists the belief persists that rigorous develop-
ment of a theory depends solely upon the development of

quantificational techniques. On these matters, J. H. Brown

writes:21

A systematized science like modern physics uses mathe-
matics in making measurements as psychology has attempt-
ed to do, but an equally important application of mathe-
matics in physics is to the construction of theories.

In any advanced science most of the measurements per-
formed depend on a close integration of theory, law,

and experiment. The older views of the scientific
method which supposed that measurements lead to laws
through the discovery of correlations between sets of
measurements on different entities have been shown to

be unsound. In actual scientific practice the theory
leads to the law and the law to the possibility of
measurement more often than measurement leads to laws
and hence to theories (1). The psychologist in his
attempt at an empiricism, based on what he supposes

to be a sound mechanistic methodology, has neglected

 

20. 92, cit., Technique 2: Theory Construction, p. 7. Also
see Quins, W. V., Mathematical Logic, Norton, lgho,
pp. 7-8.
21. 92° cit., Dsych. Theories, pp. 23u-235.

 

 

20

the possibilities of applying mattema‘ical procedures
to the construction of psychological theory. Psycho-
lgiists 11ave K8 de wide use 9i_nat1ematics an Jersrre-
ment, out have scarcely_ever used mat1eratical con-
cepts 3E heory-builoinj. 1he purpose of this paper
is to all to the attention of the mathematical psy-
cnolorg ist certain Hother tica procedures which ma3
ee us so in the construction oi psychological theories.
Lack of space prevents the mathematical development
of these concepts. T1e various references, however,
should enable the reader to pure ue tne mathematics of
this mode of attac ck further should to so desire.

-!a C

 

 

 

 

 

J;

1

Then he procee s to describe the technique most apprOpriate

to theory construction.d2
decent methooological research has also Shown us the
10st fruitful type of theory. The theory should be
ased on what ra3 be called the hypothetico-deduct-
ive method, or the method of constructs. In this
method, lvootoeses are devised to account for the
descriptive data and from these hypotheses, pre-
dictions are made which may be tested ir experiment.

The constructs used in the hypotheses must be capable
of Operational defir it'on. They must further lead to
theoretical postulates whicn may be tested in critical
experiments. There is so muc: aireement now amongst
methodolo ists on t is point trat to arrue it further

we uld require space which may better oe spent on the
‘1

development of the constructs themselves.

22. In conclusion, it is possible to give a theory some
form of rigorous development 1:itror t first havinfi established

act, formal orfianiza-

k4 L
._

any quantificational techniques. In
tion may uggest to t1e investigator certain attacks on the

problem of quantification itself.

23. lew information. Formal orga M12 tion of a scientific

 

theory may yield new information about the theory, and thus

 

 

1.311,)... ”viii
i1 H

21

may suggest certain experimental situations by which to
test the theory. This new information may be of various
sorts. Her example, a scientist may suspect that a given
system is inconsistent. Formal organization of the system
allows the scientist to test for consistency; if contra-
dictory prepositions are provable in the system, then the
system is inconsistent. Again, it is valuable to know just
what elements are basic in the system. In the present system
there are eight primitive ideas. Motions like appetite or
cathexis, aversion, sign-object, signified-object, etc.,
are reducible by definitions to these more basic ideas.

but most important is the suggestion of new experimental
"issues" which may result from the formal organization of
the system. In the present system certain theorems involv-
ing the law of’least effort, the concept of disruption,

the notion of avoidance, and the like seem quite suggestive
of new experimental tacks. Nevertheless, it must be remem-
bered that in this initial task the purpose of the present
author is to organize Tolman’s theory rather than to find
new experimental tacks. In the last chapter certain new

experimental tacks are suggested.

24. One point needs to be pointed out in this discussion.
It is not being claimed that formal organization is the cure
for all theoretical ailments. Indeed, in the present work
we shall see that the apparatus itself is, to a certain ex-
tent, defective. The above points were rather directed to

the defense of formal organization as a legitimate program

(T)

in jeneral. ihose plac S in which the particular example

.‘

of formal organization ex‘ioited in this system is efective

C) 1

will be dealt with in the final chapter.

111

ihe Function of Intervenin; Variables

 

 

25. This section deals with a general description of
lolman’s notion of the intervenini variable. iolman
characterizes his a stem” in the followina way. Purpos-
ive beha viorism consists of an asseited list of interven-
ing variables", that is, of an asserted list of terms de-
noting inferred oroce sees in t1e or :nism which are said

to operate between the presentation of a given s Mi1ulus
situation and the occurrence of a given response situation,

" sserted set of laws

and of a certain " concerninf the nature
and Operation of these intervening variables. 23 The concept
of an intervening variable is, thus, the key to Iolman’s con-
ception of a psychological system. It demands greater con-
sideration. ore preciselg, what is required is a clearer

account of the function of an interveniny variable as a

systematic instrument.

2o. Ihat is the systematic function of an intervening
variable? Let us begin with this homely observation: there

is some reason why Tolman picked "demand" rather than "Oink"

 

23. rarx, h., Psychological Theories, yaCLillan 1951, p. 90.
bee also iolman, h. 0., "1he_ueterminers of Behavior at
a Choice Point", Psych. hev., 1930, pp. l-hl.

 

23

to be an intervening variable in his system. That is, the
selection of an intervening variable is not an arbitrary
matter. Somehow, as Tolman uses the term ”demand" in his

system, it is seen to be more aoprOpriate as an explanatory

 

H .2 .1!
oirfl; or

device of certain puzzling phenomena than is
"yak". fine following explanation is not intended to be
conclusive, but rather only suggestive of the reasons why

!

iolman picked 'demand" rather than ”Oink" as an intervening

variable and, hence, directs attention to a function of

I?

intervening variables which constitutes tleir anprobriate-

ness" as intervening variables.

27. The preceding remarks suggest that an answer to the
preposed question might be found by examining the way in
which a typical theorist might construct a theory. Recess-
arily this discussion will be over-simplified. In general,
the theorist is confronted with a set of facts thich are

Stated in the form of singular propositions. In erecting

 

a theory the theorist attempts to account for the various
discrepancies which are recorded by the various singular
prOpositions. These singular propositions may be ObSCrVo'
tion statements or non-observation statements. For example,
observation statements which Tolman might be concerned with

,3"

are "mat a eats f00c , "Eat a runs to the left", "

1‘1 8 t

{b

bites experimenter", and so on. Examples of non-observation

statements are "hat a demands eating food", "hat a expects

to run to the left", "fiat a exnects that the experimenter

t , ,

will jump’, aid so on. The oifierence between these two

kinds of statements is this: observation statements are

directly_verifiable by sense observation, while non—obser-

 

vation statements are indirectly verifiable, that is, they

 

depend for their verification on the observation statements.

28. Let us suppose that the theorist is confronted with
a class K where K contains the following “£2232": hat is,
observation statements.

hat is put in front of food.

Rat eats food.

a
a

Rat b is put in front of food.

Rat b eats food.

jooo o 0

mat n is put in front of food.
Rat n does not eat food.

[What will be said here applies equally well to non-observa-
tion statements.] Suppose further that the observations con-
cerning rat n’s behavior occur two weeks later than those
concerning the behavior of the rats preceding rat n. On the
basis of the behavior of rats a, b ..., the theorist genera-
lizes that whenever a rat is put in front of food, he eats
it. There are three important things to notice in the theo-
rist’s generalizing activity: (1) he has attempted to con-

"rat a is

nect pairs of observation statements, for example
put in front of food" and "rat a eats food", by making a

conditional statement out of them. This is evidenced by the
words "... a rat is put in front of food, (then) he eats it";
furthermore, (2) he has affirmed that this conditional holds
not merely in the case of the behavior of rat a, but also in

the case of the behavior of rat b, indeed, for all rats.

25

This is evidenced by the word "whenever". In short he has
speculated that the following general statement is true:

(a) For every x, if x is put in front of food,
then x eats food.

Finally, (3), it must be noted that (a) is essentially a
prediction. That is to say (a), which has the general form
’(x)(ox D wx)’, allows that if a state-of—affairs "ez"

' will also occur.

occurs, then one may conclude that "wz'
But this generalization is falsified by the behavior of

rat n. Thus the problem; how to account for the behavi-
oral disparity cf rat n, that is, how to explain the case
in which "en" occurs but "¢n" does not occur? The theorist
considers the conditions under which rats a, b, .... and

n were operating. he may notice the following features:
(1) all of the rats but rat n were very hungry; (2) rat
n’s metabolism rate was the only one which was normal; and
so on. It is thus conjectured that there is some complex
process in the rat which will cause his behavior to deviate
under these conditions, that is, the theorist hypothesizes
a certain intervening element called "demand". The problem
now is to construct a new general preposition such that the
behaviors of rats a, b, ....., and rat n can be predicted.

The new general statement might read:

(b) For every x, if x is put in front of food, then
x eats food if and only if x demands eating food.

 

(b) requires a few remarks. The expression "if and only if"
is italicized because a relation at least as strong as "if

and only if" is required if the case

Rat n is put in front of food and Rat n does
not eat food

is to be accounted for by the generalization (b). Thus
from (b) we can easily deduce

(c) If hat a is put in front of food and Eat a
demands eating food than Rat a eats food

and
(d) If Rat n is put in front of food and Rat n
does not demand eating food then Eat n does not
eat food.
hence, (c) eiplains why hat a eats food and (d) why Rat n

does not eat food —namely, because in (c) he demanded eating

food whereas in (d) he did not demand eating food.

29. The preceding account gives a brief description of
the function of an intervening variable. It shows that

the intervening variable "demand" enabled the theorist to
formulate a reliable generalization. An expression like
"Oink" would hardly have been helpful. It is important to
notice that this characteristic of an intervening variable
enables the theorist to order the class K in the sense that
each fact becomes a constituent in a generalization from
those facts. One might say that a set of prOpositions K

allows a generalization from it in accordance with the con-

 

ditions expressed by the intervening variable "demand"; it
is the particular intervening variable which permits the
particular formulation of the generalization. Thus, we may
say that part of the meaning of any intervening variable is

its systematizing or ordering function-which cannot be re-

duced in any way to observation terms. This prOperty of an

27

intervening variable is analogous to the ’3’ in Principia.

 

The "horseshoe" allows us to arrange propositions only in

certain ways; for example, contrast its use with that of

Likewise different intervening variables allow us to arrange
sets of singular propositions in different ways by permitting
different generalizations from these sets of singular pro-
positions. Thus we see that the intervening variables have
an ordering or systematic function in addition to factual

conditions which are also expressed by them.

30. This concludes the introductory remarks. In the next
three chapters the formal organization of Tolman’s theory
is undertaken. The operations and interrelations between
the various intervening variables in Tolman’s system will
be displayed. Greatest consideration will be given to the
two fundamental notions of Tolman’s system, namely, "demand"

and "expectation".

 

[\J
(“’7

CEAPTER II

 

PHILITIVE IDEAS ARE DVFILITICNS CF SYSTEM T

l. The system to be deveIOped in this essay is divided
into two parts. The first part will be called TI; the
second TII. TI is concerned with the relationship between
the intervening variables independent of their strengths

or frequencies. TI tends to stress the ’intervening’
characteristic of the intervening variables rather than
their ’variability’ characteristic. The present chapter
and, also chapter III, present TI and are thus more con-
cerned with the methodolOgy of Tolman’s theory than with
the working consequences of Tolman’s theory; the latter
objective is met in TII. TI is more general, more abstract
than is TII. Its presentation is therefore somewhat simpler

than is the presentation of TII.

General Apparatus

 

2. In TI, small English letters from the middle of the

alphabet, ’p’, ’q’, ’r’,..., occur as propositional vari-

 

ables. Small English letters from the end of the alphabet,

’x’, ’y’,..., are used as organism variables. Greek letters,

 

’Q’, ’w’,..., are ppedicate variables. Capital English

 

letters are predicate constants (or predicates). The logi-

 

 

cal constants, both primitive and defined, are those found

 

in Principia, for example, ’.’, ’~’, ’v’, ’3’, ’5’, :=:’

 

 

 

3. The las kind of symbols used in TI are tie initial

H

ower cas— letters of words or synonyms of those woros which

0
}_J o

d s gnate concepts in T1. for example,

letter of the word

' ' s g . , r- " 1 ‘ r1 1 ‘r ~ .3 _
expressions; more precisely, the, are conSLrued as ELL.IICCI

(I)

 

 

functor-expressions. The notion of a functor is explained

 

in the following pasm a e from fans neichenbach’s Elements

 

4— '

....we turn now to a second kind cl function, which
has developed out OI descriptions, and which we call
descriptipngl functions.

Consiccr a statenent in lunctional notatirn

 

 

rm, X1) (1)
for instance, the statement ’yl is the ffther of xl’.
...we can write the statement (I), in cescriptional

notation,
3T1 : P’Tflfhfy Kl):

[that is, y equals the y such that y stands

relation f '0 x1. ’01y)’ reans ’ti “

Introducing the abtreviation
f’(Xl)

we can write (3) i

*‘t‘. ..J
‘0

J
futtinj variab es in the places of the constants,
we obta‘r

he may ay that we rave solved the functional
’f(y, x)’ for the cr; ument ’y’.

The function ’f’ (x )’ is called a Cescrirtiona 1
function, since its special values, resulting irom
specialization of ’x’, are descriptions. This kind
of function, which we indicate by the prime mark,
is to be distirm ui ned ironl propositional functions,
whose values are prep )ositions. If we want to con-
struct a proposition o; m ars Ol a descriptional
function, we must not only specialize tie yr =urnent
but also add a symbol like ’y1 = ’. “he symbol
’f’(x)’ expresses a descripticnal function in the
form of a contracted tern, since the bound variable
and the iota- -Opera tor are not incicated; the ex-
plicit form of a descri iotional lunction is indic-

 

 

 

Ir.troduction to Loaic, p3. 217-21t.
’E7: pp. 311-3150

 

 

NH
0 0
:3}?
on.
no
H'O
Hr"
Hr+
(”)0
:5»
}_J

\CJ

C~J

30

ated by the right-hand side of the definition

f’(X) =Df(jy)f(y, X) (7)

There are also descriptional functions of
more than one variable. For instance, the des-
cription ’the man who walks between Peter and
Paul’ can be used for the construction of the
descriptional function ’the 2 walking between
x and y’.

Descriptional functions can be extended.
Thus the description ’the color which is spec-
trally between red and yellow’ determines the
color orange; and it may be written in the form

e ’(r, s) f €1f)B(f, r, s) . V(f
where ’r’ stands for ’reg ’s’ for ’yellow’V ’§
for ’spectrally between’, and ’V’ for ’color’ .

¢’(r, 3) represents a descriptional function when
the arguments r and s are conceived as variables.

The distinction between preper and improper
use of descriptions applies likewise to descrip-
tional functions. In general a descriptional
function will be properly used for some arguments,
improperly for others. Thus the descriptional
function ’the brother of x’, applied to persons
as arguments, will be preperly used when x has
one and only one brother; in all other cases it
will be imprOperly used. When a descriptional
function is properly used for all values of its
argument within a certain range, it will be called
a functor with respect to this range. Thus the des-
criptional function ’the father of xf is a functor
with respect to the range given by all human beings.

Among the functors, the unique mathematical func-
tions are of particular importance. They are des-
criptional functions ..., having numbers as arguments
and as descripta. Usually they are functors with
respect to real numbers as their range. Thus when
we write a mathematical equation in the form

y=f’(X) (9)
the symbol ’f” represents a functor with respect
to real numbers as the range of its arguments. The
range of the descriptum y may be more comprehensive;
it may include complex numbers, for instance when
the functor ’f” is given by the square root.
Functors Whose descripta are numbers may be called
numerical functors.]

The use of numbers as descripta of descriptional
functions is not restricted to mathematics. There
are prOperties of physical things which are expressed
by means of numbers. Thus an individual motion-pro-
perty f can be characterized by a number indicating
the speed. This method has great advantages over
the use of names for predicates; it presents the
different preperties in numerical functor with res-

), (8)

 

31

pact to this range. The range itself then consists
in nonnumerical objects,...

As an example of a numerical predicate, let us
consider the sentence ’xl moves at 50 miles an hour’.
It can be written, d

mEQ(X1) = Df (3f)f(X1) . U(f) o (f = 50) (15)
[that 13, ’X1 moves at 50 miles an hour’ means
’There is a motion prOperty f which belongs to
x and f equals 50’] Solving the staterent (15)
for ’f’, i.e., introducing descriptionalnotation,
we obtain

@1r)r(xl) . U(f) = 50 (16)
Introducing the abbreviation (1h) we obtain
f”(x ) = 50 (17)

here the numerica functor ’f”(x)’ signifies

’the speed of x’.
4. Consider the intervening variable "demand". It is
a relation between organisms and states—of-affairs. In
order to capture the variability characteristic we construe
"demand" as a numerical functor. After formula (17) in
the above quotation, we write:

(1) d(x, p) = N
The functor is the definite description ’d(x, p)’ which may
be read as ’the strength of x’s demand for p’. The express-

3

ion = N’ written after the functor stipulates that the

functor is a numerical functor, that is, it ranges over

 

numbers. In the present system ’N’ can only be replaced

by positive numbers. hence, the entire expression in (1)

may be read as ’The strength of x’s demand for p equals

a given positive number, N’. (l) is a prOposition and,

hence, may be true or may be false. To say that ’x demands
,

p or that ’x’s demand for p exists’ or that ’it is true

that x demands p’ is to say that

(2) d(X9 p) # O:

32

that is, ’the strength of x’s demand for p is not equal to
O’. In TI and TII, we lay down the convention that O is
not greater than any number, that is, O is the lowest
number. Thus where ’)’ means ’greater than’, (2) is equi-
valent to

(3) cm, p) > 0,
that is, ’the strength of x’s demand for p is greater than
0’. Again

(A) ~ d(x, p) = N,
that is, ’it is false that the strength of x’s demand for
p equals N’ is equivalent to

(S) d(x, 1)) 7‘ N,
that is, ’the strength of x’s demand for p is not equal to
N’. Finally, every intervening variable dealt with in TI
and TII will be treated in the same fashion as "demand";

that is, they will all be treated as numerical functors.

5. Dealing with prOpositions as arguments to predicates
like ’demand’, ’expectation’, etc. creates a special pro-

blem. For we shall want, in some cases, to write:

(6) p=q

that is, "p is identical with q". In Principia ’=’, is a

 

relation between values of the variables ’x’, ’y’, ’z’ ...,.
In order to be able to write a statement like (a) we lay
down a convention for interpreting ’=’ when it holds between

prOpositions, namely; given any pair g£_pr0positions p and q,

 

 

 

i£_p_i§_deducible from q_and q’is deducible from E) that is,

 

.i£_p and q are mutually deducible, then p is identical with q.

 

 

33

To illustrate the use of this convention consider the two
prOpositions

(7) Rat a is satiated
and

(8) Eat a is not hungry.
Now if (7) is true, then (8) follows. Again if (8) is
true, then (7) follows. In short (7) and (8) are mutually
deducible propositions. In such cases we shall write, in
accordance with the convention,

(9) p is identical with q
or, in symbolism, the statement in (6) above. Under this
interpretation of identity -— with respect to prOpositions

-- the apparatus of Principia is readily applicable.

 

6. The laws for the manipulation of the logical entities

discussed in paragraph 2. are those found in Principia. The

 

laws concerning the arithmetical operations are those found

in, or which are deducible from, Real Iunbers. According to

 

the convention mentioned in paragraph A. that O is not greater
than any number, supplementing the postulate set in Egal_
Numbers in such a way guarantees that the only numbers which
may be substituted for N in

d(X. p) = N.
or in any proposition containing a numerical functor, are

positive numbers.

\p
f‘n—o
ot—

Goal-objects and States-of-affairs

 

7. It is commonplace that Tolman considers a goal-
object to be the kind of thing which organisms demand,
expect, and so on. Unfortunately it is not clear what

the Character of a goal—object 13.3 Tolman wavers between
two interpretations of "goal-object". On the one hand, he
regards a goal-object, that is, that which is demanded or

expected, as prOpositional in character, that is, as a

 

state-of-affairs, or a situation. Thus, when he is dis-

 

 

cussing the properties of molar behavior, 1e writes:u

The first item in answer to this question is

to be found in the fact that behavior, which is
behavior in our sense, always seems to have the
character of getting-to or getting-ffom a spec-
ific goal-object, or goal-situation. b

 

16 For convenience we shall throughout use
the terms goal and end to cover situations
being got away from, as well as for situa-
tions being arrived gt, i.e., for termini
g 339 as well as for termini gd guem.

 

 

 

 

Two pages later he writes:5

The animal when presented with alternatives always
comes sooner or later to select those only which
finally get him to, or from, the given demanded,
or to-be-avoided, goal-object 23 situation and
which get him there by_the shorter commerce-with
routes.

 

 

 

 

 

3. here goal-object is being used in its broadest sense,
for example, means-objects, and final goal-objects,
are goal-objects.

h. Qp, gi§,, Purposive Eehaviorism, p. 10. (my italics)

5. Ibid., p. 12. (my italics)

 

 

35

And finally his most obvious employment of goal—objects

as prOpositional occurs in the following passage having

6

to do with expectations.

In these latter cases also, the perception or
memory, as Ln expectation, is a prior "setting"
of the behavior for such'subsequent encounter
as: ("here an OpeninJ; ‘there a wall"; "here
a _smellable crevice ; and the “like. Again, the
actual encounter which verifies or fails to
verify that "tr is is an opening, a wall, or a
crevice" , is a temporally separate and later
event."

 

 

 

It is also interesting to note that in the Glossary of

Purposive Eehaviorism, he stipulates that by definition,

 

"goal-object", "goal-situation" and "goal" are synonymous.
On the other hand, he also thinks of goal-objects as things

or qualities. This is amply illustrated by the following

 

statements. When discussing the phenomenon of disruption
he writes:7

We shall suppose, in general, that in behavior
there is always immanent the expectation of
some more p£_less specific type pf goal-object."

8

 

And, again, in the same context:

The appearance of such disruption will define
the fact of an immanent expectation of the pap:
vious type of goal- object, i. e., the type _p£_
goal- object which, g§_long Ls it is resent,
does not cause disruption.

 

 

 

 

 

And finally, in his most explicit statement of goal-objects

as things or qualities, he writes:9

 

6. Ibid., p. 811. (1y italics)
7. Ibid., p. 76. (Ly italics)
8. Ibid., p. 7h. (Ly italics)
9. Ibid., p. 74. (1y italics)

 

 

 

 

36

It would, that is, undoubtedly be discovered

further: (a) that there was a definite range
Lf goal- object qualities, i. 3., those Lf bran
mash, Lr Li foods so closely similar to such

mash that the rat could not disting uish them

from the latter, which would lead to no such

disruption as long as they were found at the

eXit-bOXo

 

 

 

 

 

 

 

8. The problem then is this: Are goal-objects things
like "food" or qualities like "leafy succulence of lettuce",

"x eats food" or "x

or are they states-of-affairs like
chews leafy lettuce"? In the discussion of demand as a
functor in paragraph A. that which is demanded or expected,
was represented by a prOpositional variable, that is, by
’p’. Goal-objects were there construed as prOpositional

in character. In this essay, this convention is followed
throughout. Three arguments are offered in defense of this
convention. First, construing goal-objects as states-of-
affairs permits one to describe different behavior patterns
in which the same thing -— say, food -- is involved; con-
struing goal-objects as things does not. Secondly, certain
important behavioral situations, for example, conflict
situations, are not accurately represented when goal-objects
are construed as things or qualities. Thirdly, construing
goal-objects as things or qualities leads Tolman, in certain
instances, to an interpretation of the behavior situation
which has unfortunate implications. In connection with

this last point, in the discussion of the primitive idea of
expectation an attempt will be made to show that Tolman

himself implicitly construes goal-objects as prOpositional

 

ii.i‘l

Ik't.‘

37

in character.

9. Suppose we have a moderately hungry cat who has just
caught a fat mouse. Suppose further that our cat spends
some time in examining the mouse, for example, smelling it
or turning it over, before he eats it. now do we distin-
guish between the cat eating the food (mouse) and the cat
inspecting the food (mouse)? If goal-objects are construed
as thing-like the distinction is difficult to make. For
in either case what the cat demands -- is food (mouse).
Thus either (g£_bgth) behavior patterns would have to he
written (in the present symbolism) as :

d(x ’food’) = N,
that is, ’the strength of x’s demand for ’food’ equals the
number M’. If goal-objects are taken as situations the two
behavior patterns noted in the illustration can be discrimi-
nated. One of them can be written as:

d(x ’x inspect the food’) = N
that is, ’the strength of x’s demand that ’x inspect the
food} equals the number M’. The other may be written as:

d(x ’x eat the food’) = N
that is, ’the strength of x’s demand that ’x eat the food’

equals the number N’.

10. Consider a case of conflicting demands.lo Such a

situation is not accurately described by saying that one

 

10. These remarks also apply to conflicting expectations.

of the alternatives i§_not demanded while the other alter-

native is demanded. hather both alternatives are demanded.

 

For example, construe goal—objects as things. Suppose an
organism to have conflicting demands with respect to a thing
-- say, a door. This may be written as:

d(x, ’door’) = N. (100)
hut then we should have to write:

~d(x , ’door’) = N. (N>O)
that is, ’x does not demand the ’door”, for the other case.
Notice, however, that the conflict has to do with some relat-
ion between x and the ’door’, for example, Opening the door;
-- not merely with the door alone. To express this kind of
situation we may write:

d(x , ’x Opens the door’) = N (N)O)
that is, ’x demands that ’x Open the door”, for the one
case and

d(x , ~ (’x Opens the door’)) = N (N>O)
that is, ’x demands that ’x does not Open the door”, for
the conflicting case. In the last two cases x demands in

either case. The demands are thus in conflict.

ll. On pages 128-129 of Purposive Behaviorism Tolman

 

gives his interpretation of the behavior Of the animals in
an experiment by Robinson and Never on visual distance per-
ception. I shall quote both the experimental results and
Tolman’s interpretation of them.

We turn now, finally, to an experiment which indic-

ates the ability of the rat to reSpond to a hier-
archy of subordinate and superordinate goals.

This is an experiment by Robinson and Hever.

It indicated that the rat can choose a given means-
Object by virtue of whether or not it leads to a
given subordinate goal-Object (in this case, to

be sure, a negative, or avoidance, subordinate
goal-Object).

’Two paths, hight and Left, led from the entrance
to the food, but doors of the vertical sliding
type, and of the same material and color as the
walls of the maze, were provided....to permit the
closing of either path, as desired. Along the top
of the paths a row of electric lights gave even
illumination. At the choice point, the right and
left alleys were obscured from View by two black
flannel curtains, making it necessary for the rat
to enter the blind in order to see whether the
path was open.’

’For about every third trial both paths were left
open and the rat made his way unimpeded to the
food. But for the remaining trials both doors

were closed until the rat had passed into one
alley, had turned around and started back; then

the door of the unentered alley was quietly Opened
by means of a cord in the hands of the experimenter
and the animal thus permitted to pass along that
way.’

The tasks for the animals which we are here inter-
ested in were (a) that cfnmemonizing that the closed
door on either side meant the non-availability of
that side as a route to food, and (b) that of per-
ceiving, as soon as possible, after passing under
the curtain, the presence or absence of the sub-
goal-Object (in this case a negative or avoidance
goal-Object), the closed door. The results indic-
ate that on the first few days the rats ran way up
to the door before rejecting a given side and turn-
ing back. It appears, further, that they then
learned to turn back sooner and sooner until,
finally, each animal reached a relatively constant
level of performance of turning back at some charac-
teristic distance from the door.

12. In Tolman’s writings the expression "negative or
avoidance Object" is ambiguous. It could mean -- and in

.‘

fact it does in tlis context -- that it is false that x

M0

has a demand for the door. But according to the convention

established in chapter II Of Purposive Behaviorism the ex-

 

pression "avoidance object" means a demand for the Opposite

goal situation. Tolman is led into this confusion because

’ 9

he is treating Ehin;§_as goal-objects, that is, where 2
takes as values things like ’doors’, ’alleys’, etc.,
’d(x, 2)) O’ is the appropriate way of symbolizing a pos-
itive goal-Object. Let us write:

(10) d(X, 2))0.
An avoidance goal-object is then written as

(ll) ~d(x, z)>O.
By making goal-objects things Tolman is forced to write
that "...the mnemonizing [remembering] [of] the closed
door on either side meant the non-availability of that

side as a route to food." The implications of this inter-

pretation of "avoidance Object” are unfortunate.

13. It is fair to translate the sentence in the quotation

1

above which reads: '...the closed door on either side meant

' into

the non—availability of that side as a means to food.‘
the following statement in Tolmanian language:

(a) It is false that x expects alley L, that is, ’that side’,
leads to food,

where ’alley L’ is a ’means-object’ and ’food’ is the ’final
goal-Object’.

here an avoidance Object has been clearly interpreted as a

denial of the organism’s demand for a given goal-object (in

L31

this case the closed door at the first corner of alley L).

1h. Tolman’s reasoning here may be reconstructed as
follows. Let ’d(x, L))'O’ mean ’x demands alley L’,

’d(x, (11)) o’ for ’x demands the closed door’, ’d(x, f)>O’
for ’x demands food’, ’e(x, L 3 d1))>0’ for ’x expects that
alley L leads to food’. Given the avcidance law,

(12) [e(x, L : dl)>O . ~d(x, (11)) o] 3 ~d(x, L)> c,
that is, ’if x expects that alley L leads to the closed door
and x doesn’t demand the closed door then x doesn’t demand
alley L’, and the approach law

(13) [e(X, L 3 f)>O . d(X, f)>C] 3 d(X, L) >0,
that is, ’if x expects that alley L leads to food and also
demands food, then he demands alley L’, and the following
facts which held in the Robinson-Kever experiment,

(14) ~d(x, d1)>0:
that is, ’x does not demand the closed door’,

(15) e(x, L 3 d1) )0,
that is, ’x expects that alley L leads to the closed door’,
and

(lo) d(x, 1‘) )0
that is, ’x demands food’, we may deduce

(l7) ~d(x, L)>0,
from (12), (1h) and (15). From (17) we may deduce

(18) ~e(x, L 3 f)>0,
with the help of (13) and (lb). (18) is a symbolic trans-

lation of (a).

h2

15. The reasonin; here is perfectly prOper; but, unfortu-
nately, it does not say what Tolman wants to say. Consider

that organisms which are not even in the experimental situa-

 

tion satisfy (16) -- and what is more, (1h); an organism in
a deep sleep would make both (18) and (lh) true. These
organisms neither expect that alley L leads to food nor
demand the closed door. But surely it is not Tolman’s
intention to explain the "behavior" of organisms who do not
have demands for a given goal-object and who do ngt_expect

that given goal-objects lead to other given goal-objects:

16. A further objection is that the above reasoning does
not permit an adequate explanation of what actually happened
in the above experiment. For there is no way of inferring
on the basis of (18) and (14) the behavior of the animals
who clearly turned around and got to the food by the alley
on the right -— as the experimental results indicate. In
other words, it is not true that the following laws hold:

(19) ~ d(x, L)>o 3 d(x, R)>O

(20) ~ e(x, L D f)>O D e(x, R 3 f)>O
'where ’3’ means ’alley R (on the right)’. For the negations
of (6) and (7) are both possible; that is,

(21) ~ d(x, L))O . ~ d(x, r) )C,
and

(22) ~ e(x, L 3 f)>O . ~ e(x, R 3 f)>O
are both possible. Situations (21) and (22) would be satis-

fied by our sleeping organisms.

17. These difficulties are the product of thinking of
goal-objects as ’things’ rather than ’states-of-affairs’.
For it makes no sense to speak of x having a demand for a
not-closed door. And hence the only way of describing the
avoidance object is

" d(x, d1) >0.
To put it in other words treating goal-objects like’things’
forces Tolman to treat avoidance and approach objects as
analogous to logical contradictories when they are more

accurately treated as analogous to logical contraries.

18. Finally, interpreting goal-objects as prOpositions
would not have permitted these unfortunate consequences.
In accordance with the interpretation of goal-objects as
situations the laws (12) and (13) would have to be rewritten.
Let ’L’ mean ’x runs down alley L’, ’d1’ mean ’x runs to
doorl’ and ’f’ mean ’x eats food’. Then we rewrite (l2)
and (13) as follows:
(23) [e(x, L 3 dl)>0 . d(x, ~d1)>0] 3 d(x, ~L) )0
(21+) [e(x, L 3 f)>O . d(x, f)>O] D d(x, L)>O
(23) describes a typical avoidance situation, that is, "If
x expects that if he runs down alley L then he can run to
the door, and x demands that he not run to door, then x
demands that he not run down alley L". (2h) may be interpreted
analogously; (2h) describes a typical approach situation.
Again the "facts" (1h), (15) and (16) will have to be rewritten

under the new interpretation of goal-objects as:

141+

(25) d(x, ~dl)>0

(26) e(x, L 3 dl)>0

(27) d(X..-f‘)>0
Under this new interpretation of goal-objects we cannot
arrive at the conclusion in (18). A more apprOpriate inter-
pretation of the behavior of the Robinson-Never animals would
read:

(28) e(x, ~L 3 f)>O
or "x expects that if he does not run down.alley L then he
gets to eat food." This would mean.ngt that the closed door
on either side meant the non—availability of that side as a

means to food but rather that the closed door on either side

meant the availability of the other side, that is, alley R

 

(the Right alley) as a means to eating food. To get (28),

 

laws other than (23) and (2h) would be required. What they
may be need not deter us here. The point to be made is
satisfied by the above discussion; namely, that interpreting
goal-objects as propositional in character does not lead to
construing an avoidance object as a denial that the organism
demands a given goal-object. Further evidence for this con-
tention is shown in the fact that sleeping animals or, more
broadly, animals not in the above problem situation would
not satisfy the conditions expressed in (25) or in (28).

For the conditions in (25) and (28) require that the animals
demand and expect given goal-objects. Again, ’x runs down

alley R’ would satisfy the conditions expressed in (28).

£15

The Primitive Idea of Demand

 

19. On page hhl of Purposive Eehaviorism Tolman des-

 

cribes a demand as

An innate or acquired urge to get to or from some

given instance or type of environmental presence

or of physiological quiescence...or disturbance...
This statement suggests that demands are directed toward or
are about things; it is a thing which the organism gets to

g V

or from. T118 view of demand is subject to the difficulties
pointed out in the immediately preceding section of this
chapter; especially, is it subject to the difficulty of

not being able adquately to characterize the approach-

avoidance object distinction. On page M37 of Purposive

 

Behaviorism, Tolman defines an avoidance object as one

 

"which is to be got from". hence, he suggests that the

organism does demand something in the avoidance situation.

 

But, as has been pointed out in paragraph 12, where the
approach situation is taken as an urge to get to a given
thing, the avoidance situation must be characterised as

the denial of the urge to get to that thing, that is, the
denial of the demand for that thing. This, of course, con-
flicts with the above description of an avoidance object as
a "demand-against" or as an urge to get from the object.

In accordance with the remedy suggested in the immediately
preceding section of this chapter, the above description

of demand is reinterpreted by replacing the word ’presence’

with ’situation’ and introducing the expression ’situation of’

ho
between ’physiological’ and ’quiescence’.

20. There is another characteristic of demand which is
not made sufficiently clear in the above characterization
of demand; it is the forward pointing character of demand.
When one affirms that an organism demands a state-of—affairs
pg or come £2.22 true. Our demands or urges are for some-
thing in the future; not for something in the present or
past. For example, when I demand that my hunger be alle-
viated, I am now hungry but I am not ngw_a11eviated; the
state of alleviation is something to be brought about and
hence is something postdating my demand. The moment alle-
viation of hunger occurs, demand for it, in the particular
case, ceases. The most natural phraseology here is: x
demands that his hunger bg alleviated; the demand is for
the bringing about of some state—of-affairs. Demands are
thus forward pointing. In order to capture the forward
pointing character of demand in the above characterization
of demand the following emendation is made: Substitute for
the expression ’urge to get to or from’ the phrase ’urge to
bring about’, and add the phrase ’or its opposite’ imme-

diately after ’environmental situation’.

21. Demands, depending upon the circumstances and the
demanding organism, may vary in strength. On page 67 of

Purposive Behaviorism, Tolman writes:

 

With relatively strong nursing-need the litter was
strongly demanded; with a relatively slight nursing-
need it was but slightly demanded. And correspond-

 

1.1-7

ing to these differences in the demand the maze
performance improved and degenerated.

 

 

Consequently, we add to the above characterization of demand

the phrase ’which varies in strength’.

22. In virtue of the proposed ramifications listed in the
preceding three paragraphs, "demand" may be described as
An innate or acquired urge to bring about some
given instance or type of environmental situa-
tion (or its Opposite) or of a physiological
situation of quiescence or disturbance and
which varies in strength.
Accordingly the primitive idea of demand may be apprOpri-
ately expressed in functor notation as
d(x: p):
which means, ’the strength of organism x’s demand that p
be true’. The conventions for expressing the case where

’x demands p (or not p)’ are those discussed in paragraph A.

in this chapter.

23. Finally, demands sometimes may be drives, but the

converse is not true. On page 27 of Purposive Behaviorism

 

Tolman defines a first order drive as a
...demand for the presence of [a] specific physio-
logical quiescence (appetite) or against the pre-
sence of [a] specific physiological disturbance
(aversion) which results from initiating organic
excitements.
In short, a first order drive is a "demand for (or against)"
a final goal-object. But, on the other hand, organisms also
demand means or subordinate goal-objects like ’running down

the alley’, ’turning to the right’, etc. These latter demands

are not drives.

MB

The Primitive Idea of Expectation

 

 

24. The concept of expectation is perhaps the most im-
portant concept in Tolman’s theory; certainly it is the
most novel. It is in terms of this concept that Tolman’s
theory is usually contrasted with other theories of learn-
ing; for -xample, the s-r reinforcement theory of Bull,

the theory of Guthrie, etc.

25. Tolman conceives of an expectation as a setting of
the organism for the occurrence of a situation.11 Less
abstractly, to say that an organism expects a given state-
of-affairs to be true is to say that he ’believes’ that

the state-of—affairs will occur. This statement is not to
be taken as implying that expectations are always conscious.
Tolman’s account of expectation, as he himself notes, rests
on no assumption of the organism being conscious.12 An
expectation is a belief or judgement, conscious or uncon—
scious, that so and so will occur.13 Indeed, it might be
compared with Russell’s notion of "animal inference".lLL
The essential difference between demand and expectation is
this: demands impel or initiate the organism into action;

expectations direct the organism’s action.

 

ll. The remarks made in paragraphs 2h and 25 apply to all
kinds of expectations. The expression of means-end
expectation is described in paragraph 27.

12. Purposive Behaviorism, p. 20h.

13. Purposive Eehaviorism, p. 29.

1’. Russell, B., human Knowledge; its Scop§_and Limits,
London, 19hd.

 

 

M9
15

26. An expectation, like a demand, is forward pointing.
It is always conceived to be forward-pointing with respect
to some immediately distant or future occurrence. It is
evoked by present stimuli. On this point there is a
seemingly glaring inconsistency to be found between Tolman’s
account of expectation in chapter IV and his account of

expectation in chapter V in Purposive Eehaviorism. On page

 

8A of Purposive Behaviorism he writes:

 

 

EXpectations, those of means—objects as well as
those of goal-objects, those to be called per-
ceptions as well as those to be called memories,
are always forward-pointing. This fact of their
forward-pointingness is relatively obvious for
expectations of goal—objects. For here the
stimuli and the resultant expectations which
they release quite evidently precede the later
goal-object encounters, which verify or fail to
verify such expectations. The expectations in
such cases very evidently point forward to the
later moments of goal-object encounter and veri-
fication. But a similar situation really like-
wise obtains for expectations of immediate means-
objects. In these latter cases also, the per—
ception or memory, as an expectation, is a prior
’setting’ of the behavior for such subsequent
encounter as ’here an opening’; ’there a wall’;
’here a smellable crevice’; and the like. Again,
the actual encounter which verifies or fails to
verify that ’tnis is an opening, a wall, or a
crevice,’ is a temporally separate and later event.

here Tolman stresses the point that what is verified is
always temporally consequent to the expectation of it.
For example, suppose that we have a straight alley maze
with food in the goal-box. Suppose further the rather

trivial circumstance that if the animal gets to the food,

 

15. Purposive Eehaviorism, p. 8h.

 

It .(ll-(lilrli‘rili. ‘

he can eat the food. Let us assume that animal has been
able to build up an apprOpriate means-end expectation.

Now Tolman’s description of the test run -- in accordance
with the account in the above quotation -- might run as
follows: "The animal expects that if he gets to the food,
he can eat the food. The animal is allowed to run down
alley A so hat he gets to the food. ’Getting to the food’
is a stimulus situation. As a result there is evoked the
expectation that he can eat the food -— an activity which
is verifiable after the expectation." Contrast this situ-
ation with the one cited in the following quotation on

page 81 of Purposive Eehaviorism.

 

With such an arrangement, the stimuli coming from
the goal-object would, during the given trial it-
self, evoke an expectation as to the character of
this goal-object.
here Tolman seems to be saying: "Under the same conditions
in the artificial situation described above, getting to the
food evokes the expectation that the animal can get to the
food." But notice in this situation that is expected is
not something verifiable after the expectation; for the
activity, that is, running down the alley has already
occurred. Briefly the two situations may be contrasted in
this way: the first situation says that the animal expects
to do it, Ehgp (i.e., later) does it. The latter situation

says rather that the animal does it, then (i.e., later) ex-

pects to do it -- sort of a James-Lange theory of expectation:

27. The reason this inconsistency is only apparent is

, 0 ’ O V O o ,
because goal-obyect is being used ambiguously. On page

8h of Purposive Behaviorism, it is a state-of-affairs; on

 

page 81 of Purposive Eehaviorism it is a thing. Under the

 

interpretation of goal—objects as things the common "object"
in the above situations is ’food’. But, as we have seen

earlier, in this chapter, it is extremely difficult, if not
impossible, to discriminate between different activities in-
volving the same "object" or thing, e.g., in this case ’food’.
Tolman’s real intention in the passage on page 81 of Purpos-

ive Behaviorism is accurately exhibited by the description

 

. 1 _ , 1 Q 2 ‘ T J l 0 1: k 0 o
in the passage on pa;e ul of lurpos1ve weiaViorism. In

 

terms of that description the stimulating goal-object would
be "getting to the food" while the expected goal-object would
be "eating the food". And thus the "inconsistency" dis-
appears.

‘

28. Expectations, like demands, are to be construed as
relations between organisms and states—of-affairs. Expecta-
tions, like demands, are also variables; that is, they vary
in strength. One may have a strong expectation or a weak
expectation depending upon the situation and the expecting
organism. Evidence that Tolman conceives of expectation as

" is presented in the following statement.16

a "variable
The second feature of our system which may, perhaps,
be abhorrent to true Gestalt—ists is that we have
included among these determining variables not only

 

16. Purposive Behaviorism, p. M20.

 

52

the immanent sign-gestalts and the behavior-
adjustments but also: (a) a variety of pre-
ceding determinants; viz., capacities and

(b) a series of analyzed variables with iin the
sign-gestalts; viz., means- end— —readinesses

and means- end-expectations, and discriminanda-
and manipulanda—readinesses and -expectations.

 

In ternm of the preceding discussion we may crystallize
the rubtion of expectation as follows. ‘hen an org anism
expects a state-of-affairs he has the strong or weak con-
viction, or has the strong or weak belief, that a given
state- of- -af1 airs will oe brou ght about or will occur.
Again., like demand, an expectation is appropriately ex-
pressed in functor notation as

e(x, p)
which means ’the strength of x ’s expectation that p will be
true’. Conventions allowing one to say that an expectation

exists or does not exist are the same as those for demand.

29. Let us consider the notion of mean—end-readiness in
relation to that of means-end-expectation. In this essay,
to say tr at x has a readiness for p as a means to q is to
say that x expects that p implies q. In symbolism this may
be written:17

r(x, p, q) = Df e(x, P 3 q)-
[This definition is informal and will not be listed among
the official definitions in the present system.)
The reasons for adopting this convention are twofold. First,

interpreting means-end-readiness in this fashion does not

 

17. It should be noticed that a means-end-expectation is simply
a substitution instance of ’x expects that p is true’, that
is, of ’e(x, p)>’O’. In the definition above ’p 3 q’ has
been substituted for ’p’.

53

perceptibly change the working consequences of Tolman’s
theory. Indeed, insofar as the working theory is con—
ceived, means-end-expectations do the same job as means-
end-readinesses. Lastly, the differences between means-
end-readiness and means-end-expectancy, for example, mean-
end—expectancies are regarded as "specific" instances of

10 are concerned with a much more

means-end-readinesses,
general account of Tolman’s theory of learning than is

being attempted in this essay. As such, what is said in
this essay is not genuinely affected by such differences
between means-end-readinesses and means-end—expectancies.
Tolman’s later work seems to support these conclusions.

For there is great emphasis on the notion of expectation
and little on the notion of readiness. This seems to be
-evidence that Tolman himself, insofar as he is concerned

with the empirical working consequences of his theory, is

really concerned with expectations rather than readinesses.

30. The notion of "means-end-demand" may be defined in
terms of the concepts of "demand" and "means-end-expectations".
A means-end-demand may be "defined" as

d(x, p, Q)>O 3 Dr [d(X, q)>0 o e(x, p D C1)>O],19

 

18. Purposive Behaviorism, Chapter VI.

19. There are certain formal difficulties with this definition
which, however, do not adversely affect the development of
the present system. Hence, if the reader wishes, he may
take ’d(x, p, q)’ as another primitive and replace the
above definition with the postulate ’d(x, p, q))’0 =

[d(X, q)>O . e(X, p D q)>o]’. '-

 

that is, ’x demands p as a means to q’ means ’x demands q
and expects that if p then q’. Evidence for the legiti-
macy of the definition is found in the following passage

on page 29 of Purposive Eehaviorism.

 

It will be asserted next that the subordination

of such secondary demands to the superordinate

ones is due to the interconnection of what we

shall designate as means-end-readinesses. The

rat, who because hungry and satiation-demanding
therefore demands food, exhibits, we should assert,
an interconnecting means-end-readiness, viz., the
readinessfor commerce with trat type of food as a
means to satiation. Similarly, the rat wlo, be-
cause food-demanding, is therefore peculiarly ready
for explorable objects, exhibits another more sut-
ordinate means—end-readiness, viz., the readiness
for commerce with such and such explorable objects
as the means to food.

31. The discussion of expectation ends with consider-
ation of a problem having to do with exploratory goal-
objects and means-end-demands. Tolman seems to believe
that under the exploratory demand, every object is demanded

as a means object. For example, consider the following pass-

age on page 33 in Purposive Behaviorism.

 

It appears, in short, that it is the hungry, or

satiation-demanding rat who is the exploration-

demanding rat. And further it also appears that
at the height of hunger, the exploratoriness is

specifically directed towards food.

here Tolman is offering the assumption that in all cases

 

1

where an organism 188 both a demand for the alleviation of
exploration and a demand for some other goal-object, say,

hunger alleviation, when the demand for hunger-alleviation
gets great enough, the demand for exploration takes on the
character of a means goal-object. 1n effect, this assump-

tion seems to be saying that the demand for the alleviation

k.)

f‘
v

I.
}

 

 

v.7.-

-.a
-..V-
.. .'

r x
' -
.-._. :

u- '
u

.. ~
u‘~

v

p

._ '
-i‘

 

 

 

 

s ' ‘_
“fl: .
\
.,_
“kva
_ a
‘V
s-.‘
Q. 7‘
I V
\‘ 1
..
k
\l
I
‘;
I.
' A
§ Q ‘
\n. ~
.
\
.5
. ,
‘i v‘

55

of eXploraticn is always instrumental in character. This
assumption seems dubious. for the exploratory demand is,

in some cases, what Tolman calls an "ultimate demand" and
hence not always a means demand. It is not being denied
that what is learned under exploratory demand is available
for use in order to satisfy a demand for, say, hunger satia-
tion. however, it is being denied that in fact such know-

ledge is always utilized by the organism when his demand for

 

hunger satiation, or the like, reaches a certain intensity.
It is only utilized when the organism establishes a means-
end-expectation which enables him to connect the exploration
demand with the demand for hunger-alleviation. Speaking
plainly, some organisms fail to make this connection because

they are probably not as smart as others.

32. The above conclusion is supported by the Euxton study
on latent learning. in this study, (1) different groups of
rats were allowed to explore a 12 unit T-maze for three,
four, six and nine nights respectively; (2) the animals

were deprived of food for hB hours and then fed in the food
boxes in the maze for 20-30 seconds; and (3) the animals
were put in the starting boxes of the maze and allowed to
run the maze with no possibility of retracina., These latter
were the test runs. Fifty percent of the animals attained
the error criterion on the first run. The animals’ learn-
ing was said to be latent because they demonstrated their
knowledge which was acquired in the exploratory period when

other conditions, that is, hunger, called such learning to

the fore.20 however, the animals that we are interested in
are the ones who did pg: reach the error criterion on the
first run or indeed on any run after the first run.
Tolman’s initial assumption requires that all of the ani-
mals in Euxton’s experiment reach the error criterion.
This did not occur. horeover, Thistlethwaite, in his
a
review of latent learning, writesz‘l
Additional amounts of exploratory training did
not produce larger percentages of animals that
could meet the error criterion.
Hence, it seems plausible that perhaps some of the animals
had a demand for exploration as an ultimate goal in itself.
Further, the fact that various animals would have had to
take a greater number of trials to reach the criterion,
if indeed they ever did reach the criterion, would seem
to indicate that a certain connectivity factor is necess-
ary to exalain their temporary or permanent inability to
establish, in Tolman’s parlance, a means-end-expectaticn
between the exploration demand and the hunger-alleviation
demand. The point is this: Tolman has over-intellectual-
ized the concept of expectation. That is, though the ex-
perimental observer perceives that there is a connection
between the exploratory situation and the hunger, thirst

situation, this does not permit him to suppose that the

learning organism has either a built in means-end—expecta—

 

20. hilgard, 3., Theories of Learnin", p. 285.
21. Thistlethwaite, D., Critical heview of Latent Learning
and Related Experiments, Psych. Bulletin, v. MB, 1951.

 

57

tion for the former situation relative to the latter or

that he automaticallji acquires this readiness at some

 

stage in the test situation. Tolman seems to have for-
gotten that a means-end—expectation is a cognition relat-
ive to the cognizer. Learning; does not proceed in an

"as-iffy" fashion:

The Primitive Idea of sensor; Reception

 

 

33. The notion of "sensory reception" is a replacement
for Tolman’s "commerce-with". ri‘he primitive ideas of TI
are all construed as relations of one sort or another

which stand between organisms and propositions or situa-

 

tions; the relation of "commerce—with" obtains between

organisms and things. This is the principle difference
—————h—

between the meaning "sensory reception" and the meaning

"commerce-with". On page Lino of Purposive Eehaviorism,

 

he writes:

Commerce-with. Any behavior—act in going off
involves an intimate interchange with (support
from, enjoyment of, intercourse with) environ-
mental features (discriminanda, manipulanda,
and means-end-relations). For such interchanges
or enjoyments with behavior—supports (q.v.) we
have coined the term co..r:runerce-with.

 

i: should be noted that "environmental features", “dis-

inanda", "manipulanda" are thing-like in character.

ice the definition of "com.1erce—with" betra‘s the ver
, J

Lngr- Tolman emphasizes in Chapter V of E‘urposive E'ehavior-

k...’

 

"cominerce-with" is a relation between organisms and

 

Lna‘s. If one substitutes for the expression "environ-
.——-—h———-

S8

mental features", the expression "environmental situations"
and omits "discriminanda" and "manipulanda" in the above
quotation, one thereby obtains a pretty fair picture of

the meaning of sensory reception.

3h. In the above explanation of the meaning of "sensory
reception", appeal is made to expressions such as "intimate
interchange with", "enjoyment of" and "intercourse with".

As in the case of ’ex ectation’, these concepts do not imply
consciousness or awareness. These expressions suggest a very
important characteristic in the meaning of sensory reception,
namely, that of immediate verification or confirmation. In—
deed, what is here being called "sensory reception" seems

quite similar to Carnap’s notion of direct confirmation;22

 

confirmation by immediate sense-inspection. For example,
the state-of-affairs ’There is a white card before x’ is
the kind of thing sensorily received by x; it is what one
means when one say "x sees the white card before him".
Furthermore, this "intimate interchange" between x and the
state-of-affairs ’There is a white card before x’ amounts
to a direct confirmation by x that there is a white card
before x. Confirmation, in Carnap’s sense, is synonymous

with "takes to be true".

35. In TI, we treat sensory reception as an ordinary
relation (that is, not as a functor) holding between organ-
isms and states-of-affairs. Again, sensory reception is

treated in the past tense, that is, as sensorily received.

 

22. Carnap R. Testability and Neanina Ya e Universit
1950. ’(See especially pages 455 and 11 y,

This relation may be symbolized as follows:

_ 8
p11: x,

which means ’p is sensorily received by x’.

36. The kinds of things which may be substituted for

’

’p may be either discriminanda situations, for example,
’There is a white card before x’, or manipulanda situations,
for example, ’x runs down the alley’. Tolman’s distinction
between discriminanda and manipulanda is abandoned in the
concept of sensory reception. As a matter of fact, Tolman’s
distinction between manipulanda and discriminanda does not
seem to be of very great value either experimentally or
methodologically. For example, Tolman, on page 86 of

Purposive hehaviorism, writes:

 

Actually, of course, in any given case, a rat will
be set for, i.e., expect, both discriminanda and
manipulanda. Thus in Elliott’s experiments the
rat obviously was actually set for, not only the
immediate maze—parts to "look" and "smell" and
"feel" so and so, i.e., discriminanda, but also
for them to "be" so and so for the purposes of
running, turning, swimming, i.e., manipulanda.
And, conversely, in Carr and Watson’s and in
hacfarlane’s experiments, the rat was, of course,
actually set for not only the maze-alleys to "be"
so and so for running, swimming, and the like,

but also for them to "look" and "feel" and "smell"
so and so. The one sort of "set" (expectation)
can never actually function without the other.

now if it is true that an expectation of the discriminanda
cannot occur without an expectation of the manipulanda ——
and vice versa -— the purpose in discriminating between
them becomes quite unclear from either a methodological

Or experimental viewpoint. For, in either case, it is

Clear that the consequences of the one will be the same

5.
v.

 

 

‘ . . A y . . _ .
w _ A. L... ~.~ ..W a .l. er. L,- 5 . a d u a. ,L.« . t a. \
..., Ahv ; p . L v
e u s v elk
||l| I'llllll‘ I." 1 F»
I
a
I
I

 

as the consequences of the other.

37. Treating sensory reception in the past tense has
another advantage. It emphasizes the backward-pointing
character of sensory reception. In this matter, sensory
reception is different from demand and expectation and is
like the next primitive idea, "confirmation". For example,
when ’There is a white card before x’ is sensorily received
by X, the sensory reception, that is, the direct confirma—

tion, postdates the occurrence of the state-of-affairs.

38. There are two principle reasons for requiring a
concept like sensory reception in Tolman’s system. First,
it has value in explicitly limiting the range of situations
which may be characterized as stimulus situations. This
latter notion is somewhat vague since the determination of
the spatio-temporal limits and the degree of intensity nec-
essary for reception—excitation have not been generally
established to the satisfaction of all psychologists or
physiologists. As such, the elimination of the vagueness
associated with the notion of sensory reception is an
empirical problem and thus falls outside the purview of

this essay. Let me proceed to an illustration.

39. It is well known that the conditions which Tolman
puts upon the responses of an organism include those of
demanding and expecting. That is, before an animal res-
ponds to a given situation, -- is stimulated by hat situ-

ation, —- he must not only demand it but expect it. This

.
I

I. w
a
a v
. »
s
Q r O
.
,
h
v 2
. A
c :
. ,7.
.. h ,v
.. .
.
h
.;
r
h
u
3
5.
.
v
I.
‘ A
J
.—
P
.
5.
C
on
L
_.
:.

 

 

 

 

 

 

61

is a restatement of Tolman’s position that not all situa-
tions in environmental proximity to the animal are stim-
ulating situations. In more established terms, unless

the animal "attends to" the situation, it will not evoke

a response. But now certainly Tolman does not intend

that any old demanded and expected situation will induce

a response in the organism to that situation. Eor ex-
ample an animal might expect that if he’s put in the start-
ing box of maze A and furthermore runs down alley E of that
maze, then he gets to food. Furthermore, he may be hungry,
and may demand running down the alley. But as long as the
animal is in some way prohibited from the sensory reception
of being in the starting box he will not respond -- that
is, he will not run down Q_ley B! In short, only sensorily

received situations are stimulating situations.

ho. The second reason why sensory reception is required
in T1 is this: it assumes, in part, the responsibilities
delegated to the notion of "commerce-with" in Tolman’s
theory. Since each primitive idea in TI takes as values
of its variable organisms or states-of-affairs (or situa-'
tions), the notion of sensory reception as a replacement
for "commerce-with" is required for the sake of the co-

herence of TI.

The Primitive Idea cf Confirmation

 

 

Al. The difference between confirmation and sensory re-

cnption is a matter of degree. Indeed, "confirmation" might

62

be explained as an indirect intercha 3e with, an indirect
enjoyment of, or an indirect intercourse with environ-
mental situations. As sensory reception corresponds to
Carnap’s direct confirmation, the present concept of con-

firmation corresponds to Carnap’s notion of indirect con-

 

firmation.23 To put it another way, to say that a state—

 

of-affairs has been confirmed is to say that its confirma-
tion is based on confirmation by sense inspection (sensory
reception) of certain other states-of—affairs. For ex-
ample, consider the case where x has sensorily received
that there is an open alley before him, that is, x "sees"
the open alley before him, and has sensorily received that
the door is Open at the end of the alley. Cn the basis of
this information we might say that x has confirmed (by
induction) that the alley which turns to the left at the
Open door leads to food. Confirmation, in our sense, is
an indirect taking to be true; an inductive taking to be

true.

M2. Confirmation, like sensory reception, is (1) treated

in the past tense and is (2) taken to be an ordinary relat-

ion between organisms and situations. hence we may write:
xCp

which means ’x has confirmed that p is true (or exists)’.

Again, like sensory reception, confirmation is backward

 

23. Op. cit., Testability and reaning, pp. 11 and MES.

.11—

63

pointing. That is, when x has confirmed trat tte alley
which goes left is free of obstacles, t1e confirmation of

this situation postdates the occurrence of tlat situation.

h3. The next consideration has to do with the forward
pointing character of expectation chains. That is, before
a given stimulus can "release" various expectations in a
chain, the conditions for the releasing of these expecta-
tions must be, at least, indirectly confirmed. Let us
examine a concrete example. Suppose that we have trained
an animal in a straight alley maze. Suppose further that
the animal has built up a means-end-expectation (means—end-
readiness) during this training that if when he is in the
starting box he runs down he alley, he gets to food. In
the test series our animal is put in the starting box.

This is a stimulus situation. The means-enC-expectation
that if he runs down the alley th n he gets to food is

thus "released". This means-enc-expectation is "released"
by the fact that the animal has confirmed or verified the
first term in the expectation chain, that is, he has con-
firmed that he is in the starting box. The result is that
the animal’s confirmation of being in the starting box
takes on the character of a stimulus whicL in turn "releases"
the expectation of getting to food. The following passaae

on page C5 in :urposive Lehaviorism seems to support this

a

 

View.

This statement of the duality of stimulation and
verification is but another way of saying that any
behavior-act requires not only stimuli to release

 

,
fl,“—

wr—

0-..4

 

 

it, but also, later, more substantial environ-
mental actualities such as fulcra, media, and
planes, to support it (i.e., verify it, make it
possibka). Stimuli by themselves are not enough;
supports also are needed. behavior cannot go off
in vacuo. It requires a complementary "support-
ing" or "holding-up". The organism, as a result
of stimuli, expects that such and such "behavior-
supports" are going to be in the environment.

A rat cannot "run down an alley" without an actual
floor space ahead to catapult into. And in a dis-
crimination-box, re cannot "choose" the white side
from the black without actual choice. behavior-
acts and their immanent expectations are released
by stimuli; but they demand and are ustained by
later coming behavior-supports.

In parenthesis it may be remarked that this fact
that supports, and not merely stimuli, are needed
for the actual going—off cf any act and are ex-
pected by such an act, is a feature about behav-
ior which orthodox psychologies, both stimulus-
response psycholOSies and mentalisms, seem hith-
erto to have overlooked.

And further on pages 66 and 87, Tolman writes
lhe final definitions of expected discriminanda
can, it must now be noted, be determined in the
last analysis only by a whole series of experi-
ments. Suppose, for example, we discover that a
given behavior seams to be "eXpecting" the pre-
sence of a certain specific color. This behav-
ior it is found, will, under the given conditions,
continue to go off only so long as this specific
color proves actually to be there.
an. Onefinal point; in the above illustration we use the
more general "has confirmed" in order to release the expec-
tation for two reasons. First, Tolman himself takes a very
broad View of what "releases" or "fires" a chain of expec-
tations as is evident in the above quoted passages. Second-
ly, it is a law in the present system that sensory recept-
ion implies confirmation. ln symbols, this law is written:

phex 3 xCp.

hence, in Carnap’s terms, if we allow that an indirectly con-

65

firmed state-of-affairs may set off a chain of expectations
then we must allow that a directly confirmed state—of-
affairs may set off an expectation chain. Indeed, the
illustration in paragraph h3 depicts direct confirmation

as releasing the described eXpectation. nevertheless, an
expectation chain can be set off by indirect confirmation,
for example, by the kind of induction described in para-

graph hl.

f".

he Primitive Idea of Response Tendency

 

 

AS. Ihe term "response" is used in at least two dis-
tinct ways by psychologists. It often means each indi-
vidual occurrence of a certain type of activity which is
‘nitiated by a given state-of-affairs. for example, when
I stick my finger with a pin, I respond by snapping back
my hand to the left; or I may snap my hand back to the

right, back and above, etc. The point is this: the type

of activity constitutin.

(J‘

the response to the stimulus which
is described by the proposition ’x sticks his finger with

a pin’ is that of "snapping back the hand". Let us desig-
nate this meaning of response as ’Rl’. The second mean—
ing of response is more accurately described as the frequ-
ency of occurrence of R1. For example, consider the case
Where the psychologist wants an animal to learn always to
jump to the white card in the jumping stand. Suppose the
criterion of learning is 1h correct choices in IS consec-

utive jumps. In such a case, the psychologist often means

 

 

 

 

 

by "response" the frequency of occurrence of a certain type

of activity, for example, here, ’jumpin to the white card’,

8
which is initiated by a given state-of-affairs. In other

words to sav the orranism has erformed is to sa'"r the oraan-
: a, .5 t-

P.
U)

ism has responded, in th latter sense, to a given state-of-
affairs. Let us designate this second meaning of the term
"response" as ’fig’. In TI, "response" means response in

the sense of R2; more specifically, R2 captures the mean-

ing of "response tendency".

as. "Response" in the sense of ’R2’ clearly is an arith-
metical variable. For examdle, during a block of five trials
it might be predicted that the organism would make three
correct responses (in the sense of R1) out of 5 possibilities.
lhe organism would then be said to have the tendency to res-
pond in a given manner to a given state-of-affairs 3 times
out of S; or at the ratio of 3/5. It is clear that the
notion of reSponse tendency is easily expressible in functor

notation. how do we write this idea?

47. Notice first that the concept of response tendency
stresses the particular type or kind of resultant activity
to a given state-of-affairs. It suggests further that the
only conditions under which one may be allowed to say that
the prOposition x responds by so and so to such and such a
state—of-affairs is when the frequency of that activity
reaches a certain predetermined level. Again, this result—
ant activity is causally consequent on an initiating state-

T-
'l

of-affairs. pith these points in mind the notion of res-

6?

ponse tendency may be written as essentially a functor having
three arguments, that is, as

P(X, w: p)
which means ’the tendency of x to respond by the type of
activity o to the state-of-affairs p’; ’o’ is a predicate
variable, ’x’ is an organism variable, and ’p’ is a pro-
positional variable. hence, in accordance with the remarks
at the beginning of this paragraph, if we let the number 1
be the predetermined learning or performance criterion, then
the prOposition that g responds by o to p is the same as
saying that

P(X, Q: p) = 10
Indeed, the following law would seem to hold:

(2?) fix, <9, p) = l 3 (PK,
that is, ’if X’s tendency to respond by p to p equals 1 then
ex is true’. Interpreted, this law might read in a given
case, ’if X’S tendency to respond by "jumping to the white
card" to the state—of-affairs "there is a white card before
18 equal to 1, then "x does jump to the white card".
When the conditions in law (29) are met we might say that
’o’ is a realized predicate. When the number is less than
1 but greater than C (the performance criterion number),
that is, when

(30) ML <9, p) = 1x: . O<N<l
is true, ’o’ is a realizable predicate. Finally, to say
that x has a tendency to reSpond by p to p we may write:

MK, (9, p)>0o

 

v

I-.-

 

u

...-

b-v

\ -,

Ir-..

.

o.“

.v.

-

‘t.

u .

a..-

Q

._

.‘.
o .
a...

u

--.

n

a".
.- b.“

t

'.

~u

1
r .

i;-
‘._
'zy.
‘L¢-
A
r “.
'1. .'
2‘3,
u...
0

A._
7)..

u
L-.-

Trh

4“

 

   

68

h8. There are certain problems connected with this View
of response tendency. Notice that, in a given situation,
predicting a certain strength of response tendency say,

r(x, $9 p) = .70,
is like assigning a certain probability to ’r(X, o, p)’.
how to make this assignment is the problem. Generally,
we would make this assignment in one of two ways: (1) on
the basis of the known total number of responses in a given
situation or (2) on the basis of the number of possible res-
ponses or trials in arbitrarily selected blocks of trials
for each of those block --say, blocks of 5 trials each.
In the case of (l), we seldom kngw_in a given situation
the total number of responses which it is possible for the
organism to make and hence the basis of the assignment of
the probability number to ’r(x, e, p)’ is questionable. We
might fall back on method (2). But obvious difficulties
occur here also as soon as we begin comparing the increase
in tendency to respond in, say, blocks a_through b_with
later blocks d_through g’or tre increase in tendency to res-
pond in the total blocks of trials in one study with the
total blocks of trials in another study where the two totals
are different. The solution to these problems, however, lies
outside the scope of the present study. It is the hope of
the present author that despite these difficulties the notion

of response tendency may prove to be useful to the investiga-

Ho

tor at least as a su' estive dev

LC

ce.

h9. ihe final point concerns the circularity of stimulus

69

and response. huch ado is made in systematic courses in
psychology about the so-called circularity of stimulus and
response. The discussion usually proceeds in this fashion:
"In order to study behavior we must start with certain under-
stood concepts. Among these understood concepts (’stimulus’
and ’response’), the one 'hich is not taken as undefined or
understood is defined in terms of the other. here a spec-
ial problem arises. Suppose, for example, we take ’response’
as understood. Then.we define a stimulus, quite generally,
as ’that which evokes a response’. But now suppose we ask
what it means to be a response? The answer to this question
amounts to this: a response is ’that which is evoked by a
stimulus’. hence we have the problem of the circularity of
stimulus and response." I should like to point out that

the problem of circularity of stimulus and response, inso-

far as the logic of system buildin-

c:

is concerned, is a
pseudo-problem. In the above example the question concern-
ing the meaning of response in invalid. First of all, there
may be an ambiguity in the question —— probably associated
with the speaker’s use of the word "meaning". Does the

question ask for a definition of response or does it ask

 

for a characterization of response -- for example, such

 

as one gives in the case of the primitive idea of alter-

nation in the system of Principia? If the former is meant,

 

the question is clearly improper. For the question would
be askirg: what is the definition of the undefined term

"response”? 0n the other hand, if the second case is in-

7O

tended there would be no question of circularity because
the intent here is not to define reSponse, but rather to
give some clue as to how the term "response" is to be
interpreted. The circularity then is merely apparent
because the intention is not to define "response” in

terms of "stimulus", but rather to characterize or ex-
plain, independently of its occurrence in the system, its
general use. Indeed, in the present system, on the basis
of the above account of response tendency, it is very easy
to define "stimulus" in the following terms:
pSX = Bf (3@)(I’(X. (P, p) >0),

hat is ’ is a stimulus of X’ means ’There is a such
,

that x has a tendency to respond by m to p’.

Two Concepts of Docility

 

50. In lolman’s theory the concept of docility is diffi-
cult to grasp. The difficulty is largely the result of
using "docility" in two distinct ways. Strictly speaking,
there is no single primitive idea of docility in Tolman’s
theory; rather there are at least_tw9 distinct primitive
ideas of docility. The first meaning of "docility" is
"teachability". The second meaning of ”docility" is
"taught". Surely these are distinct concepts -- though
they do have some features in common, for example, both

are variables. Let us take up these ideas one at a time.

51. When one eXplains "docility" as meaning "teachability"

he is treating docility as a disposition predicate. A dis-

71

position predicate designates a disposition or capacity of

the organism- Ihis does not mean that the capacity is al-
ways being put to work, that is, is active. We character-

ize people as having drives even when they are not in any

OJ

way impelled to act in accordance with that drive. In

A

short, a disposition is similar to what John Locke refers
to as the "power" to do something or act on something.
52. "Teachability" means essentially "the capability of

. 1

s posSlole to define "teachability"

H.

being taught". Thus it
in terms of "taught”. however, the meaning and formulation
of "capability" is an extremely difficult and subtle thing

to accomplish. both of these terms, then, will be regarded

as primitive in TI.

53. "Teachability" is a variable. For example, we may

 

characterize one animal as more teachable than another.

93

Again, "teachability" is predicate holding between organ-

isms and states-of-affairs which are means to other states-
of-affairs. Teachability is thus apprOQriately expressed
in functor notation as

“X. p, q)
which means ’the degree to which x is teachable with res—
pect to p as a means to q’. Other conventions governing
the use of functors as described in paragraph u. of this

chapter are appropriate here.

Sh. hhen one treats ”docility" as "taughtness" he is

treating docility as a non-diSpositional predicate. As

 

 

 

 

 

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72

suggested above, "taughtness" is really the activation of

the disposition. Thus when the child adds the figures 2

and 2 and gets A rather than S, we say he is docile in the
sense of being taught. he has been taught that the correct
addition is that 2 and 2 are A. In general, when an organ-
ism is docile in the sense of being taught, one is saying

that he has been led to see the "correct" (best, most

efficient, etc.) means of solving a problem.

55. "Taughtness" like "teachability" is a variable.
Witness, for example, the following cases; "So and so has
been better taught", "So and so has been really taughti",
etc. It is, too, a relation holding between an organism
and at least two states-of-affairs. hence it may be des-
cribed in functor notation as

tA(X, p 3 Cl)
which means ’the degree to which x has been taught that p
is a means to q’. Other conventions governing the employ-
ment of functors as described in paragraph A. of this

chapter are apprOpriate here.

So. The employment of "docility" as "teachability" by
Tolman is evidenced in his explanation of the phenomenon

of disruption.24 Tolman explains that when a "better" goal-
object is substituted for a "poorer" one during the course

of an experiment, he behavior of the animal will indicate

 

2h. Purposive Eehaviorism, p. 7b.

 

 

 

f
'v

 

..«

 

i‘ .
.
a; ...‘f-
“I .
‘V
I. a
.. y.
..‘
fir i
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er
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5. ~, .- _
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73

"surprise", that is, the behavior will show a trial-and-
error character. however, after the disruption effect,
provided that the animal is (and L88 been) docile with
respect to the better goal-object, the behavior of the
animal will tend to becore systematic and the choices of

the better goal-object will exceed the choices of the

poorer goal-object. here iolman is employing "docile"

as "teachable"; for the animal at the time of disruption

has not been taught anything. To be sure, it is not poss-
ible to determine teachability unless the animal can be
taught. Eut the point above that Tolman is emphasizing

is that the disposition of teachableness is required through-
out the experiment in order that the animal can be taught;
that is, will choose the better or more demanded goal-object
more times than the poorer goal-object after disruption. ln

other words the animal will not recover unless he is teach-

able with respect to the better goal-object.

57. In contrast, Tolman’s characterization of "docile"

as evidenced by the fact that the organism always picks

the more efficient of the routes to a final goal construes
the concept of docility as "taught”. in other words to say
that x has been taught that a state-of-affairs p leads to

a state-of-affairs q amounts to the claim that for any
given set of routes, if p is the most efficient of those
routes to q, x will choose p more often than any other route
as a means to q. Of course, this would imply that the ani-

mal is also "teachable". but the above is an explanation

m

of an active teachabilitlitkat is, of a "taughtness", if

 

you will.

at. Two final points: (1) It is evident from the pre-
ceding discussion that "taughtness" implies teachability.
The converse is not true. It follows that any law holding

for teachabilitg holds, also, for taughtness: (2) The
concept of taught is required in order to make more clear
the concept of fixation employed by lolman. her though we
may say that when someone is fixated on something ’p’ he
1as not been taught with respect to p, we may not say that

this were

F13

when he is fixated he is not teachable. for i
true we could never break down a fixation. ibis point will
be considered in the discussion of tie theorems of CI in the

next chapter.

g List of The Primitive Ideas

 

59. The primitive ideas of TI are listed in the order of
their occurrence in this chapter.

Pl ’d(x, p)’ means ’the strength of x’s deaand that p
is true’.

P2 ’e(x, p)’ means ’the strength of x’s expectation
that p is true’.

P3 ’phex’ means ’p is sensorily received by x’.
Pu ’xCp’ means ’x has confirmed that p is true’.
PS ’r(x, o, p)’ means ’the strength of x’s tendency to

respond by e to p’.

P6 ’t(x, p , q)’ means ’the degree to which x is teach-
able relative to p as a means to q’.

P7 ’tA(x, p, q)’ means ’twe degree to which x has been
taught tnat p is a means to q’.

 

The Definitions of i;

60. because some of tne postulates of TI are expressed
in terms of defined ideas rather than in terms of primi-
tives, it is apprOpriate to list the definitions first.
There are five definitions.

$1. 1.0 d(x, p, q)>o = Df[d(x, q)>o . e(x, p 3 q)>O]
This is the definition of means-end-demand. It reads: ’X
demands p as a means to q’ means ’x demands q and expects

that if p then q.

61. The following passage on page 29 of Purposive Behav-

 

iorism supports the accuracy of this interpretation of means-
end demand.

It will be asserted next that the subordination of
such secondary demands to tne superordinate ones
is due to the interconnection of what we shall de-
signate as means-end-readinesses. The rat, who
because hungry and satiation-demanding therefore
demands, food, exhibits, we should assert, an
interconnecting means-end—readiness, viz., the
readiness for coinerce with that type of food as

a means to satiation.s Similarly, the rat who,
because food-demanding, is therefore peculiarly
ready for explorable objects, exhibits another
more subordinate means-end-readiness, viz., the
readiness for commerce with such and such eXplor-
able objects as the means to food.

TI. 1.1 pI-a: = 3,» (Squad, 10. q)>01

‘V

This

H.

s the definition of means-object. It reads: ’p is
a means—object of x’ means ’There is a q such that x demands

p as a means to q’.

 

#~%_~ “~_~.i-

 

i
i
i
i

 

~.. ‘

 

76

TI- 1.2 plfx = if [d(x, p)>0 . ~(3q)(d(x, 13, Cd) 0]
This is the definition of an ultimate goal-object. It
reads: ’p is an ultimate goal—object of x’ means ’p is
demanded but p is not demanded as a means to any other

state-of-affairs, q’.

62. In Purposive sehaviorism, Tolman’s remarks on the
notion of ultimate goal-object are a bit confusing. Con-
sider, for example, the following passage on page 36 of

Purposive Behaviorism.

 

The ultimate goal-objects for the rat, or other
animal, are certain finally-to-be-sought, to to-
be-avoided, ph;siolo;ical states of quiescence
and disturbance due to initiating physiological
states or conditions. Subordinate to the demand
for or against these there are various types of
environmental presence, e.g., food, electric
grill, etc., demanded for or against as the last
steps in reaching such quiescences or in avoid-
ing such disturbances. And subordinate to these
latter there may be still other types of still
more subordinate environmental presences also

to be sought and avoided.

There are really three kinds of goal-object described in
this passage. The first sentence describes what Tolman
calls an ultimate goal-object. The second sentence des-
cribes what might be called a final goal-object. And the
last sentence describes a means-object. The confusion
arises in this way. Tolman often uses final and ultimate
goal-objects as synonyms. Thus an ambiguity is created.
in this essay ultimate (or final) goal-objects are used
in the sense in which we talk about hunger-satiation,

tzii

F3

st-satiation, and the like as ultimate goal-objects.

 

 

 

 

77

hence,vmatiblman takes as final goal-objects, drinkirg
umter,etc.,shall be construed as means-objects. Other
conshhnathnm reinforce this decision. nor example, it
nmkeslitthasense to speak of conflicting ultimate (physio-
lo;ical)gxmls. If an organism is hungry he does not have

conflicting demands atxnrt the demand.fku~lnni;er satiaticru

ut hezmg*be in conflict wit: respect to the means for

['71

satisfwhr.hunzer. Accordin;lv if ultimate aoal-ob'ccts
d t. a, a, J!
were situations like "eating food" etc., we should have to

reject the above View about conflict with respect to ulti-
mate goal-objects. For it is clear that we can be in con-
flict with respect to "eating food". furthermore, it seems

that the employment of "ultimate goal-object" described
above is consonant with the way in which Tolman actually

uses it in his interpretations of experimental results.

There is another point in this definition oi ulti-

e3.

mate

goal-object. The above definition should not be
taken as categfiaizing in.some absolute manner those goal-
cflxflasts which.axe ultimate from those which are merely

"finer it should be taken as suggesting that in

means. ha
arrf givem1:yituation what is designated as an ultimate or

firurl goalxddbject is not a means to any other goal-object.

Ihi£31nearu3'tnat.an.ultihate goal-object in one situation,

for example, alleviation of need for urination, might be
taken as a means object in another situation; for example,
a means to enJOyin; the ride in the automob-

cnn a 'tripr, as

78

ile. Indeed it may prove to be the case that one and the
same goal-object can be treated as both a means and/or
an ultimate goal object in the same situation. If this
latter case were found to be true, fl. 1.2 would have to

be abandoned.

TI. 1.3 1“(X, p, Cl) =1;,f[d(xy p: Q)>O o "(3P)[XC(I’="P)
0 d(x, I‘, Cl)>O]]

This is the definition of "fixation". It reads: ’x is

fixated on p as a means to q’ means ’x demands p as a means

to q and there is no r which has been confirmed by x to be

the same as not p and which is also demanded by x as a

means to q’. In effect, thio definition shows the out-

itv of the fixated organism;

U

Q.

rioht "stubbornness" or rifi
L)

’K‘

i

drastic means are needed in order to change his course.

64. In this definition, I have departed from lolman’s
writings, but, I think, not from his real intentions.
First of all Tolman’s discussion of "fixation", "cognition"

and "means-end readiness (or expectation)" in Purposive

 

Behaviorism leads to an inconsistency in his system. Con-

sider the following statements.
(a) Something is a cognition if and only if it
is a means—end-readiness (or expectation).25

(b) No means-end-readiness is cognitive, if it

18 fixated.

 

25. Ibid., p. Lglgo.
26. Ibid., p. 9h.

79

(0) Some means—end-readinesses are fixated.2?

L_.

From this set of preposit ons it is rather easy to deduce

the contradiction of (c), that is tne statenent which reads:

s fixated. As can be seen in the

P.

No means-end-readiness
above set of statements, the problem consists in being un-

able to determine whether or not ihere is such a thing as

(O

a fixated means-end—readines Tolman seems to say that

"you can" and "you can’t" have such a state-of-affairs
(of. especially his discussion on pages 29-31 in Purpos-

ive behaviorism). But, as tne above argument shows, this

 

situation is absurd. I have therefore taken the liberty
of rejecting the view that when an animal is fixated he
has no COgnition. lhis amounts to a denial of the state—
ment (b) above. nence, I arrive at the already prOposed
definition of fixation. from this definition we can con-
clude that
F(X, p, q) 3 (Eq) (d(x, p, q) # 0),
that is, when an organism is fixated on p, he demands p as
a means to another state—of-affairs q. That this is Tolman’s
real intention is supported, in the following passage on
page 31 of Purposive behaviorism.
It must be pointed out finally, however, that unless
the rats would show a tendency on further training,
finally to be docile to this fact that the larger

seeds are really no better, and, if anything, Iorse
than.the smaller seeds, then tne above described sub-

 

27. Ibid., p. 31.

80

ordinate readiness for the larger seeds would
after all be not trul; judgmental. In this
latter case it would have to be conceived,
rather, as of the nature of what we might call
a means-end-fixation.

TI. 1.3+ pix :Uf (Bap) [1“(x, <9, 13)) O]
7*is is the defin'tion of "stimulus". It reads: ’p is a

..Lllio

stimulus of x’ means ’ihere is a e such that x tends to

respond by it to p].

5—1

'-“..—..

This chapter presents the postulates and theorems

ihe postulates are distinguished from the defini—
tions and theorems by the prefix,

TI. 2.N.

lhe whole number which replaces E in the above prefix is
the number of th particular postulate. An analogous con-
vention is adOpted for the theorems. That convention will

be discussed when we come to the presentation of the theo-

rems.
. e(x, p 3 q) )0 . e(x, q 3 r)>O] 3

e(x, p 3 r)) 0

TI. 2.0 reads: if x has confirmed p and expects that p

implies q and also expects that q implies r, then he ex-
pects that p implies r.

2. TI. 2.0 affirms the "restricted" transitivity of
imolicative expectation. lt permits the develOpment of

an expectation chain. The addition of ’xCp’ to the ante-
cedent is a.necessary restriction. For, to use Tolman’s

chains cannot be developed "in vacuo";

words, expectation

they wayiire "supports". Again, Tl. 2.0 suggests a certain
provdjyional.claracter to all chains of expectations. For

exanmflxa, consider the case of an organism who has built up

8. "I expect that when

the Ikitlowing means-end expectation

82

I mngnn;in the starting box, I can turn right. I also

enqmct that if I turn right I will get to food". How the

question is this: under the supposed circumstances will

thecnfipnism expect that if he is put in the starting box
then he will get to food? lhe answer is: it depends.

he will if he has some evidence for the truth of p; that

is, if in some sense, he has "taken p to be true" - if he

has confirmed that p is true. For example, in the above

situation, it would be quite possible on, say, the second

or third trial where tie animal is not put in the start-
! ..

ing box, but rather is put on an Open stand in the same

position as the original starting box, that the animal

would not expect that being put in t1e starting box was

(or is) a means to getting to food.

TI. 2.1 [d(x, q)>O . e(x, p 3 q)>O] 3 d(x, p)>O

II. 2.1 reads: if x demands q and expects that if p then

q, then x demands p.

3. There are four points to be considered in the dis-
cussion of TI. 2.1 (1) T1. 2.1 suggests that the develop—

:ment of means-objects moves backward. Essentially, this

is Tolman}s contention, that states-of-affairs which are

expected_as nmans to others may become demanded objects in

thei1*cnna right. That is, that a state-of-affairs, p, which
is eiquzted as a means to another, q, is itself a demanded

cflaject is contingent upon the presence of a demand for q.1

 

s the evidence

1. flolnwui explains this principle and gi
haviorism.

v
ftns it on.pages lap-151 of Purposive E

6
e

83

(2) rrhe Opposite case, that is,
[d(X,p)>O . e(x, p 3 q)>C‘] 3 d(X, q)>0,
which reads, "if x deixlands p and expects that p is a means
to q, tnenx demands q", is sometimes false. This is evi-
dent upon the substitution of the prOpositions ’x crosses
the maze’ for ’p’ and ’x will be shocked severely’ for ’q’.
(3) ’p’ in 'I'I. 2.1 is a means-object. A theorem later in
this chapter will demonstrate this point. In this sense,
II. 2.1 differs from the next postulate which is the "cor-
relate" of "II. 2.1 for avoidance objects. For in the case
of the "correlate" of T1. 2.1, ’~p’ cannot be shown to be a
means-object. (LL) TI. 2.1 describes tlte typical approach
situation of ordinary psychological discussion and investi-

gation.

0

T1. 2.2 [d(x, ~q)> . e(x, p 3 q)>0] 3 d(x, ~p)>O
‘I'I. 2.2‘reads: if x dez‘uands ~q and expects that p implies
q, then he demands ~p. Another way of reading; this postu-

late is: if q is an avoidance object and x expects that p

leads to q, then p is an avoidance object.

[1. TI. 2.2 is the correlate of ‘II. 2.1; it expresses

the typical avoidance situation. hemarks (1) and (2) in

the d‘ scussion of TI. 2.1 app-1;," equally well in the case

)1“ T1. 2.2.

I. 2.3 [d(x, p)>O . d(x, ~p))C] D‘pMX

2. 3 reads: if x denands p and also ~p, then p is a

F":
O

earls—object of x.

5. The antecedent of TI. 2.3 is not to be construed as
a conflict-of-demand situation. In paragraph 1‘“. of chapter
II a typical conflict situation was described. notice that
the two conflicting cases described in paragraph 10. not

only showed X as derrianding; both p and ~p but also that x

demanded these contradictory states-of-affairs with the

38.2718 strength. The antecedent of TI. 2.3 requires only
that the two demands are greater than 0. It is not diffi-

cult to find a case in which an organism can demand con-

tradictory states—of—afi'airs at different strengths and still

not be in conflict. For example, suppose an animal to have

built up expectations that two and only two mutually ex-

clusive alleys, one longer than the other, lead to food.
If he has a demand for hunger alleviation, then in accord-
ance with postulate TI. 2.1, he will have a certain demand
,strength for running down either alley. Let us call he
lxnnger alley“’Af and the shorter alley ’B’. The demand

strength for running down alley A will be less than for

rwmind down alley B (in accordance with the law of le ast

effort). but notice that a demand for running down alley B
satisfies the prOposition that X demands not running; down
alley A. ladders 10100, this situation may be described in

symb ols as follows .

(l) d(x, ~A) =11,
’x’s demand for not runninp' down alley A is equal

 

 

(2) d(x, A) = Li?

’
that is, ’x’s dem -nd for runninj down A is equal to FI’

.
The conjunction of (l) and (2) satisfy the antecedent of

ii. 2.3, but clearly x does not have conflicting. demands
here; that is, he is satisfied with this arrangement. The
only case where demands are in conflict is where the demands

for two contradictory states—of-affairs are at the same, or

nearly tie same, strength.

6. nevertheless, we shall want 'l‘l. 2.3 as a postulate
for the reason that it allow-as us to prove, that if p is
an ultimate goal-object then if x demands p he does not
demand ~p. In other JOI’dS, if p is an ultimate goal-
object of X the contradictory of p cannot be demanded
{nor indeed can it be an ultimate goal-object). This con-
forms with t;;;:e interpretation of goal-object given in

1‘1. 1.2. These statements will be proven as theorems later

in this chapter.

TI. 2.4 [3:01) . e(x, p D q))O] 3 e(x, q)>O
TI. 2.L,r_ reads: if X1188 confirmed that p is true and also

expects tliat if p then q, then it expects q.

7. 7559 have seen in the discussion of confirmation that

if an expectation chain is to be "fired", at least con-

firms ti on (in the weak sense in which we mplo; it in this
$38.37, that is, as an indirect "taking; to be true") of the

irst term in that chain is required. This is why ‘l‘olman’s

86

useoftietmrd "support" in the quotation cited in that
dianmsimiis so apprOpriate here; an expectation cannot

p

that expectation

m less the chain in whic

be "released u11
we do not

is anembmris suoported. AnthrOpomorphically,
penfli:ourexpeotations free rein without grounds or at
ll. 2.h thus helps guarantee

least certain convimruions.
character of expectations; and hence

the forwa°d poiiitingg

of demands.

[e(x, 13))0 . 223(C1 3 ~p)] 3 ~ e(X, q)>0

TI. 2.5
e has confirmed

TI. 2.5 reads:
nat q implies not p, tnen he does not expect q.

/\

when x expects p and when L

Guards against an overly rational-

lhis postulate C

4 V

O.
istic interpretation of expectation.
to expect that he will do something at

how

Eor example, sup-

pose an organism
a certain time. Suppose that time is an hour later.
it seems Coqent to suppose that the same organism might

also ezgmxyt to do somethin; else incompatible with the

the same time. Cf course, if he realized

first action at
or*cn1nfirmnwd that the two actions were incompatible, it
seenm; fair°'to suppose that he would reject one or the
it is exactly this kind of situation that TI. 2.5

other.
lr1<3ther words, an organism might have conflict-

aJLLouma.
ezqnectmrtions so long as he does not veriiy that the

irq;
Another and

expected states-of-afi‘airs are incompatible.
perhaps more intuitive way of showing this restriction can
SllOVfll i1: ifine following theorem which is deducible from

7-
U3

87

II. 2.5, namely,
(e(x, p)>C- . e(x, ~p)> C) 3 ~xC (~p 3 ~p)
which, in effect, says that if x has conflicting; expecta-

tions relative to

*G'

, then he has not confirmed that p is

incompatible with not p.

TI- 2-5 [d(X, (0)0 . e(x, p 3 (cpx 3 q)))O . piiiex] 3
I‘(X, (9: 13)) 0

M. 2.6 reads: when x demands q and expects that if p t7::en

if ox then q and when furthermore p is sensoriljf received

by x, then x has a tendencj to respond by (p to p.

9. Perhaps, it would be helpful to give an interpreta-
tion‘ of TI. 2.6 in English. Suppose we have a typical dis-
crimination learning situation. Substitute ’x gets to the
food-box in back of the white card’ for ’q’, ’x jumps to
the white card’ for ’ox’ and ’there is a w}:.u.ite card on the
left’ for ’p’. ‘Ihen, in this case, TI. 2.6 affirms that
when an organism demands tE-nat he get to the food—box in
back of the white card and furthermore expects that if
there is a. white card on the le ft, so that if he jumps to
it, he gets to the stand in back of it, and finally,r senso-
rily receives that there is a white card on the left, he
tends to respond by jumping to the white card in relation

to the state-of-affairs that there is a white card on the

left.

10. 1'1". 2. 6, more than any other postulate in ‘11, marks

88

twedifikrame between Tolman’s theory of learning and

rning. TI. 2.6

hull%ss-rreinforcement theory of lea

2

’“l

.. 0
.LJ.

smpeststmat not every state-of-affairs p which is merely
stimulating state-of-a airs.

a

sensorily received.i§s
, expected as

In addition, p must be ”attended to", that is
airwanS'M>some other state-of—affairs, if i
a sthmfliw. null, on tie other hand, denies this content-
ion. fik>put it briefly, and thus a bit loosely, hull ap-
parently conceives of every state-of-affairs which is

igramatically, the

sensorily received as a stimulus.3 Ep
hull believes an organism

issue might be put as follows
learns something about everything; Tolman believes ttat
the organism learns something about only something.

TI. 2.6 expresses the conditions under which an

11.
organism will tend to respond to a given state-of—affairs.

However, it is not being claimed that these are the only

rule, when a gun is

:_J.IA.L

conditions under which an organism will tend to respond.
Under certain.circumstances,-Ixn'exav

firfxilmaaind an.unsuscectinr subject’s head -an organism
a. .J 9 ..

'will ixnni to respond to a state-of-affairs though he does
ruit dengumi or expect anything relative to that state—of-
afikrirs. Exotice, however, that such a stimulus situation,
(scapulsive stimulus situation, - does not falsi-

-oall it a

 

2.
”.11

\J

lhxrncmxive Eehaviorism, pp. 35—36.
3. lfiocli, c;., ark L. hull", Lodern Learning Theory,
Agnolertori Century Crofts, 195H(Cf. especially, p. 9).

fyl.7.LL Ihlother words the "promise" that wten an organ-

isncmnan03513tate of- ffairs q, when re expects that p

leads U>qm.wticn in turn leads to q and finally when he
sensoribrreceives p, then he tends to respond by e to p

is nottnoten‘when a compulsive stimulus Situation occurs.

Purthenmnmg the psycholosist is really concerned with the
non-cdqnflsive stimulus situation. TI. 2.6 is one way of

statinp the conditions for response in a non—compuls1ve or

situation. Clearly the investigator as—

—l—

"normal" stimulus
laws pertaining

U1

sumes "normality" of the situation in hi

to stimulation and learning. rurthernore, the tact that
the compulsive stimulus situation is not the "normal" kind
of stimulus situation makes it a much more rare and hence a

much less scientifically interesting situation -—at least,

as far as learning is concerned.

12. Finally, evidence postulate is a reason-
in the following

able translation of Tolman’s views is given
‘passages. Cn.page 35 of Purposive Pehaviorism iolman writes
.Einally we must now note a itu atio as redards

11 rats and other oroorions w;icn nstimulus-

” psycholOgies, as well as "behaviorism "
r, la argely to rave overlooked. It is a
tion whicl orthodox mentalisms we re well aware

‘Ihe latter sought to care ior it by their doc-
trdxues of attention and apperception. It is the
fact; Uiat rats and men have hur ndreds, not to say
tinmgsands, of stimuli impinging upon them every
irustant.of their waking lives; and yet to by far

S 86151

 

2+. ji‘verfif food.e} {ample of a 001pulsive stimulus situation
is irolnmnn’s 'initiating physiological state”

9O

thenwjority of these stimuli they do not, at
fingiven moment, respond. But in order now,
in.our system, to explain.this choosiness as
Mastimuli, we have merely to refer to these
facts of superordinate and subordinate demands
2mm.means-end-readinesses as just outlined.

Consider the case of food-stimuli. the satiated
rat "pays no attention” to food. he even lies
down and goes to sleep in its presence and so,
also, does the satiated human being. Ehe reason
the hun;ry rat is responsive is, we would assert,
(a) because he is demandinj hunfer-satiation,

and (b) because he is provided with a means-end-
readiness (innate or acquired, "qugmental" or
"fixated”), to the effect that comnerce with the
type of food, presented by the given stimuli, will
lead on to satiation.

his most direct statement on this matter appears on page

MO? in the sane source.

ihe organisn responds to the given stimuli only,
by virtue of an initiating physiological state
which, given his innate or acquired means-end-
readinesses, gives rise to demands, (superordin-
ate or subordinate) —-one or more of which leads
him to respond to the given S(timulus) as pre-
sentinj an appropriate means-object. These de-
pending demands control the whole line of the
S(timulus)-- R(esponse) process.

This list of quotations is concluded with a concrete ex—

ample of Tolman’s views concerning stimulation. The pass-

age is found on page 330 of Purposive hehaViorism.

But it appears obvious, to us at any rate, that
‘mse conditioned "approach" reSponse made to 82,
the white side of the discrimination-box, in-
volves different supports, i.e., expectations of,
alui commerces with different discriminanda and
Jnanipulanda, from those involved in the original
‘unconditioned response made to 81, the food.

ifise response which comes to be mace to 82 is, in
:flsort, not only, as we pointed out in the pre-
cedirg;sections, appropriate to the sign-cha°acter
of‘ifliis immediate object; --it is not only approp-
Ifiiate to the fact that this object (the white side
oi"the box) is a Sign for leading-on-ness to the
focmi (the object presented by the unconditioned

91

s timulus Sl)

-— but it is also appropriate
‘to the immediate discrininanda and manipul-
exnda characters of this imnedi

o ate 82 - object.
{to sum up, we note: (“

a) tiat the conditioned
:response is a response to the sign-relation-
shig S ---S . And this means that it goes off
only so lon; as that sign-relationship is
"believed” in by tne organism.

‘l‘l. 2.7 r(x, cp, 10))0 3 pjex
iii. 2.7’:reads: i1 x tends to respond by Q to p then p

is :sensoqdly‘received by X.

'13. This postulate is important. One night thirk that

a.{;iven state-of—affairs must exist in order to be a stin-

\£Lus. But this contention is false. For p might be an
‘illusory'state-of-affairs. Ievertheless, the illusory

state-of—affairs is sensorily received, that is, it is

taken to be true by sense-inepection. hence, the post-
ulate TI. 2.7.

T1. 2.8 tA(x, p , q))0 3 d(", p, q)>C>
T1. 2.8 reads: if

x has been taught that p is a means
to q then he demands p as a means to q.

in other words

if an organism has no demand he cannot be taught.

1h. ll. 2.8 employs one of tne meanings of docility

dimnnsed in the last chapter. In the discussion of the
pnhntive ideas of "taughtness" and "teachability" it was
poinhfilout that "teachability" could be defined in terms

of"tmnmtness" if an adequate analysis of what "capability"

Inmnsvms at hand. however, also, it was pointed out that

O
. .
.

I
.
.
a
C . .
. g Q
I P
I I \

 

 

92

Stufli an.analysis was not immediately forthcoming. Rever-

tflualess an."0perational definition" of teachability can

be {given in TI. For it is provable that

13AM. p. q)>0 3 [t(x, p, q)>0 = d(x, p, qDOJ;
thai;:is, if x has been taught that p leads to q then x is
teachable with respect to p as a means to q is equivalent

to x demands p as a means to q. This theorem is important

'because Tolman Speaks of teachability as that which "object-

ively defines demand". "Teachability" is the "mark" of

~emand in virtue of the fact that x cannot be taught that p
is a means to q unless x is teachable with respect to p as

a means and also demands p as a means to q. hence, we may

say that if x has been taught that p is a means to q then

he is teachable with respect to p as a means to q. And

since teachability is the "mark" of demand, then it follows

that taughtness is a "mark" of demand. The point is this:

one must get it out of his thought that teachability

"causes" or "entails" demand. But since Tolman’s test

fer demand is via taughtness, teachability may be regarded
as the mark of demand in the sense that if x is not teach-
able one need not go on to test for demand, because it

ibllows that x cannot be taught. hence, one may regard

teachability as objectively defining demand; for unless x

hstfiachable, demand cannot be tested for.

15. Lot only is "teachability" (and hence "taughtness")

anmrk of demand (purpose), it is also a mark of expecta—

tion.5 For it follows directly from T1. 2.8 that

tA(X. p, q)>0 D e(x, p D q)>0

lb. The evidence that Tolman himself believes taught-
ness implies expectation is deducible from the fact that

taughtness implies demand is given in the following quot-

6

ation.

rinally, it is to be noted that purposiveness and
cognitiveness seem to go together, so tlat if we
conceive behavior as purposive we pari passu con-
ceive it also as cognitive.

 

TI. 2.9 tA(x, p ,_ q)>0 D the, p: q)>0

i1. 2.9 reads: 1f x is taught that p leads to q, then x
is teachable with respect to p as means to q. This post-
ulate makes explicit the relationship between "taughtness"
and "teachableness" discussed in paragraph 56. in chapter

II.

‘11. 2.10 (cpx)Ux 3 ~ r(x, cp, p)>C

Tl. 2.10 reads: If ex is an ultimate goal—object of x,
then it is false tgat x tends to respond by e to p. This
postulate merely affirms that no ultimate goal-object is a

response to anything.

'11. 2.11 d(x, 9. q)>0 3 [tA(X. p, q)>0 v F(X, p, q)]

TI. 2.11 reads: If x demands p as a means to q, then x

 

p. Purposive Eehaviorism, pp. lh-17. See "Glossary" for
equivalence ofgfldemand" and "purpose".
6. Purposive Eehaviorism, p. 13.

 

 

9h

has been taught that p leads to q or he is fixated on p
as a means to q. This postulate is consonant with the
remarks concerning "fixation" in the discussions of the
definition of "fixation" and the concept of teachability

in preceding chapter.

TI. 2.12 phex 3 xCp
TI. 2.12 reads: if p is sensorily received by x, then x

has confirmed p.

17. This postulate reaffirms a suggestion made in the
discussion of "confirmation" in the last chapter (Cf.
paragraph M4). Since ’xcp’ contains as part of its mean-
ing ’is taken to be true’, it does not follow that

x3p 3 p;
that is, that if x has confirmed p, then p is true. For
not everything which is taken to be true is true. The
converse also holds. dence, it is not the case that
e

ph x D p;

0 "1

that is, that 11 p is sensorily received by x then p is true.

Again, the converse is also true for sensory reception.

18. There are borderline cases which are hard to deal with
in the case of T1. 2.12. This is because the difference
between ’pRex’ and ’x3p’ is a matter of degree. aeverthe—
less, we are able in a more or less vague way to say something
about the extremes of that continuum. TI. 2.12 is really a

statement which holds when we are willing to say definitely

95

p is sensorily received by x or x has confirmed p.

g Replacement fiule 'n 'I

 

19. The system of Erinciqia Mathematica is called a truth-
functional system. A system is a truth-functional system
hen every propositional function in it is a truth—function
of its constituent prOpositions. ror example, the truth

of ’p E q’ is a function of the truth of its constituents

’p’ and ’q’. ’p E q’ is true when both ’p’ and ’q’ are

true or when they are both false; in all other cases ’p q’

is false. lhe present system (ll and TII) is not a truth
functional system. lhis can be shown in the following way.
If the present system is truth functional then every pro-
position in it should be a truth function of its components.
hence, if ’p’ and ’q’ are the only propositional components
of ’e(x, p)>O’ and ’e(x, q)>0’ and if they are true, then
’e(x, p)>»O’ and ’e(x, q)>>O’ should be both true or both
false. Indeed, any relation obtaining between ’p’ and ’q’
should also obtain between ’e(x, p)> O’and ’e(x, q)>0’.

For example,

(1) p q 3 [e(x, p)> O E e(X, q)>O],

which reads: if the prOpositions ’p’ and ’q’are equivalent
then ’e(x, p)>O’ is equivalent to ’e(x, q)>O’. (1) can
be shown to be false. For example, substitute the prOpos-
itions ’Lambert has decided to buy a car’ for ’p’ and

’Eisenhower will run for reelection’ for ’q’. Eoth ’P’

and ’q’ are true. hence ’p E q’ is true. But ’e(x, p)>>0’

96

is not equivalent to ’e(x, q))’O’ where ’x’ is ’Eisenhower’
because Eisenhower does not know Lambert. hence ’Eisen-
hower expects he will run for reelection’ is undoubtedly
true but ’Eisenhower expects that Lambert will buy a car’

is surely false.

20. The present system is not a modal logic either. A
logic is modal if it contains an Operator ’C? which means
"is possible", that is, "is not logically inconsistent".
how, to say that p and q are mutually deducible, that is

(2) P " q,

is to say that it is not possible that p s true and q is

false and also it s not possible that q is true and p 18
false, that is,

(3) ~0(p . ~q) . ~<>(q . ~p).
It has been shown that the truth functional connective
:_:

: , when in main position in a formula in Princinia, can

A

1

cs "strengthened" to ’=’, that is, ”equivalence" can be
"strengthened" to "mutual deducibility". bor example,
the frincipia formula

(LL) pap

can be "strengthened" to

 

(5) p =p.

This ca be done because all the formulae of Principia are

 

analytic and hence are not logically inconsistent. There
are some cases where p = q does not materially imply that
e(x, p)>O = e(x, q)> O, that is,

(b) p = q D [e(x, p)>0 = e(x, q)>O]

97

is, in some instances, false. ror example, let ’p’ be
’(p . q) 3 r’ and ’q’ be ’p 3 (q 3 r)’. In Princitia
the following law holds:

(7) [(p-q)3r15[p3(q>r)]
According to the principle of strengthening (7) may be re-
written as

(b’) [(p . (1)3 r] = [(p 3 (q 3 r)].

Thus, under the above substitutions, the antecedent of (e)
is true. but there is good reason to believe that the pre-
sent consequence is sometimes false. ror though it is true
that

(9) e(x, p 3 (q 3 1’*)))O-—>e(x, (p . q) 3 r)>0
the converse of (9), that is,

(10) e(x, (p . q) 3 I')>O-99(x, p 3 (q 3 r))>O
does not always hold,7 For example, let ’q’ be a stimulus
situation, say, ’ihere is a white card before x’, ’p’ be a
condition consequent on the occurrence of ’q’, say, ’x jumps
to the white card’, and let ’r’ be a situation postdating
the occurrence of ’p’, say, ’x gets to food’. Then (10)
reads: "x expects that if x jumps to white card then if
there is a white card before him, he gets to food" is
deducible from "x expects that if both he jumps to the
white card and there is a white card before him, then he

gets to food". The trouble here is that the "if, then"

 

7. ’pfiq’ is usually defined as ’~0(p . ~q)’, hence
’p—9q’ means ’p is deducible from q’; or more commonly
’p strictly implies q’.

98

relation in the consequent of (10) does not seem to capture

the feature of consecutivity present in Tolman’s analysis

 

of expectation. This is more dramatically seen if in the
above application of (10) one rephrases that application
using "is a means to" rather than "if, then". Of course,
this leads to the conclusion that the material (or truth
functional) ’3’, that is, "if, hen", is too weak a relat-

"is a means to" in the notion

ion to express the meaning of
of means-end expectation. This point will be considered

again in the last chapter of this essay.

21. Since (10) can be false, then it is possible for the
present consequent of (b) to be false. hence we conclude

that the present system is not a modal system.

22. In Frinci

H33

ia, if a law of the form

 

P 5 q
holds, then if ’p’ occurs in any other formula, ’q’ may
replace ’p’ in that formula. This is the rule of bicondi-

tional replacement. but the results in the precedinq para-

 

‘D O

graphs will not allow us to employ this rule in T1 without
restriction within the contexts of expectation, demand, con-

firmation, etc. Let us call such contexts propositional

 

attitude contexts. Our revised rule then reads: if a

 

Principia formula of the form

 

P E q
also holds when governed by a given prepositional attitude,

for example,

99

e(x, p)>0 ':‘ e(x, C1)>O:
then if ’p’ occurs in any formula governed by that prepos-
itional attitude, ’q’ may replace ’p’ and vice versa. Eor
example, the following preposition is true in TI.

(11) d(x, p, q)>e a [d(x t, p) )0 . d(x, q))c]
that is, if x demands p as a means to q, then x demands p and

x demands q. The Principia law

 

p E ~(~p)
also holds within the prepositional attitude context of
demand. That is,
(12) d(x, p)>0 E d(x, ~(~p)) )0
holds in TI. By our rule of restricted biconditional re—
placement, we get from (11), in accordance with (12),
(13) d(X, ~(~p), (1))0 3 [d(X, ~(~p))>0 . d(x, q)>O].

lhis rule is used tacitly in II.

 

Proof Procedures i___l_
23. Two proof procedures are employed in T1. The first

is a rather full proof and is quite similar to the proof

technique in Principia. The second is an abbreviated pro-

 

cedure which, in effect, makes every line in a proof a

theorem. Let me illustrate.

'l'I. 3.0.00 d(x, p, q)>O D d(x, q))O

d(x, p, q)>o : [d(x x, q)>e . e (x, p 3 q)>0]: (Id[d( xn )>O],

p
and TI. 1.0) (l)

[d(x, p, q)>0 3 CH X. q)>01 . [d(x, :3. q>>0 D e(x, p 3 q)> 0]

/

(l) and *h.7o [d(x, p, g))’O, d(x, g))>O, e(x, p 3 q)> O] (2
P q r ‘

d(x, p, q)>O 3 d(x, q))C (2) and Simp [d(x, p, q)>O 3
p
d(x, q)>O, d(x, p, q))O D e (x, p D q)>C]
q
The first line in the above example is not a line in the

proof; it is the theorem to be proven.

2L. If the proof is rather difficult, then the above is
the form the proof will take. In this example the numbers
and abbreviations to the right hand of any line indicate
the laws which sanction that line gr_the number of a line
in the proof; I mention no methods in any proof in TI.

The numbers beginning with the asterisk and the abbrevia-
tions, for example, "Simp", are the expressions used in
Principia to designate certain laws in that system. Any
other number designates a postulate, theorem, or definition
in TI --or a line in the proof. The definitions are repres-
ented by TI. l.fi while the postulates, are denoted by the
prefix TI. 2.N. Thus the first line in the above proof

cites a law from frincipia and a definition in TI. The

 

number of any line in a proof in written immediately after

the justification for that line.

25. ’[]’ after a sanctioning law indicate a substitution
into the law immediately preceding the brackets. hence, in
the first line in the above proof they indicate a substitu-
tion instance in the Principia law "Id." In general, how-

ever, the substitutions will only be noted in the more diffi-

cult cases.

l

101

26. In some cases the last line, but not the laws which

sanction it, may be replaced by "prop."

in accordance with

the conventions of Princip_a. For example, the last line

 

may have been written as; prop. (2) and Simp.

[same substi-

tutions], which indicates that the result of (2) and Simp

is the desired theorem.

2?. however, many of the proofs in TI are the result of

only two or three steps since, in general, what normally

would be taken as a line in a proof is proven
Thus the abbreviated proof procedure in TI is
by the following example

d(x, p, q) >0 3 [d(x, q)>0 . e(x, p D q)>C]

d(x, p, q)>0 3 d(x, q)>0 TI. 3.0.0 and

as a theorem.

illustrated

28. Notice (1) that TI. 3.0.0, since it precedes TI. 3.0.00

in logical order, constitutes a line in the proof of TI. 3.0.0C;

(2) that the numbers of the laws sanctioning Tl. 3.0.00 re-

present a "telescOped" justification of TI. 3.

0.00 --fOI’

example, the extended proof of TI. 3.0.00 in paragraph 23.

contains reference to *h.76 in its second line. Telesc0ping,

is done in cases wnich seem to follow obviously; (3) that

the number of a line is now the number of a theorem; (N) that

‘1‘

the sanction of the line is given with the theorem to be proven;

and (S) that there is no mention here (and in most cases there

will not be) of the requisite substitutions.

(Cf. paragraph 25)

102

Numeration of the Theorems f TI

 

 

29. The theorems of TI fall into two classes; (1) those
which follow from the definitions alone and (2) those which
follow from the postulates alone or in conjunction with the
definitions. T1088 which fall in class (1) are designated
by the prefix

TI. 3.h.fi;
thosefalling in class (2) are designated by the prefix

r11. u.1v'.1~.5.

30. All theorems in El are subdivided into theorems and
corollaries of theorems. For example, consider the following

set of theorem-numbers:

(A) TI. h.0.0
(a) TI. u.o.oo
(3) TI. h.0.0l
(D) TI. h.1.o

In this set, the number replacing ’h’ in the prefix

T- 0 LL. "

l

T T“
.L. l‘

F7!

Po

identif es a given subset of theorems. If the number which

replaces ’N’ in the prefix in
TI. M.N
is ’0’ then the prefix designates the first theorem in the
given subset. If the number which replaces ’N’ is ’00’,
then the prefix designates the first corollary of the first
theor r in the given subset. For example, in the above set
TI. u.o.o
identifies the first subset of theorems which depend upon

the postulates in TII and also the first theorem in that

103

subset. The number

Tl. u.C.CO
designates the first corollary of the first theorem in the
first subset of theorems which depend uuon the postulates
in ll. Finally,

Tl. 4.1.0

designates the first theorem in the second subset of theo-

rems which depend upon the postulates of TI.

31. There can be corollaries of corollaries. For example,
Tl. h.C.ClO

designates the first corollary of the second corollary of

the first theorem in the first subset of theorems which

depend upon the postulates in TI. All of these remarks

also hold true for those theorems following from the defin-

itions.

 

 

 

Grouo g; Consequences f the Definitions

32. The theorems in Group A are deduced solely from the
definitions without any appeal to the postulates. They are
arranged in subgroups, the first subgroup depending exclus-
ively on the first definition, the second subgroup on the

second definition, and so on (with slight modifications

which will be explained when tie, arise).
33. The following theorems deoend on definition TI. 1.0.

TI. 3.o.o: d(x, p, q)>O 3 [d(}:, q)>0 . e(x, p 3 q)>O]

Id and T1. 1.0

10h

1

f x demands p as a means to q, then x

l—lo

TI. 3.0.0 reads:

demands q and expects that if p then q.

'11. 3.0.00: ex : d(x, q)>o Tl. 3.0.0 and Simpa
TI. 3.0.00 reads: if x demands p as a means to q, then x

demands q,

TI. 3.0.01: 8x 3 e(x, p 3 CU >() 11. 3.0.0 and bimp
TI. 3.0.01 reads: if x deranes p as a means to q, then x

expects that if p then q.

.1.

‘11. 3.0.1: [d(x, q))0 - e(x, p 3 q) )0] 3 d(x, :3. q)>0

TI. 3.0.1 reads: if x demands q and also expects that if p

then q, then x demands p as a means to q.

3“. The following theorems are derived from T1. 1.1

either alone or in conjunction with T1. 1.0

[1'10 30100: p1iX D (Eq)(d(x, p, C1)>O) TI. 10]., Id 811d Siffl’p
ll. 3.1.0 reads: if p is a means-object of x, then there

is a q such that x demands p as a means to q.

 

(N

o. In theorem T . 3.0.00, there occurs an abbreviation which
will be regularly used throughout the remainder of this
work. "3A" ("same antecedent") stands in the position of
antecedent in any theorem (or line of a proof) to indic-
ate that the antecedent of the theorem (or line) is the
ame as that in the immediately preceding theorem (or
line ) o

 

n n

. .

O

u o r

, . o

a . ' o
n . .

s
I
.‘ I

p I r

4 . '

 

 

 

 

105

’1‘1. 3.1.00: pm 3 (3g) (d(x,o )))0

Proof: (q)[d(x,p q))():>ci(:e,c0,>(d 11. 3.0.00 and *9.13 (l)
(Bq)(d(x, p, q))C) D (3q)(d ))C) (l) and 6610.28 (2)
pix D (3q)(dbx, q)>(fl (2) and TI. 3.1.0

Tl. 3.1.00 reads: if p is a means object of x, then x

demands some state-of-affairs.

T1. 3.1.0t0: (q)(d(X,C1) = C) 3 ~(p3x) $1. 3.1.CC, lransp,
*1C.252 and hhg

Tl. 3.1.0C0 reads: for every q if x does not demand q, then

it is false that p is a means-object of x.

11. 3.1.01: pLx 3 (Bq)(e(x, p 3<q) )()) Proof is similar to
proof of TI. 3.1.0C.

11. 3.1.01 reads: if p is a means-object of x, then there

is a q such that x expects that if p then q.

TI. 3.1.1: (3q)(d(x, p, q):>0) 3 pix T1. 1.1, Id and bimp.

TI. 3.1.1 reads: if there is a q such that x demands p as a

means to q, then p is a means-object of x.

r1‘1. 3.1.10: d(x, p, q)>0 3 p13: Tl. 3.1.1, -::-10.23
and *lO.l.

TI. 3.1.10 reads: if x demands p as a means to q, then p

is a means-object of x.

(151. 3.1.100: [d(x, q)>0 . e(x, p D q)>0] 3 pI-‘x TI. 3.1.10
and TI. 3.0.1

 

9. All references to the laws of Real Runners will be referred
to as simply "BL".

 

100

ll. 3.1.100 reads: if x denands q and expects tflat w is a

‘J
a

means to q, then p is a means-object of x.

35. the followin; theorems are derived from 11. 1.2

either alone or in conjunction with TI. 1.0 or 11. 1.1

(or both). hereafter, except in tne most difficult cases,

English langua e translations of tne t1-eorer:s will be

omitted.

TI. 3.2.0: pUx 3[d(x, p)>0 . ~(3q)(d(x, 7;), q))O] T1. 1.2,
Id and Sinp

11. 3.2.00: pUx 3 d( , p ))43 TI. 3.2.0 and Simp

II. 3.2.000: pUx 3 (Eq)(cq)>C))11. 3.3.00 and *10-20

11. 3.2.01: pbx D ~(3q)(d(x, p, q),>0) TI. 3.2.0 and bimp

TI. 3.2.010: ptx D ~d(x, p, q))’0 TI. 3.2.01, *10.01 and

£310 0 1
TI. 3.2.0100: pUx D[d(x, q)) 0 3 ~e(x, p 3 q);>0] T1., 3.2.010,
TI. 3.0.1 and
Transp.

TI. 3.2.01000: [e(x, p 3 q))O . plix] 3 d(x, q) = 0
TI. 3.2.010c0,
lransp, Exp.
and RE

TI. 3.2.011: ptx 3 ~(p1x) T1. 3.2.01, T1. 3.1.0 and Transp.

TI. 3. 2. 0110: pix D ~(pUx) T1. 3.2.011 and Transp.

'1‘1. 3.2.012: pUx 3 (3q)(~e(x, p 3 q) )0)

Proof: ~(3q)(d(x, p, q))O) D [d(x, q))O D ~e(x, p

and Transp
p'Ux 3 [d(x, q))C‘ 3 ~e(x, p 3 q) )0] (1) and 11.

J):
\35:
O
l...‘
[\\

(3q) (d(x q))O) 3 [pLéx 3 (3q)(~e(x, p D q)>0)] S2)

3“ In!

 

. . v
1
. I
o ' '
9
v
v D r n . -
O f‘
I
. r < 1- . . v
‘ . . , . I
. . . . . . t
I
I I . . I‘
I t n
.
. c p .
, t u
\
.
. . . u u I ' ' '
t 0 ' ‘ .
. r ‘
l a t
t
3. v c
c
0

 

 

 

 

107

prop. (3), T1. 3.2.000 and Taut.
T1. 3.2.1: [d(x, p)>0 . ~(3q)(c.(x, p, q))C] 3 plix T1. 1.2,

Id and
3 imp

Proof: [~(pl;x) . d(x, p))0] 3 p‘fo T1. 3.1.1 and

prOp. (1), (30mm and LXp.

T1. 3.2.100: d(x, p),>0 D [pLx V pUx] T1. 3.2.10 and *0.6
T1. 3.2.101: d(x, pd,>C>3 [pLx.f ~(pr)] T1. 3.2.10 and
‘11. 3.2.011

36. The following theorems are derived from T1. 1.3 in

conjunction with TI. 1.0, 11. 1.1, and/0r T1. 1.2.

11- 3.3.0: F(x, 9, q) 3 [d(x, 9, q)))C . ~(3r)(xC(r=~p) .
d(x, r, q))CH T1. 1.3, Id and Simp

TI. 3.3.00: E(x, p, q) 3 d(x, p, q))>0 11. 3.3.0 and Simp

TI. 3.3.000: J‘(x, p, q) 3 [d(x, q) >0 . e(x, p 3 q))O]
11. 3.3.00 and T1. 3.0.0

TI. 3.3.0000: F(x, 0, q) a d(x, q)>’0 T1. 3.3.000 and simp

aL

TI. 3.3.00000: 9(x, p, q) 3 [qUx v qfix] 11. 3.3.0000 and
T1. 3.2.100
T1. 3.3.00001: F(x, p, q) 3 [qUx E ~(qhx)] TI. 3.3.0000 and
TI. 3.2.101

11. 3.3.001: F(x, 0, q) : pix 91. 3.3.00 and T1. 3.1.10
T1. 3.3.0010: fi(x, p, q) 3 ~(pUx) T1. 3.3.001 and T1. 3.2.0110

T1. 3.3.01: E(x, p, q) 3 [~(3r)(xC(r=~p) . d(x, r, q):>0)]
T1. 3.3.0 and bimp

TI. 3.3.CIC: SA D ~[x0(r=~p) . d(x, r, q))>0] TI. 3.3.01 and
'X‘lC‘ o 1

T1. 3.3.0100: [x0(r=~p) . d(x, r, q),>0] 3 ~F(x, p, q)
T1. 3.3.010 and
Transp.

Inn-J” ”a

 

 

 

 

 

108

TI. 3.3.1: [d( x, p, q)>0 . (3r) )x( 0(r=~p) . d(x, r, q))CH
F(x, p, q) T1. 1.3, 1d and Simp
it. 3.3.10: ~F(x, p, q) 3 [d(x W‘>{)D (3r) fl(r=~p) .
d(x, r, q))0)] TI. 3.3.1 and Transp

'11. 3.3.100: [~B‘(x, 0, <1) . d(x, p, q))o] 3 (MM 3(r=~p))
'11. 3.3.10, Inp,
*10.26 and Simp

37. The following theorems are derived from TI. 1.h in

conjunction with T1. 1.0, T1. 1.1, T1. 1.2 and/or T1. 1.3.

TI. 3.h.0 pr 3 (3o)(r(x, o, p))>0) TI. 1.h, 1d and Simp

T1. 3.L.1 (3@)(r(x, @, p),>CJ D p3x T1. 1.4, Id and Simp

H

T1. 3.4.10 r(x, @, p)3>0 D pr T 3.h.1, %10.23 and %10.1

Group 2; Consequences of the Postulates

 

 

38. The theorems in Group B are deduced from the postul-
ates in conjunction with other postulates, definitions or
theorems resulting both from other postulates and the de-
finitions. The theorems in this section are not subdivided
into groups depending upon any given postulate.

131. 11.0.0: [d(x, ¢X)>O . pliex . e(x, qu>>0 . e(x, q 3

(0X 3 3.1x))>0] 3 MK, (3): p) >0

Proof: [xCp . e(x, p3q))'0 . e(x, q 3(ox 3 px))><3] .
((px D Q,X)))O r1‘1. 2.0 [<px I) 333x] (1)

I”
[d(X, 31%)) 0 . e(x, p 3(1)»: 3 11:30))0 . max} 3 r(x, <9, 1)) >0
T1 2.6 [fl] (2)

xCp :> ([d(x x, 33x) )0 . pRex . e(x, qu)>O . e(x, q 3(pr3 31x) ))>0]
3 P(X, $y ) ) ) 2) ano PXP. (3)

prop: (3), TI. 2.12, Imp and Taut.

o
c , . .
- I 1 r
O
r r p
O I l’ 0 I I
. . . c ,
, ‘ . r I
I‘ D u 0 | r f l
_ ' .
c
r
0 a r c e f
L
l. f
L I
a .
' I‘
1 ¢ :

 

 

 

 

109

39. This theorem allows us to assert that x has a tend-

ency to respond by p to a state-of—affairs p when x demands

¢X2 has sensorily received p and when x expects that p leads

to @X via the intermediate event q which intervenes between

p and 0x.

x . e(x, p 3 q))0 . e(X: q 3

1 cp ))0 T1. 11.0.0 and
p

q))O . e(x, q 3M»: 3 0x)»

TI. 0.0.000: [(wx)Ux . phex . e(x, 3
.00, TI. 2.10 and Iransp

0] 3 ~(px)Ux TI. u.
LO. ‘his theorem shows that, under the same conditions pre-
vailing in T1. h.0.0 -except that ’x’s demand for wx’ is
replaced by ’wx is an ultimate goal-object of x’— @x is not
an ultimate goal—object of x. This can be seen more clearly
if one compares ox which we may allow to mean ’x eats bran
mash cubes’ with wx which we may allow to mean ’x is (hunter)
satiated’.
TI. 11.0.01: [d(x, (3,-x)>0 . pfiex . tA(x, p,_' q) )0 .
tA(x, q,f (cpx D \L’X))>O] 3 r(x, (p, p)>0 ‘11. 11.0.0
and T1.2.8

T1. 0.0.02: [d(x, wxjj>0 . pRex . F(x, p, q) . F(x, q, 0x 3 0X)]
p)> 0 11. 11.0.0 and 11. 3.3.00

11'. 11.03020: [(d(x, 333x)>0 . phex) . (th, p, q) >0 .
tA(x, q,(¢x D 0x)):>0) V (F(x, p, q) .
F(x, q, ex 3 wx))] D r(x, p, p)>:‘ T1. u.0.02 and
TI. uoOoC'l
01. This theorem shows that when an organism demands that

1

0x, -say, ’x be picked up’ --, has sensorily received that p,

110

--say, ’There is a white card on the left’-—, and, finally,
hen he exhibits a chain of taughtness or a chain of fixa-
tion both of which involve p, q, -say, ’x moves, on the
stand, toward the white card’-, mx, -say, ’x jumps to the
white card--, and wx, x has a tendency to respond to the
fact that ’there is a white card on the left’ by ’jumping
to the white card’.

11.1.0: [x0p . d(x, p, q (1))0D . (,x p, r)>0] 3

[d(x, r))0 . 801133))“

Proof: [d(x, q)>0 . d(x, r)>0] 3 d(x, r)>0 Sil'rlp (1)
[(xCp . e(x, p 3 q)) 0 . e(x, q,3 r0‘>0) . d(x, q)) 0 .

d(x, r)) 0] 3 [d(x, :0 >c:. e(xq p 3 Ifl‘>0] (1), T1. 2.0 and
533.1f7 (2)

pI‘Op. (2) , iz—LE-.32’ 0010.131 and TI. 10C‘
11. L1.1.00: .5311. 3 d(x, r)>0 11. 11.1.0 and Simp
TI. L)-.1.0l: SA 3 e(x, p D r))0 TI. 11.1.0 and. Siam

A.

10:. u. 1. 02: EH13 d(x,:p,xfl )0 TI-lpluo and‘TI-S%C%1

ha. Theorem TI. h.l.02 expresses the restricted transitivity
of means-end demand. That is, it expresses a condition under
which a demand chain is "set off" --to use Tolman’s suggest-

ive terminology.
TI. 0.1.020: SA 3 pr 11. 0.1.02 and 11. 3.1.10

0.1.0200: 5A a [phx . qhx] T1. 0.1.020, T1. 3.1.10 and
333 01)-? o

h}. T1. h.1.0 0 00 shows that p and q, because they are

demanded as means to other goal objects in the demand chain,

 

ll “III! 1"“ .
[I .ll 1
ll II' (

 

 

111

are, therefore, proximate or means-objects. In this con-
nection it is interesting to note that a similar law for

expectation chains cannot be derived. This is important.

 

For where ’p is a sign object of x’ means

[pRex . (3q)(e(x, p 3 q))0)]
the failure to deduce such a law conforms wi ith Tolman
requirement that a sign object becomes a means-object when

and only when it is demanded.10

TI. 11.2.0: [xCp . e(x, p D q))O . e(x, q 3 r)>O .
d(x, r)>0] 3 d(x, p)>0 Tl. 2.0 and TI. 2.1

11. This theorem shows that an approach situation can

I

be extended along an expectation chain.

( o
d(x, r) 0] D d(x, p) 0 TI. 1.2.0 >and TI. 2.12

11. 11.2.0100: [r(x, (p, o)>o . e(x,p D <px)>O. e (x, 1px 3 r)>0
. d(x, r O] 3 d(x, p))%3 ‘Tlu h.2. 00 [£_] and
q TI. 2.?
ME. This theorem reads: if x has the tendency to respond

by p to p and expects that p is a means to mx and expects
that ox is a means to r and demands r, then x dm ands p.
This theorem shows a circumstance under which one caiinfer

a demand from a certain combination of response and expecta-
tion conditions.

TI. [1.2.1: [xCp . e(x, p 3 q))C . e (x, q 3 r))0 .
d(x, ~r))0j 3 d( x, ~p)>0 TI. 2. C and TI. 2.2

 

17'

10. Cf. Purposive behaviorism, Chapter A

 

 

...,?

 

 

112

M6. This theorem shows that an avoidance situation can be
extended along an exiectation chain.

h.2.10 [phex . e(

X, o
d(x, ~r)>0] and TI. 2.12

11.2.100 [r(x, (p, p)>0 . e(xp 3 cpx))0 . e(x, cpx D r) )>O .
d(x, ~r))0] 3 d(x, ~p)>0 Tl. 11.2.10 and TI. 2.7
TI. 11.2.2: [xCp . e(x, p 1 q))O . e(x, q 3 r))0 . d(x, r) =
d(X, ~r) = >0] 3 [d(X, p)>0 . d(X, ~13) >0]
kroof: [xCp . e(x, p D q))’0 . e(x, q 1:r))(3. d(x, r)) O .
d(x, ~r) C] 3 [e(x, p))0 . d(x, ~p))0] TI. 11.2.0 and
'11. 11.2.1 (1)
[d(x, r) =11. 1-1>o.d(x, ~r) =1;.1>c . xCp . e(x, p o q)>0 .
e(x,q r)>C] D [d( (x, p))O . d(x, ~p))0] (l) and
13.13 (2)
[d(x, r) = d(x, ~r) = 1.1)10 . xCp . e(x, p 3 q) .

C
e(x, q 3 r))0) D [d(x, p) ))t . d(x, (0)30] (2) and 9613.03
)0. e(x,q3r)>0. d(x, r)=d(x, ~r)=
(x p)e>O . d(x, ~p )>0] (3), 11:1 and Com.
MY. TI. 4.2.2 is a very interesting theorem. Iotice that
the expression "d(x, r) = d(x, ~r) = 1U>Cfi depicts the typical
conflict-in-demands situation. hence, TI. h.2.2, in effect,
says that if an organism has conflicting demands with res-
pect to the last member of an expectation chain, then he
demands both the occurrence and the non-occurrence of the
initial goal-object. Notice that one cannot infer that the
organism is in conflict with respect to the initial goal-
objects. This comports with ordinary experience; for some-
times one is and sometimes one is not in conflict with res-

pect to the initial goal-object under t1e above conditions.

113

TI. 11.2.3 [xCp . e(x, p 3 q)>0 . e(x, q 1 r) >0] 1 e(x, r)>0
TI. 2.0 and
11. 2.1

Proof: [xCp . e(x, p 3 C1)>0 . e(x, q 3 r)>0 . xC(q 3 ~r)J 1
‘ ~e(x, q))»C TI. h.2.3 and TI. 2.5 [3] (l)

[pr . e(x, p 3 q))O . e(x, q 3 r))0 . xC(q 3 ~r)] D [e(x, q))O
. ~e(x, q)>O] (1), TI- 2-1—2— €3.11? (2)

[xCp . e(x, p 3 q))>0 . e(x, q 3 r).>0] 3 ~xC(q 3 ~r) (2), Transp
and Id (3)

PrOp. (3), Imp, Transp and ixp

MB. This theorem, TI. h.2.30, affirms that when x has con-
firmed that q implies ~r and, also, has confirmed p and ex-
pects that p leads to q, then the Chain of expectations is
"broken" with respect to the goal-object r -that is, then x does

not expect that q leads to r.

TI. h.3.0 d(x, p, q))10 3 d(x, p))»0 TI. 2.1 and TI. 3.01

’11. 11.3.00 d(x, p, q) )0 3 [d(x, p)>0 . d(x, q))C] TI.11.3.0
and TI. 3.0.00

, ..—

49. T1. h.3.CC asserts that if x demands p as a means to q then,

he demands p and he demands q.

11. 11.3.01‘c [11p . d(x, p, q))o . d(x, q, r))0] 3 [d(x, p)>o
. d(x, q)) 0 . d(x, r))»0] TI. h.3.00 [3}, TI.h.l.00,
q 563.117
50. The above theorem claims that all of the goal-objects

in a demand chain are individually demanded.

11. 11.3.1101: th, p, q))o 1 [d(x, p)>0 . d(x, q)>e]
TI. h.3.00 and T1. 2.8

llu

‘l‘I. Li-.3.CaC2: Mx, p, q) :3 [d(x, p)>0 . d(x, q))C]
II. u.3.“’ and TI. 3.3.C‘
II. li.3.LC3: [d(x, p)>c 3 "Cl( ~p) >0] 3 ~d(x p, ~p) )0
ll. L.3.0C [:pj and iransp
q
:1. TI. 4. 3. CC3 aff irms that ii x’s demand for p implies

that he does not demand not p, then it is false that he

demands p as a means to not p.

m. L.-.3.Cl: p x a d( p)>0 121‘. 11.3.0 and TI. 3.1.0
iI. 4.3.010: [pLx V ptx] 3 d (x, p)>(3 WE; L43.Cl and TI. 3.2.00

TI. h.3.ClCC: [pr E ~(pLx)] D d(x, p))>0 TI. h.3.010 and
' TI. 3.2.011

TI. L;-.3.ClCCC-: d(x, n)>0 :- [nix

}
I
l
A
J
kl~
r"!
V
L——’
Li

fI. .3. ClCCC and
TI. 3.2.1C1

52. This theorem, TI. h.3.ClCCC, ariirns that x’s hat ing
a demand for p is equivalent to p is an ultimate goal—object

of x if and only if p is not a proximate goal-object of X.

131‘. 1.3.3.011: [q.~'-x V qUx . e(x, p 3 q))O] 3 d(x, p )

TI. 2.

TI. 4.3.012: [qax V qUx . e(x, p 3 q);>0] D plx TI. h.3.ClC
TI. 3.0.1 and
{111. 3.1010

53. TI. 3.3.Cl2 asserts wien q is a proxirate $081-OCJBCC

or an ultimate goal-object and when x expects that p leads
to q, then p is a proximate goal-object. however, this is
not the case when we are dealing with avoidance situations.

That is, we cannot prove that

CA) [("O)hx V (~C)Fx . e(x, p 3 Cfi )(1113 (~p)Lx,
though it is easy to prove that

(E) [(~q)l-x V (~q)[.x . e(x, o 3 q))C] 3 d(x, ~p)>0.

-

And indeed we want this result in our system. The point is,
that under the conditions specified in (A) and (E), ~p is

demanded by x, not with the expectation hat it will lead

 

to ~q (an expectation required if (A) is to be true) but,
so to Speak, with tie hope it will lead to ~q. (To expect
~p to lead to ~q under the indicated conditions is, so to
speak,to commit the logical fallacy of denying the ante-

cedent).

TI. L3-.h.0: [e(x, p 3~q)>0 . e(x, q 3 r)‘>"* . d(r, r)>0] D

d(x, ~p))0 . TI. 2.1 [51, r] and TI. 2.2 [:1]
P q q

TI. h.h.l: [e(x, p 3 q) 0 . e(x, ~q 3 r) O . d(x, ~r) 0]
3 d(x, p) 0 TI. 2.1 and TI. 2.2

flu. These two theorems are interesting. The first des-

cribes an approach situation relative to q in a means-end

expectation chain. mhe second describes an avoidance situ-

ation under tue same conditions. If we substitute ’x turns

to the left’ for ’p’, ’x will find a closed door’ for ’q’,

I _

and ’x gets to food’ for ’r’, tEe first theorem reads, if

x expects that if he turns to the left, then he will find

a closed door and expects that if he doesn’t find a closed
door, then he can get to food and demands trat he get to

food, then he demands that he not turn left. The avoidance

situation represented by the second theorem can be illus-

trated by substituting ’x turns to the left’ for ’p’, ’x

can walk alonq a wooden path

over the electric grid’ for

’Q’, and ’x gets severely shocked’ for ’r’.

TI. u.5.0: [pnex . e(x, p 3

TI. 11.5.00: [r(x, (p, p) >0 . e(x, p 3 q)>O] 3 e(x

CN>OJDengL>CCM.2
TI. 2.12

a q)>O
J. h 5
I. 2.7

$.11."

.M and

TI. h45.000: [r(x, m, p)>I). e(x, p 3<m<) )>C] 3 e(x, ex x)>(3

55. These three theorems,

r110 11105.00
[QEI
q

TI. b-0500 -' 0C0, (1980321139

various ways in which a member of an expectation chain can

be released. -The first theorem shows that ’e(;, q))bO’ is

released when p is sensorily
is a stimulus, and the third

realizable state-of-affairs,

reCeived, the second, when p
shows that when ’px’ is a

it is released as an expecta-

tion if x has a tenrency to respond by e to p. (Cf. para-

graph A? in chapter II) These various ways of releasing an

expectation find their nus Hi

U

III through V of Iurposive Eehaviorism.

 

TI. h.6.0: [(”Q)hx V (~q)tx

. e(x, p3q))C] 3d(x, ~13 ))0

.LI. 2. 2 and 110“.

E6. This theorem is the avoidance situation correlate

of TI. 4.3.011. Like TI. h.3.011 it is important for this

reason: it shows quite clearly that x’s demand that ~p

is a consequence of his expectation that p leads to q when

the end object in this expectation -namely, q- is eitler an

3.0

117

ultimate or means avoidance object.

TI. lg-.7.0: x ~q) )>0 . e (x,

p 3
x] 3 r(x, o, p))()

Proof: [d(x, ~q)>0 . e(x, my}: 3 q) )0] 3 d( (,x, ax) )0

d(
. p

p
prop. (l) and TI. 2.6 [ii]
q
57. Tl. h.7.0 asserts that when x demands ~q,both ex-

pects that p leads to ex which leads to wx and eXpects
that ~¢x leads to q and, finally, when p is sensorily rec-
eived by x, then his tendency to respond bv p to p is

greater than 0.

TI. 4.6.0: [d(x, p)>0 . d(x, ~p)>0] 3 [(~p)1- x :‘E vaTx]

Proof: [d(x, p)>0 . d(x, ~p) >0] 3 [(~p).~.x~

. pux] TI. 2.3 L22]
and II. 2.3 (

l) p

prop. (l) and *5. l

58. TI. h.b.0 asserts that in a situation where x demands
both p and ~p, the means object ’(~p)hx’ is equivalent to

the means object ’phx’.

TI. L1..b.l pUx 3 ~d(x, ~p)>0

Proof: pUx 3 [d(x, ~p);>0 3 pix] TI. 2.3 and TI. 3.2.00 (1)
pUx 3 [ptx 3 ~d(x, ~p))'C] (l), iransp and TI. 3.2.011 (2)
prop. (2), Imp and iaut

TI. 4.8.10 pUx D ~(~p)ix i1. u.6.1, TI- u.3.01 [:EJ and Trans?
D

—.

 

 

118
Proof: pLx D ~d(x, ~p)> 0 i1. 6.1 (l)
~d(x, ~p)>b0 D ~((~p)Ux) II. 3.2.00 and Eransp (2)

prop: (l) and (2)

59. TI. h.8.ll affirms that when p is an ultimate foal-
object its nefate is not. Indeed the two theorems TI. h.€.10
and TI. h.8.ll, permit us to assert the followini very stronfi

condition:

TI. h.8.100 pUx D [~(~p)Ux . ~(~p)hx] TI. h.8.10 and TI. h 8.11
‘l‘l. 4.8.2: pUx 3 ~[d(x, p) = d(x, ~p) = 14>C]

Proof: [d(x, p) =1v'i.i-L)0 . d(x, ~p) = L;.Il>0] 3 plix TI. 2.3.14
*13-13 (1)

[d(x, p) = d(x, ~p) = h.R)’C] D pLx (1) and *13.03 (2)
[d(x, p) = d(x, ~p)==1;)(fl 3 pLx (2) and RN (3)

~(phx) D ~[d(x, p) = d(x, ”D) ==3Q>Cfl (3) and lransp (h)

prop. (h) and iI. 3.2.011

60. TI. h.t.2 affirms that if p is an ultimate object of

x then x does not have conflicting demands with respect to p.

1: X3”) 0 0

II. h.9.0: [r(x, c,jp)> 0 . (ox)fiex . d(x
' '))))0] 3 r(x, ‘1', pr))0

e(x, p 3 («psi 3 (wk

Proof: [xCp . e(x, p 3(ox )(Wx 3 xx))))>0] 3 e(x, ex 3(wx D xx))>0
TI. 2.h [ex 3 (gx D vx)](l
q
[d(x, )(x)) C . e(x, ex 3 (wx D )(x))>0 . ((px)Rex] D r(x, «x, <px)>C
III. 200 [12.—7:, 11-, E] (2
10 <9 <1

[xCp . (ox)Rex . d(x, XXX) 0 . e(x, p 3 (ox D (wx D xx)));>0]

D r(x, v, <9X>>O (l) and (2) (3

[pnex . (Qx)hex . d(x, xx)> O . e(x, p 3 (ex 3 (wx D xx))))>0]
3 r(x, 15X: ox) )0 (3) and 11. 2.1 (1;.

}_1
I..J
\O

prOp. (h) and TI. 2.7

61. TI. h.9.0 shows how the tendency to reSpond moves
along an expectation chain. It is more dramatically re-

presented in the next theorem.

u.9.00 [r(x,cp p)>C~ . ()gox 5x . d(x, xx)>0 .
(e(x, p DUPX DHX D xx)))>0)] 3 r(x, v, pr)>0
TI. u.8.o, II. 2.7 and TI. 3.11
62. TI. h.9.00 reads: if x tends to respond by p to p

such that @{ is a stimulus to x and x demands xx and expects
that (the initial stimulus condition) p leads to (the con-
sequent stimulus condition) ex which in turn is a means to
¢x which heads to p<, then x has the tendency to respond by
W to the stimulus situation ex. This theorem shows how a
"response" becomes a stimulus to another "response" whose

order and direction is guided by an expectation chain.

LL.10.0: xC(q 3 ~q)] 3 ~e(x, 0))0

J.

Proof: [e(x, q))O . xC(q D ~q)] D ~e(x, q))C TI. 2.5 [q] (l)

xC(q 3 ~q) 3 [qe(x, )>0 3 ~e(x, q))O] (1), Comm and Exp (2)
prop. (2) *4. 62 and Iaut

TI. u.10.00: [xCp . xC(q 3 ~q)] 3 ~e(x, p 3 q)>*0 TI. u.10.00,
TI. 2.h and
Transp

TI. h.l0.000: [phex . xC(q 3 ~q)] 3 ~ e(x, p 3 q))-0 TI. u.9.00
and II. 2.12

TI. u.10.0000: [r(x, c, p))>O . xC(q 3 ~q)] 3 ~e(x, p 3 q))(D
TI. M.10.CCC and
T1. 2.7

II. [1.11.0 : [xCp . d(x, p, q))C] D e(x, q))O II. 2.11 and
TI. 3.0.01

”F’-

 

 

 

 

120
II. Marco: [xCp . tA(x, p, q )]>0 3 e( x, q))O ‘I‘I. 1;.11.o
and TI. 2.8

TI. LI.ll.Ol: [xCp . F(x, p, q)] 3 e(x, q)>0 'I‘I. h.6.0 and
TI. 3.3.00

n.12.0: [d(x,q )>p0 . e(x, p 3(ch D q))}O] 3
[r(x, (P: )>0 E p“ ex]

Proof: [déx, q))O . e(x, p 3((px 3 q)))O] 3 [r(x, cp, p))O 3
pm x] II. 2.7 and Simp (l)

prop. (l) and II. 2.6

63. This theorem, II. h.l2.0, asserts that x’s having a
tendency to respond by e to p is equivalent to x’s having
sensorily received p provided that he demands q and expects
that p leads to ex which leads to yx. In general, this
theorem gives an "operational defir ition" -though incom-
plete- or the notion of response tendency by p to p. It
provides the basis for the O‘ganisms’ action in a given
situation.
II. h.l2.00: [d(x, q))»0 . d(x, g, ox qu)>’0] 3

[r(x, (p, p) >0 E pt. x] 'I'I. LL.12.0 and TI. 3.0.0
TI. h.lZ.0CO: [d(x, q)) 0 . tA(x, ep,‘ (ox 3 q)))tO] 3

[r(x, o, p))>0= pr ex] TI. u.ll.00 and TI. 2.8
cu. TI. n.12.000 seems to express a iundamental contention

of Purposive Behaviorism, namely that x’s tendency to res-

 

pond by Q to p is equivalent to x’s having sensorily received
p provided that x demands q and has been taught with respect
to p relative to the means-end situation p: 3 q. In Ctaener 1,
if an organism has been taught with respect to a potential
stimulus-response pair, he will actualize that stimulus-
response situation if and only if he has sensorily received

what turns out to be stimulating state of affairs.

121
TI. Li.l2.0C'OO: [r(x, (p, p)>O . d(x, q))O] D [t[‘(x, p, (ox 3 q))
)0 D pnex) II. 2.7, *3.ul and Expt.

TI. 11.12.0001: [paex . d(x, 0) )0] : [tA(x, p, (ch a q))>0
3 r(x, m, q))'0] T1. h.l2.0CO gimp and Imp

Theorems TI. 4.12.0CGO and II. h.12.0CCl may be taken as a
pair of Carnapian reduction sentences for the term ’tA(x,
p, (ox 3 q))’ in the prOposition ’tA(x, p, (ox 3 q)))‘O’.
TI. b.12.CCC10: [phex . d(x, q))>C] 3 [tA(x, p 3(ox 3 q))>’O

3 pbx] TI. h.l2.0COl and TI. 3.h.10
TI. n.12.CCClC affirms that when p is sensorily received by x
and x demands q, then if x has been taught with respect to p
relative to the means-end situation mx 3 q, p is a stimulus

to x.

TI. u.13.o: [d(x, p. .q>>ow<x,p,q)1 a d(x, 1:. q) >0
TI. 2.0, 131. 3.3.00
and II. 2.11

TI. n.13.l: [F(x, p, q) . xC(r = ~p)] 3 ~tA(x, r , q)>>O

Proof: [3(x, p, q) . xC(r = ~p)] 3 ~d(x, r, q))io TI. 3.3.010,
£314-. 51 , 93);-.. 632
and Imp (l)

prop. (l) and TI. 2.6

TI. h.l3.l and its corollary require discussion. TI. h.l3.l
asserts that if x is fixated on p -sey, ’running down the
left alley’ as a means to the end q and he has confirmed that
’running down the right alley’ is the same as ’not running
down the left alley’, then he has not been taught with res-
pect to ’running down the right alley as a means to end q.
This theorem suggests that despite the fact that other routes

may lead to the end q, if x is fixated on p he ignores the

122

others as means to q —superior or inferior though they may

be.

TI. h.lh.0: tA(x, p,. q) )0 3 [t(x, p, q

TI. h.lh.0 pictures teacnability as the "mark" of demand and
hence of expectation. (3f paragraph 1h. in this chapter).
This concept, that is, "teachability", will be employed in
TII rather than its non-diapositional correlate taughtness.

hence every place "teachability" is said to imply somethinr

C.)

v

or other it follows that "taughtness" will also. 7e gain

generality by using teachability.

123

ChAPTfiR IV

 

SISTEL TII

 

l. The purpose of TII is to present a part of Tolman’s
working system. It is mainly concerned with the production
of certain laws appearing in Chapters III and IV of Purpos-

ive :ehaviorism. It also presents the deduction of some

 

versions of the latent learning principle. In some cases

he postulates are rarely elaborations of the postulates

in TI. Finally, the postulates of TII are so constructed
that they allow the deduction of certain laws concerning
fundamental relations such as demand, expectation, res-

ponse tendency and so on in virtue of their various strengths
over a given period of time. TII, in other words, is con-

I

cerned with the "variability' character of the intervening

variables.

Time Arguments in the Formulae 'n TII

 

 

2. Throughout TI, the major emphasis was on the exist-
ence or non-existence of demands and exoectations: bhat
conditions give rise to a demand or expectation, how the
existence of demands or expectations are related to an-
other, and what are the consequences of there being or not

being a demand for or an expectation \f some state-of-

O

affairs. In TII, on the other hand, we are concerned to
note that not all demands or expectations exist with equal
strength and to investigate the consequences of these

variations in strength. Thus, while in T1, it was suffi—

cient to write such things as "d(x, p)>*C", here in ill
the formulas will compare the strength of one demand (or
expectation) with the strength of another. hence, we
should expect to find such formulas as "d(x, p))>d(x, q)"

more nearly what will be required.

3. Khan we first consider comparing strengths of

1

demands, we fin" tnere are several basic ways in wnic

‘

n
a comparison might be made. Let us use some English

paradisms to represent tlese types of comparison:

i. x is more hungry than he is thirsty.
ii. x is more hunpry than is y.
iii. x is more hungry now than he was an hour ago.

Still other modes of comparison will occur, for exalple,

x is more hungry than y is thirsty, or x is more hungry
than 3 was an hour ago. but all of these other modes of
comparison can be handled by some ccmbination of the methods
necessary to handle the three listed modes of comparison.
Let us take up one after the other the special problems
emerging as we try to symbolize the three typical modes of

comparison cited above.

a. For situation i, the symbolism already suggested
would be adequate: "d(x, p);>d(x, q)". ihere are, to be
sure, circumstances in which a more flexible symbolism
would be useful; but let us leave consideration of that

until the other cases have been examined.

 

 

 

125

5. ln the case of situation ii, it is easy to see that
the gigs: arguments to the demand functor will vary from
"X" to "y", as they did not in case i, above: "d(x, );>
d(y, )". But perhaps it is less easy to see that the
second arguments must also be different one from the
other. nevertheless, they must be. If x is hungry, he

is demanding, not food (except as a means), nor merely

I 1

ation; he "s demanding his food satiation. That

Ho

food sat
is, il "d(x, p)" represents X’s hunger, that is, the

I! H

strength X’s eemand for food satiation, the p is repres-
enting that state of affairs which we could express in
English by "x is food satiated”. how, keepina this mean—
ing for "p", if we were to write "d(x” p),>d(y, P)" this
would mean that X’S denand tlat x be food satiated is

greater than y’s demand that é be food satiated. This

 

miThE comnare X’s "food-exotism" with V’s "food altruism".
C; - a .1

But it does not compare their hunger drives.

6. Thus it 18 plain that we cannot compare X’s hunfer
to y’s by keeping the second arguments to the demand func-
tion identical. On the other hand, to write "d(x, p)>
d(y, q)" misses the whole point that we are comparing X
and y on a single drive. It would as well represent "x is
hungrier than y is thirsty". The solution lies in repres-

enting the character of the drive by a predicate variable,

 

nd replace p"

m

and "q" in the above formula by apprOpriate
proPOSitional functions:

d(x, (PX) >d(:-;", w)

 

126

(Incidentally, we could now even represent the greater
"food altruism" of the mother who sacrifices her meal
to the child: "d(x, <p:,x))d(y, <px)"3 ) rihe more elaborate

symbolism reouired for case ii, can he useful for case i:

d(x, (PX) >d(x, M)

'1'}

7. fine symbolism adequate for case ii is, however, in-

adequate for situation iii. For in situation iii, were we

to use the symbolism given above, both sides of the inequa-
tion would be written in the same manner:

d(x, 4px) )d(x, ox) .

S
(.1.
l—- 0
C0

..... requisite is that the symbolism includes some

Sign to mark the difference in time at which different

demands of x for food satiation occurred.

6. The purposes of TII will be met by a somewhat crude
but simple "dating" device. It is the organism-at-a-certain-

time which has the demand. Lence in discriminate the

2

EEC

(\fi

two sides of the inequation by discriminating the organisms-
at-a-time:

d(xtl, (PX) >d(Xt2, (PX)

‘* D

‘nat is, the demand cl X-at-time-tl, that x be food-satiated

F3

is greater than the demand of x-at—time-tg. No other sub—
scripts than time subscripts will be made on the organism
arguments to our various functors. hence the "t" may be
drOpped to give

d(xl, pr) >d(x2, (px).

127

9. Further consideration of the kind of time involve—
ment in the postulates and theorems of TII, togetter with
the necessity of keepin; the symbolism as simple as poss-
ible, lead to the adoption of certain conventions for
interpreting the time notation. (In the concluding

chapter of this essay, certain inadequacies of this nota-
tion will be pointed out and discussed). Generally speak-
ing, the system is oriented toward utilization to repres-

ent the laboratory situation of the experimental psycho-

Q)

legist. here, the details of date (e.3. January h, 1956)
on which he ran.an.experiment, are immaterial. Also, it
is immaterial that he cannot run all of the rats involved
in an experiment simultaneously. Uhat is important is the
internal, relative dating of a series of situations, for
example, trial runs of a given maze. Thus, in general, the
dating subscript refers to the trial run in a temporal series
of trial runs. For example,

d(x2: cpx)>d(Xl, (PX):
says that on x’s second trial he was hungrier than on his
first, whereas

d(xl, ¢X) = d(yl, my)
Says that x’s hunger on his first trial run equalled y’s
hunger on his first trial run. (Perhaps measured by 2h
hours food deprivation each.) It does ngt mean that x and
y were equally hungry at 10 A.M. Perhaps x is run regul-

arly at 10 A.h. and y at 10: S. Then it would mean that

x’s hunger at 10 A.h. equalled y’s at 10:15.

128

10. A typical sort of experimental situation arises when
the experimenter keeps a drive constant through one part of
a series of trials and then varies it to a new constant.
(Cne or several animals might be involved, perhaps a con-
trol animal or group with the drive kept constant and
another animal for which the drive is varied.) hepresenta-
tions of these varieties of situation can be achieved by
various manipulations of the following deVice.

(i) [céiék D d(xi, ex) = h].
The above says that on every trial from the cth to the kth,
the strength of x’s demand for ex equals L. Variations on
this device, such as,
(i) [céifik 3 d(xi, ex) = d(yi, oy],

will be self-explanatory or explained as they occur.

11. Four further time conventions must be explained.

(l) The numerical constants, "l", "2", "3", etc. for times
represent consecutive trials, with "1" representing the
first trial. (2) Also alphabetical symbols (variables)

for times "j", "k", etc. represent earlier and later trials
according to their alphabetical order, but alphabetically
consecutive letters do not necessarily represent consecut-
ive trials. To represent the trial next after j we write
"j+l", rather than "k". j+l may be identical with or earlier
than k. (3) The expression "(i) (céiék 3 ...)" occurs

so frequently and is so cumbersome, that we have abbreviated

‘ I O ’i :" . ° -'
it to "(101) (...)". inis symbolism is more or less parallel

‘I

In

 

 

129

to a similar symbolism in mathematics, for example,

2% (fx) and 1 (fx).
hotice that no essential distortion is produced by this
convention. The normal logical operations on any uni-
versal quantifier are applicable here. For example,
from ’(i§)(exi)’ we may conclude, by *10.1, ’exk’.
Carried out in terms of the expression ’(i)(céfiék 3 exfiy
the Operation is as follows: by *10.1

cékék 3 ka.
The antecedent of this conditional is true (that is, it
is analytic). hence by a rule of inference we get

@Xk
whidiis the same result as in the case of the abbreviated
procedure. (A) Lastly, only organism variables in the
formulae of TII are subscripted. Strictly speaking,
every variable should be dated. however, in T11, there
is no gain in such a procedure. He thus adopt the more
abbreviated form of subscription. For example,

(p(.Xi, a)
and

d(xi, (pXi)>O

and so on.

C any-

Primitive ideas of

—\
_.

H I

}

 

12. The primitive ideas of TII include all of those of TI.
Two of these primitive ideas, namely,

tA(X, P 9, Q)

130

that is, "taughtness", and

xCp
that is, "confirmation", due to space and time considera-
tions, are either not used in the present version T11 or
are restricted in their importance as compared with their

use in T1.

_ r-
13. T11 contains only one additional primitive idea: E
F‘
O O i O 1 I} D f‘ . i
i is the idea Ci greater efiort. ureater effort W111 be f

symbolized by ’g)’. 1t will appear in contexts like

Txi €> WYj
which means ex at time i requires greater effort than my
at time j’;

(pXi E) WXJ'
which means ex at time i requires more effort than ¢x at
time j’;

@Xi E> ¢y3
which means ’px at time i requires greater effort than my
at time j’. Tolman construes this concept as meaning a
"greater expenditure of energy".1 It is, of course, the
analogue of "greater action" in physics. There is only one
point to be considered here; greater effort makes no refer-
ence to final goals. For exammle, we can say that a newsboy
walking up two flights of stairs to deliver a newspaper
engages in less effort than an old man going to his office
two flights up. Effort is somehow measured by reference

1. Purposive iehaviorism, p. ht.

 

131

to the agent’s capacity. Thus the newsboy going

up two
flights expends less effort than the old man, not because
the newsboy weighs less than the old man, so that less

weight was hoisted (although that might be a contributing

I! H

factor), but because he has more zip and go than the
old man: he is less completely used up by the expendi-

ture of effort than was the old man.

:3

l':

1h. A more complete analysis of Tolman’s working sys-

f

tem would also include two other concepts as primitive;

namely, he incentive value (or valence) of a goal—object

 

and the efficiency of goal-objects.2 These concepts are,

 

however, not symbolized in System TII. Tolman considers
them, nevertheless, quite important. It may be considered
objectionable to separate greater effort from greater effic-
iency on the grounds that one is reducible to the other.

The defense here is that it is Tolman who makes the separa-
tion.3 however, it is the present author’s belief that the
separation is a sound one. his point will be taken up

again in the last chapter.

15. As a result of the above omission of valence and

 

2. Purposive fiehaviorism, p. 1h.

Compare the remarks on efficiency on p. 1h of Purposive
Eehaviorism with those on pages 110 and 179 having to do
with effort. It will be argued in the final chapter that
those behavior patterns which tend to get the animal more
easily and quickly to a given goal are not necessarily
those which involve lesser effort.

 

U)
o

 

\

 

   

efficiency from $11, all of the postulates and theorems of
ill are to be understood as holdina true provided these
‘- W—_

0.

factors of valence and efi ciency are held constant! On
this convention we may drop consideration of efficiency
and valence. This is done, in part, because too little

is said about these concepts or, at least, their inter-

relationships in Purposive Eehaviorism.” Hence, T11 does

 

contain certain speculation concerning the prOperties of
’§>’. ihe "prOperties" of this concept and its relation
to the notion of demand and expectation will be made clear

in the discussion of the postulates.

Procedures and Few Symbols 'n TII

 

16. The replacement rules, proof procedures and numer-
ation of the formulae in TII are the same as those in T1.
There is one difference. In ill, we do not include theo-

rems deduced from the definitions alone under a separate

heading. For example, in T1 theorems following from the

l “I

definitions alone were denoted oy the prefix
TI. 3.12.1013.
hence, in TII, the prefix

TII. 1.33.

denotes a definition,

 

4. For example, the discussion of "least action" (that is
least effort) in relation to shortness-easiness prefer-
ence covers in its entirety, at most, two pages (cf.

pp. 110 and 179 of Purposive Eehaviorism). however,
Tolman has a lot to say about efficiency throughout his
book.

 

 

’.

 

 

133

TII.2.W
a postulate, and

TII.3.h.K
theorems which follow from the postulates either alone or
'in conjunction with other postulates, definitions and/or

theorems.

17. As has already been indicated, we shall make liberal

use of predicate variables in TII. According to the con-

 

ventions of TI, Greek letters like, ’o’, ’w’ and ’X’ are
predicate variables. however, in TII, we may use as many
as eight predicate variables in a single formula. hence,
in TII we supplement the Greek letters with English capital
letters from the beginning of the alphabet. He shall avoid
any duplication of an English capital letter which repres-
ents a constant in either TI or TII. hence, the English
capital letter ’C’ will not be used because it is used in

the primitive idea of confirmation in TI (that is, ’xCp’).

The Definitions f TII

 

TII. 1.0 (p, g, ...) A(x, x) = Df [ex 3 Xx . wx 3 xx, ...]

This definition reads: to say that p, w ..., are available
to x as means to X is to say that ex implies xx and wx

implies xx and ....,.

18. Tolman’s system requires an idea like means-end avail-

abil ty. For it is in terms of such a condition as is ex-

Ho

pressed by the concept of means-end availability that we are

able to inputs to the organism expectations of the elements

I.-

13h

in a given problem situation. RXpectations are personal-
ized affairs. be assume that the organism expects some-

thing in a situation on the basis of that something’s

availability to the oraanism as a means to something else.

K.

The experimenter, by constructing the problem situation in
such and such a way, makes certain things available to the
organism. Then he imputes to tie organism expectations of
these things after the organism has had a certain amount
of acquaintance with them in the problem situation. In
erecting this concept we are perhaps stretching the use of
the sign ’3’ (that is, truth-functional implication) a bit.
For what ’px 3 xx’ is meant to portray is a situation of

the followina sort: if x can make ox true then indirectly

 

x can make xx true. In other words, it is via x’s being

 

able to make ax true trat he is indirectly able to make xx

 

true.

bilitv in relation to the

19. This notion of realiz

‘3."

values of the variables is not entirely new in TII. It

was tacitly present in Tl: wien we wrote e(x, p 3(ox 3 q)))O

H n

the only ppropriate substituends for p were sensorily
received (by x) prepositions and for ’px’ and ’q’ sensorily

receivable (by x) or realizable (by x) prepositions.S

 

‘
u

5. For example, consider the postulate TI.2.6. There ’p’
is sensorily received and ex is sensorily receivable or
realizable (in the sense of "realizable" eXplained in
.paragraph A? of Chapter II). hence, ex could not re-
place p because this would have conflicted with p’s
being sensorily received. For though something which
is realized is realizable, the converse is not necess-
arily true.

135

however, in TI those restrictions on prOpositions substi-
tutable for "p" were limited to certain argument positions
for "e", "d" and definitionally derived concepts. Eere in
TII we must consider the hypothesis that something is ob-

jectively available to x.

20. Strictly speaking, we have here two unexpressed
primitive ideas: oAVx: @X is directly realizable by x;

pfiq: the world being what it is, p’s being true would be

 

sufficient to bring about the truth of q.

here these PI’s formulated means-end availability as

 

VA

defined in TlI.l.O would be the result of a definitional
chain such as is retresented below.

i ¢A(x, X) = Df [QAVX . oxn (xAVx)],
that is, ’Q is available to x as a means to x’ means ’ox

is directly realizable by x’

and ex would be sufficient
to bring about the state—of-affairs (necessarily implies)
that xx is directly realizable by x.

ii (w: w) A (X, x) = Df [@A(X, x) . wA (X, x)]

Finally, we get to TII.l.O in the following form

iii (o, w,...) A (x, x) = Bf [oA(x, x) ¢A(x, x),...]

21. Since (pnq) 3 (p 3 q) is valid, it is true that
¢A(x, x) 3 [ex 3 xAvx]
But since "xAVx" is only unofficial the best that can be

written in ill, on the basis of (phq) 3 (p 3 q), 18

¢A(x, x) 3 (ox 3 xx)

136

bhile the converse does 222 in general hold, we can and do
undertake to reduce the complexity of ill by not making

replacements of the definiens by the definiendum in accord-
ance with II. 2.0 unless the informal conditions suggested

in the above unofficial definitions hold.

 

T10 1-1 (W) Re(X, y) = 3f [exfiex . @yRey]
TI. l.l reads: ’@ is sensorily received by x and y’means

’ox is sensorily received by x and so is by by y’. g,

2. T1. 1.1, like the next four definitions lS primarily

{\3

abbreviatory. however, the expression ’meex’ bears some
discussion. The expression ’mx’ may depict x as either an

asent or merely a location point. For example, let ’e’ be

 

’jumps to the white card’. Then ’oxRex’ means ’x has senso-
rily received that he jumps to the white card’. here x

is an aaent; he sensorily experiences his jumping to the
white card when he does it. This is essentially a res-
ponse condition [but which may be a taking on of prOperties
as a stimulus to something else, that is, ’x jumps to the
white card’ might be a potential stimulus]. The second
case: let’w’ be ’to the left of the white card’. Then
’mxhex’ reads ’x has sensorily received that x is to the
left of tne white card’. here x is a location point. This
latter is more descriptive of merely a stimulus situation.
Again, these ideas are not new in TII. For example, con-
sider the expressions ’phex’ and ’(ox)he’ in the hth line

of the proof of theorem TI. h.9.0. ’p’ is merely a stimulus

L

137

condition; ’ex’ is best interpreted as a response condition

getting ready to become a stimulus. Indeed, this very point
is proven in the next theorem. But the point is ’p’ could
have taken as a substitution instance ’x is to the left of
the white card’ where x is a location point or ’p’ could
have been ’x jumps to the white card’ where x is an agent.

The same might be said for ’QX’ in ’(wX)HeX’ in TI° “'9'O°

111. 1.2 s%‘h’k [(E, D, G), (@,x), (m, 3)]

 

(r(xi, B, Gxi)>0 . Exi) D cpxi . (px
‘>O . Dxi) 3 XXi . XXi 3 Exi) . (ih
. Bxi) 3 X131 . XX: 3 Exi . (r(xi, i), Gxi)>0 . hxi 3

vxi . @X1 3 wX1)]

TI. 1.2 defines ’at trial h+l in the series l-h-k there is
substituted with respect to (organism) x and (his responses
by) B and D relative to (the stimulus) u, (the goal—objects)
o for x and (the goal-objects) w for E’ as ’during each of
the trials from the lst to the hth (l) x’s response by B

to the state of affairs Gx implies ex and o is available

to x as a means to W and (2) x’s response by D to the
state—of-affairs Gx implies xx and X is available to x as

a means to h and_during each of the trials from the h+lSt

to the kth (3) x’s response by B to the state-of-affairs

Gx implies xx and x is available to x as a means to h and
(h) x’s response by D to the state-of-affairs Gx implies

ex and o is available to x as a means to w’.

23. This definition is thus a definition of substitution

138

as is described by Tolman in chapters II through V of

Purposive Lehaviorism. Notice that expressions of the

 

Ho

form ’r(xi, B, Gxa),)Cl. Exi) occur in it. Th s is the
notion of response in the sense of R1 discussed in para-
graph 47. of chapter II of this essay. hence the defin-

‘l

ition suggests, in part, by means of this expression that
the animal has been trained. Again, according to the sub-
stitution conventions adepted in the discussion of means-

end availability the substituends of ’Qxi’, ’wxi’, ’xxi’

and ’hxi’ are only realizable states-of-affairs.

2h. A good way to picture the above definition is this.
Think of a Y maze with different goal-boxes at each end.
Substitution occurs when the "rewards" (e.g., bran mesh
and electric shock) in the two goal-boxes are inter-
changed on trial h+l and kept in their new locations
through trial k.

The conventions of ill and as make the following bicon-

ditional valid.

a- . . . k

mil. 1.3 <1§><¢xi> a [<1§)<@x1> . (lh+1)(@Xi)]

TII. 1.3 reads: for every trial i from c to k, cxi is
true if and only if for every i from c to h pxi is true

and for every i from h+l to k oxi is true.

25. TII. 1.3 deserves further comment. First of all,
according to the conventions of TII (as represented in

paragraphs 10 and 11 in this chapter), céhék. Suppose now

139

that c=k. Then h=c; also h=k. hence, h+l = k+l. Under
these conditions the left hand member of the above bicon-
ditional would be equivalent to

(PKG :
but the right hand member would be equivalent to
and thus the right band member would not be implied by

the left band member. Accordinslv, the following con-

L41al‘.‘“;—m '- - “Bi

H

vention is adopted. Tl . 1.3 is always used under the
tacit assumption that c<:k; an assumption in practice
satisfied in all of he series of trials constituting
psychological experiments of the sort undertaken by ex-
perimental psychologists. secondly, TII. 1.3 is not
strictly a definition, but its use is primarily abbrevia-
tive, hence like that of an abbreviative definition. It is
for this reason that TII. 1.3 is listed amen? the definitions.
It really belonys to the conventions of the symbolism and
the presupposed system of arithmetic, that is, 3:, Mhen a
replacement in accordance with it is required in a proof,
it is more illuminating to appeal to TII. 1.3 than to

merely "Li".

a

.1-
lI

The Postulates of

 

 

TlI.2.0 oxi Q) WXj D ~(¢xji@> oxi)

TII. 2.0 reads: i

H:

ex at time i requires greater effort

than ¢X at time j, then the converse is not true.

 

 

__

 

 

 

1H0

26. lhe truth of this postulate is relatively obvious.
It expresses the asymmetry of greater effort. From it
we may also deduce that greater effort is not reflexive;
that is, substituting ’o’ for ’w’, and j for i we may de-
duce

"((PXj -) @Xj)

which again is self-exolanatory.

TII. 2.1 e(xi, (exi §>-WXj)L>~O 3 e(xi, (wxj E) exi)) = O
TII. 2.1 reads: if x at time i expects that exi requires
more effort than jo, then he does not expect at time i

that jo requires more effort than @Xi-

27. This postulate, like the preceding one, is self-ex-
planatory. It states the asymmetry of X’s expectation (at

a given moment) of greater effort. Again, from TII. 2.1,

we may deduce the irreflexivity of X’s expectation (at a
given moment) of great effort. Substituting ’e’ for ’w’
and j for i, we get

e(xj, (exj E @Xj)) = 0.
Notice that, in T11. 2.0 and TII. 2.1, we need not con-
sider the time variable over a given series because these

two laws are true for all times.

- . , .k
$11.. 2.2 (11) [d(Xi, in) = d(Yi: W1» 0 ° e(xi’ (ch1 E) Xxi)»

e(yi, («pt-Ii E) Byfl) . ('4), x) A (Xi, v) . (<9, HAG/*1, w 3
[e(Xk, (>09; 3 vxk))>e(yk, (Eyk 3 much]

TII. 2.2 reads: if during each of the first k trials, (1)

the strength of X’s demand for ex is kept eoual to ‘nat

!
v

of y’s demand for fly at a vQ.ue above 0, (2) :’s expect-

ation (or belief) that ex is more effortful than xx 18

greater the; y’s belief that ey is more effortful than Ty

and (3) e and x are available to x as means to W and e and
E are available to y as means to w, then on the kth trial

X’s belief that xx leads to wx will be stronger than y’s

belief that Ey leads to $Y°

1

. This postulate might be called "the postulate Of

CC

2
discrimination of effort". It might be represented by
the following kind of situation: when there are two ani-
mals (or two groups of animals) run under the same type
and degree of drive and so trained that one group of ani-
mals is better able to discriminate the difference in

effort between two actions A and b (where both A and E

are means to satisfying the drive) than is the other group
with respect to the actions A and C (where both A and C
are means to satisfying the drive) then the group with

the better discrimination will have a clearer cognition
that B leads to satisfying their individual drives than
will the other group that C leads to satisfying their in-

d'vidual drives.

(Bxi 3 Q'Xi))>e(Yi: Gvi D ( yi 2) xyi)) I) (6(Xi, Bxi)
>d(y1, WiH]

TII. 2.° reads: if tie strenfith of X’s demand for bx at
) l L

n2

tine i is Kept equal to tLat of y’s demand at time 1 for
xy at a value above 0 and x’s belief at time i that if Gx
then ex is a means to wx is stronger than y’s belief at
time i that if Gy then my is a neans to xy, then x’s

demand at time i for fix will be stronger than y’s demand

at time i for my.

29. This postulate is an analogue of the postulate ll. 2.1.
It characterizes the greater tendency of an animal x to
approach a goal—object in View of nis greater knowledge
when compared with another animal y. TII. 2.3 thus des-

cribes a kind of approach situation under the conditions

of the same drive but greater knowledge, that is, stronger

}_Jo

vs. weaker beliefs. This postulate finds justification n

part in chapters III and l? of Purposive Eehaviorism.

 

2:11. 2.14- (111:) [d(xi, Mu) = d(yi, byi>>0 - W11 E>XX1 -
"UPS": 13> “3731)
(xi, w) . w, 1:) A (51,31 2 [e(xk, <ka E>xxk))>e(yk,
((PZYk 13> Db’kH]

TII. 2.h reads: if during each of the first k trials, (1)

. 4m 12) m) . ~<<pyi 12> mi) . (<9, ‘4.) A

the strength of x’s demand for wx is kept equal to that of
y’s for By at a positive value above 0, (2) ex requires
more effort than xx, my does not require more effort than
Dy, ex does not require more effort than ey, ey does not
require more effort than ex, (3) both e and x are avail-

able to x as means to W and both a and D are available to

V as means to B then on the kth trial x’s exnectation that
u 3 3 4.

"V
E

I If I h .- “1.3.-\an

ex is more effortful than we is greater than y’s expecta—
tion that ey is more effortful than Dy. The point of
TII. 2.u is this: if the difference in effortfulness
between ex and xx is greater than that between ey and By,
then x will acquire in a given series of trials stronger

antiCination of the fact of difference.

.L

30. It should be noted in this postulate (and indeed,

- a hflk‘.‘ PE

in all of the postulates which prescribe a training period 5~
for k trials and a consequence of that training at the kth
trial) that if k is not high enough the difference pre—
dicted in the conclusion will not be discernible even
though it is there. For example, consider a maze in which
x (and y) cannot retrace on one trial so as to examine both
alternatives on one trial. Then the predicted difference
will not even exist unless k is nigh enough to allow explor-
ation of both alternatives. Notice again that the greater
the disparity between ex and xx as compared to that between
ey and By, the lower k may be and still allow the predicted
difference to be discernible by the experimenter, for ex—
ample, in terms of the frequency with which x chooses WK
rather than e: as compared with the frequency with which y
chooses Dy rather than qi. _What this means is that the
postulates and theorems should be written, if complete
strictness were to be observed, in the form

(3k) [Postulate]

In general, if a postulate holds for k then it holds also for

k+l' that is, ii k is high enough that i

2

worry about; one can’t get k too hig‘.

always true. For

8

all one need

But this is not

example in postulate TII. 2.7 to follow,

if k is too high the postulate will not hold.

TII. 2.5 [(d(xi,

TII. 2.5 reads

) = d(yi, wfl>0

5Y1 3 (Qyi 3 in))

to y’s demand at time i for wy and x’s

e(Xi, EXi D

(E)he(xi, Yi)) 3

i for WX is equal

expectation at

time i (or anticipation) that if Ex then if xx then WK

is greater than y’s expectation at time i that if By then

if my tnen wy and

"N.
.-<
J—z

is sensorily received by both x at

time i and at time i then x’s tendenc1 to respond at
y , I] -

time 1 by x to Ex is greater than y’s at time i by e to By.

The point of this postulate amounts to this: the greater

the expectation that upon the occurrence of a certain stim-

ulus if a certain response is made then a certain goal will

be attained, the greater the tendency 13 to make that res-

ponse to that stimulus.

31. It will be seen that this postulate is no more than

an extension of postulate II. 2.6 in the preceding chapter.

here, again, we are comparing different animals with differ-

ent strengths of anticipation.

TII. 2.5 as the response postulate.

hence, we shall refer to

11.4 n. IOA“.£_ in'
I

11:5

: Xxi: \l’ix )(>d :71! (pyi! 3:71) 0 d(xi’ \Uxi) :
(r xi, D, 3x1);>0 . Dxi) 3 Xxi] . [(r(yi, D,
]

3 [e(xk, ka 3 (ka 3 uxk)))'e(Yk, Gyk

TII. 2.6 reads: if during each of the trials from 1 to k
(l) x’s demand for xx as a means to px is greater than y’s

demand for py as a means to By, (2) x’s demand for px is

E

kept equal to y’s for E3 which is greater than 0 and (3)

1. Per ..rmn'.‘ o 0‘.

x’ 3 response by D to Gx implies xx ar d y’ 3 response by D

O O

to Gy implies py, then on tne kth trial x’s anti01pation
that if Gx then if Dx then wx will be stronger than y’s
that if Gy then if Dy then By. ihis postulate provides
the inferential basis of Tolman’s contention that routes

to more demanded or "‘

oetter goal-objects" are chosen more
often than routes to less demanded or "poorer goal-objects"
as means to the alleviation of some drive state (cf. pp.

71-77 in Purposive Eehaviorism).

 

32. Attention is directed to the k in the quantifier;

k is a variable taking as values any number down to and
including 1. The point is this: though we don’t know

how many, some trials are needed to build up the expectations
hypothecated in the consequent of TII. 2.6. Indeed if k = 2,

then these expectations could have been built up in one trial.

 

hence,v¢e allow in this postulate the possibility for one

trial learning. (cf. Eurppsive Eehaviorisr, p. 73.)

 

° “3121) D XBi- Xyi 3 Lyl] ° [3X [(2 9 ~‘: G) 9 (’9, It) 9 (\1': F) J]
k f‘ "" I“ T‘
3 (ih+l) [e(vi, cyi 3 (:yi 3 ¢y1)))'e(xi, in 3 (:yi 3 wx;))]

[.1
F11
p
U)

III. 2.7 reads: Throughout each of k trials if (

. 1 . . 1 x -. o . o o o a ’
not identical with D and 0 is nOt identical with X, (2) x s

demand for WK is kept equal to y’s for Wy which is above C,

[a
’3 response bi E to G7 implies v and is available
- a.) - u
to y as a means to w, and y’s response by D to Gy implies L;

“y and X is available to y as a means to H and (h) there
is substituted for x at trial h+l in the trial series l—h-k

‘9‘ a

with respect to L anc h relative to G, e for X and W for F,
then for every trial i from h+1 to k y’s anticipation that
if Gy then if By then WY is stronger than x’s expectation

that if Gx then if Ex then gx.

33. Quite briefly this postulate says that where two
animals are compared under the same drive of the sane
strength and where one of these groups experiences a sub-
stitution and the other no substitution, then the animal
experiencing the substitution will, at some time after the
substitution but before the end of the experiment, show
less a tendency to expect that the original path leads to
the old goal-object than will the animal who did not ex-
perience substitution. This postulate will be called the

:ay be found

U

7

...I

postulate of "substitution”. Its justification

in chapter IV of Purposive Eehaviorism.

 

11.9-7

3h. This postulate would not hold without the stipula-
tion of the differences between'the responses B and D and
the goal-objects o and x. For were they allowed, in some
cases, to he the same there would be no substitution and
the predicted consequence would not follow. ihis is im—
portant because the consequent of this postulate shows a

2*

certain disruptive character in the behavior of the animal

-?‘\

petting the substituticn. (of. Chapter V, Eurposive Tehav-

 

iorism). Tolman is quite exp lC’t abort pointing out that

l i
disruption effects are only ob erved in substitution situ-

U1

ations. One would not find disruption effects in latent
learning because there is no substitution takinv place in
tnese studies.

in. 2.6 [(apx- E) XXi . (P‘Ji 3 XYi . @271 E>XX1 - x31 3

\L'Yi - d(Xi, in) = d(I‘j’i: WiDO - “Xi, )CXi: ~1rXi>>0) D
(d(Xi: XXi: u!Xi))d-(Vi: W1: W1”

TII. 2.8 reads: where ox at time i requires more effort than
xx at time i, ey at time i requires more effort than xy at
time i and my at time i involves rcre eiiert twan vx at time i

and vv at its i leads to WY at time i and x’s demand at time i

1.0

for WK is equal to y’s at time i for wy, where x at time i is
teachable with respect to XX as a means to wx, then x’s demand
at time i for xx as a means to ¢x is greater than y’s at time

s that

(D
H.

i for my as a means to ¢y. In effect, this postulat
the less effortful goal-object for animal x is a better goal—

ob ect for x than is the more effortful foal-object for y

LJ.

provided that x is teachable with respect to better goal-object.

 

1‘: Vfifi—efl

lh8

35. hotice that this postulate is so "rigged” that its
truth depends upon the valence and efficiency conditions
being held equal. In other words, tbs kegs effortful

goal-object (where there are only two worthwhile possibi-
lities) is the better goal-object provided the conditions

of valen y and efficiency are held constant. This post-

“If

ulate is useful in the present version of TII as a means

to gettin an operational definition of docility.

m.
:J
g.)

ll"‘“

III. 2.9 [(iime 75 D . <p 7‘ x . d(xi, taxi) = d(y1, wi)>0

. xi E) xxi . cpyi 13> xyi . cpyi El) xxi . (r(yi, E, G—yi))0

. Eyi) D an . «>31 3 W1 - (r(l’i: D: Gyi)>o ' “71) 3

xyi . xyi a 4yi> . si'h‘k [(2, D, G)(@, x), (w, n>Jii a
[(r(yj, jg, uyj)>r(xj, E, Gx.) . r(xld 1:, ka)>r(yk, QB, Gyk))
D (il)(t(xi, xxi. ¢'X1)>O)]

J

K.

III. 2.9 reads: if durin; each of the first k trials (1)
B is not identical with D and p is not identical with v
(2) x’s demand for wx is kept equal to y’s for WY which is
above 0, (3) ex is more effortful than Xx, ey is more effort—
ful than xy and ey is more effortful than xx, (h) y’s res-
ponse by E to Gy implies @Y and oy implies wy, (5) y’s res-
ponse by D to Gy implies xy and xy implies fly and (a) there
is substituted for x at trial h+l in the series l-h-k with
respect to b and 3 relative to G, p for x and w for B, then
if on the jth trial y’s tendency to respond by E to Gy is

greater than x’s tendency to respond by B to fix and on the

ktn trial x’s tendency to respond by B to Gx is freater than

1&9

y’s tendency to respond by h to Cy, then throughout every
trial from l to k x is teacnable with respect to xx as a

means to wx.

36. TII. 2.9 presents certain conditions under which it
is possible to infer the teachability of x with respect to
a given means—object. It is therefore called the "teach-

ability postulate". 1t amounts to this: given disruption

 

in x’s behavior on the jth trial preceding the kth trial

if recovery by x on the kth trial is made in terms of the
least effortful object which was substituted at trial

h+l in the trial series l-h-k, then x is teachable through-
out that series with respect to that least effortful object.

The justification for this postulate may be found on pages

14, 7h, hh2 and AA} of Purposive Eehaviorism.

 

37. One final point. This postulate shows why we require
response in the sense of R1 described in cnapter II of this
essay, that is, why we need an expression having the form of
(r(xi, PB, Gxi)>O . P-xi).
For we must be able to claim that the animal had experience
with the goal-objects during the early part of the experi-
ment. notice hat we could not zse the notion of response
in the sense of R2, that is,
r(xi, E, fixi) = 1.
For this notion says that the irequency of response (in the
sense R1) is equal to 1. In the above postulate both ani-

mals would then be able to proceed along the various appro-

150

priate paths, say, of a maze, only when the frequency of
response reacted l. rut tien the consequent which shows
x having a greater response tendency on the kth trial
than y for the apprOpriate path would be false because
y’s response tendency and x’s response tendency for the
appropriate path already equalled l (the highest possible

number) during the training. nesponse in the sense of El

avoids this consequence. It says that x has the tendency

 

to respond by E to Gx and :x is true. hence x (and y)
will begin to accumulate knowledCe of the apprOpriate
paths of the maze only when botn of these conditions hold

true. In reneral, both of these conditions would not be

r'n

met on every trial. hence the r‘ifference from

O
N
O
H
(-
{—1
A
Ho
l—‘V’
A
N
r.
O
N
H
‘
:7
N
P.
v
II
C
U
(L
N
H.
‘0
X
N
H.

II
"3
\/
O

0

E21 3 ((r(zl, \i’: lZi)>O . Qrzi) 3 uzi, b) .

(tzi . $21) 3 ~Gzi, b . (in . wzi) 3 ~Dz-, a] .

0h " T'; ‘ ' _ " r— _

(11) [:xi . ~ .cyi . d(xi, 1‘~’.Xi) -— d(yi, uyi) — t<r .

I". .‘1+2 0 I: ~
t‘Hxi, (pxi , xxi)> o] . (114,1) [Ja] . (1mg) [:xi .
)

= d(yi, I-Tv-) = s>r . Ja . (Ja . Dxi, a) 3

in . (da . ayi, a) 3 Evil] 3 [e(xk, Exk 3 (¢Xy 3 ka))>
J

e(yk, Eyk 3 (97k 3 I'l'Iy’kH

TII. 2.10 reads: if (I) during the first k trials, for
every 2 it is true that: (1) 2 does not demand hz implies

that z’s demand for xz is equal to r which is greater than

151

O (2) o is not identical with ¢ and D is not identical
with G, (3) Ez implies that if z responds by e to :2

then Bz,a and tz also implies that if z responds by w

to Ez then Gz,b, (h) E2 and mz implies not Gz,b and £2 and gz

implies not Lz,a, and if (ll) during the first h of those
k trials :x and not by and x’s demand for fix is equal to
y’s demand for by, which is equal to t which is less than r,

and X nas been taught that ex is a means to XX and if (Ill)

‘0
I

‘V 124'. a _ ‘2 "I!

during the trials h+l and n+2, Ja, and if finally (IV)
during the trials h+2 to k, (1) both BX and By and (2)
X’S demand for hx equals y’s demand ior hy which is equal

to s which is greater than r and (3) Ja and (h) Ja and

Bx,a implies hx and Ja and ‘3

\O
93
Ho
('3
K

lies Ny, then on the
ktn trial X’s anticipation that if Ex then ex leads to
fix is greater than y’s expectation that if Ey then ey

leads to Ly.

39. This postulate is called the latent learnin;
.rinciple. What it says is briefly tnis: given a
situation in which one group of animals has prior train-
ing under some drive and another group does not under

that drive, then when both groups are introduced into

the same situation (but with the drive changed) the

group which had the prior training will show transfer-
ence and hence their perfornance will be better than the
non-trained group. This claim is supported by the follov—

ing illustration of TII. 2.10. Let ’HZ’ be ’2 alleviates

152

‘his thirst’, ’vz’ be ’2 satisfies his curiosity’ ’Ez’

A
be ’2 is in the starting box’, ’o’ be ’taking the right
route’, ’Dz,a’ be ’2 gets into food-box a’, ’w’ be
’taking the left route’, ’Gz,b’ be ’2 gets to water-box b’,
’Ja’ be ’a contairs food’, and ’Lx (and y)’ be ’X (and y)
alleviates nis hunger’. Under these conditions, TII. 2.10
reads: if (I) during the first k trials, it is true for
every 2 that (1) 2 does not demaid that he alleviate his
hirst implies that his demand that he satisfy his curio-
sity e-uals r (which is greater than C) (a) takinj the
right route is not the sane response as takint the left
route and getting into the food-b x is not the same res—
ponse as gettinv into the water—box, (3) z is in the
starting-box implies that if he responds by taking the
right route to the fact that he is in the starting-box,
then he gets into the food-box a and z is in the starting-
box also implies that if he resyonds by taking the left
route to the fact that he is in the startinf-box, then
he gets into the water-box b and (a) when 2 is in the
starting-box and takes the right route, he does not
get into water-box b and also when he is in the start-
ing—box and akes the left route, then he does not bet
into food-box a, and if (II) during the first h of
those k trials (1) x (an experimental animal) is in
the starting—box but 3 (a control aniral) is not (2) both
X’S and y’s demands that their hunyer be alleviated is

equal to t (which is less than r) and (3) x has been taught

 

that x takes the right route leads to X satisfying his
curiosity, and if (Ill) during the trials h+l and h+2
(food-box) a contains food, and if finally (IV) during

the trials h+2 to k, (1) both x and y are in the starting-
box (2) their demands for hunrer-alleviation are equal

to s (which is greater than r) (3) (food-box) a contains

food and (h) if wden (food-box) a contains food and X

gets into the food-box a then X’s hunger is alleviated

(- At. w;

and if when (food-box) a contains food and y gets into I
the food-box a, then y’s hunger is alleviated, then on

the kth trial X’s anticipation that if he is in the start-

ing-box then if he takes the right route, his hunger will

be alleviated is greater than y’s anticipation that if he

is in the starting-box then if he takes the right route,

113 hunger will be alleviated.

40. Because of its importance for Tolman’s theory, it
would be well to discuss this postulate a bit more. First
of all the latent learning irinciple as presented in ill

is typically illustrated on a maze which has two distinct
goal-boxes and whose mutually exclusive routes to the goal-
box are so arrange‘ that (l) retracing can be made possible
or not possible and (2) the amount of effort involved in
running one route is the same as the amount of effort in-
volved in running the other. (but this latter is not in-
cluded in the postulate because the influence of the effort

factor may be either non-existent or negligible in this

kind of learning situation. At any rate, the postulate

is neutral on this matter and the illustrative conditions
are in cautious language.) E amples of mazes wnich would
satisfy the above design are simple T mazes, simple Y
mazes, rectangular mazes whose routes are the same length,
and so on. secondly, equality o: taughtness for either
route is measured by equal amounts of training on those
routes, for example, by 50p of the runs on one route.

(It should be noted, however, that equality of taughtness
on either route could be measured by a certain criterion
of accuracy for picking the route leading to food, and so
on.) lhiPQlT, we are supposing the animals in both the
control and experimental groups to be animals of the

same size so that no inequality of effort is established
between groups through some physical advantage in one
group as Opposed to the other (but of. the first point
above). Fourthly, the control group in this version
-which is represented by the variable ’y’- is always the
group which does not receive preliminary training. Pifthly,
we are assuming equal intelligence for all the animals.
(indeed, one may regard the Euxton version of latent learn-
ing —where 50% of the animals never mastered the maze per-
haps as the result of their relative stupidity- as an
"intelligence test" for the animals.) Sixthly, as usual,
we are assuming that the factors of valence and efficiency

are being held constant.

13
Ml. how in the light of these conditions let us exar-
ine the above postulate. lhat part of the postulate pre-
fixed by (I) describes the common situation into which
both the experimental animals, represented by ’x’, and
the control animals are introduced. The part of the

3

postulate nreiixed by (II) describes the experimental

.L

group’s pre-training in the common situation. The part

r.

Cl the postulate prefixed by(lllbindicates the intro—
duction of something into the goal—box(or goal-boxes)
and the last part of the postulate (IV) describes the
test series where both control and experimental animals
are introduced into the common situation. The advantage
predicted for x is based on his ability (due to prior
training) to discriminate the different routes to the
goal-boxes; the control group has not had a chance to
make these discriminations prior to introduction in the
maze at trial h+2. The point to notice is that the post-
ulate employs certain concepts in Tolman’s system and,
furthermore, appears to be justified by the remarks

(especially) on pages 3h3-3hh and in chapter III of

Purposive Eehaviorism. If these claims are justified

H.

t

H.

s easy to prove that latent learninf in at least three

of

I—Jo

ts versions (as classified by Thistlethwaite) can be
deduced from iolman’s theory. The Elodgett version is not
so deduced; it will be discussed at an appropriate time in

the section on "The Theorems of TII".

 

‘P'

III. 2.11 [‘Xi E wyj 0 IEIYJ’ E> sz 3 ‘Pxi E>XZ’:

ill. 2.ll reads: if ox at time i is more effortful than

I

ny at time j and 9y at time j is more effortful than xz

I

at time k, then ex at time i is more effortful than yz at

time k. this postulate states the t ansivity of freater
effort.

The Theorems of TII

 

 

It. -t;.-:_g “rug!

5

rho followihj theorems are derived from the postulates
either alone or in conjunction with other postulates,

definitions and/or theorems.

'i'l'I. 3.0 ~(cpxi E) qui) III. '] , €31.01 and ’i‘aut.

N
O
0
b
Lp-Jo

T.“

ill. 3.1 e(xi, oxi a) exi) = O iiI.

[\J

1 I
Y

'1 [.23 %]3 5310019

iaut and KB

L2. ill. 3.0 and ill. 3.1 present, respectively, ele-
mentary properties of the ideas of "; eater effort” and
"the expectation of Creater effort".

T1]. 3.0 asserts tla ex at time i i~ not more effortful

C)

than itself.
ill. 3.1 asserts that x at time i does not expect that ex

requires more effort than ex.

(Lp,j.:) A (iii, ‘3'.) . ((9, D) A (371, (1)] D [e(xk, (q)):k 33> X321{)))

 

 

 

 

 

157

Proof: m. 2.1L, 1111. 2.11 [$113] [$ng prop.

ill. 3.2 affirms that if during each of the first k trials

if x’s demand that WX is equal in strength to y’s demand

 

that my which is greater than 0, and ex involves more
effort than xx, and ey does not involve more effort than
Dy and ex does not involve more effort than @y and ey does
rs
not involve more effort than ox but nevertheless Dy in-
volves more effort than xx, and o and x are available to 1
x as means to w, and o and D are available to y as means
to w, then on the kth trial X’s knowledfe (i.e., expecta-
tion) that ex involves more effort than Xx is greater than
y’s knowledge (i.e., expectation) that my involves more

effort than Dy.

A3. This principle, Tll. 3.2, seems to express the
Tolmanian version of the law of least effort. There can
be no doubt that Tolman’s system requires such a law, as

is evidenced by Tolman’s remarks in Purposive Eehaviorism.(3

 

The distinctive mark of folman’s version of least effort
is seen in the consequent of the above theorem. It will
be noticed that wiat is expected is the difference in
effort between two goal-objects. In short, before the

or anism acts on an actual difference in effort between

0'73

goal-objects he must learn (that is, acquire the know-

ledge) that there is such a difference. It should be

 

O
o
O
...b
0
U
H.
U)
0
:1
U)
0)
H.

on on page 110 of Purposive Behaviorism.

 

158

noticed that this law makes little sense whatever unless

we remember the proviso stated at the beginnine of this
chapter, namely, that we are assuming that tie valence
conditions and the efficiency conditions with respect to
the means objects are held constant whenever the ante-

cedent of any theorem contains the expression ’3) ’.

a k . 3.

(xi, (1')] 3 e(xk, (rpxk E) XXk))>O i:
'9; _
The proof of this theorem will be more or less fully ’

develOped in order to show the general character of the
proofs in Tll.
Proof: [(ilf) [d(xi, (txi) = d(xi, "Xi ))O . ¢X1E>XX1 .
..(chi E) (PXi) . ~(cpxi E) (9X1) . ~(goxi E)cpxi) . (pXi E )(Xi
. (@y X) A (Xi, v) . (¢: ¢) A (Xi, w)]] 3 [e(xk, (@Xk E)

. __ (. '
xxk))>e(xk, (szk E> cpxk))] Til. 3.2 [TgfiE] (l)

[(1%) [d(xi, M1) = d(xi, ,lrxi))01 . (:1 (mi 3)xx.) .

(111‘) Mai :21) 3x1) . ~<<pxi 3) 3x1) . ~ («0x1 Ewan .

(ii) [(3, x) A (xi, 3) . (3, a) A (xi, 3):] a so (1), *10.2
and Taut. (2)

Nil) [d(xi’ Wxi) = d(xi: WIN)“ - (ii) [W1 E>XX11 -

(if) [(v, X) A (xi, v) . (w, ¢)A(Xi, 3)]] 3 SC £( ), TII . 3.0
an *.9 13 (3)

[(il)[d( xi, wxi )])o . (11f) [<prL :3) xxi] . (:11) [(q), xM

(Xi, W) 0 (CP, (P)A(Xiy ‘1!)1] 3 SC (3), Phi—"5 (LL)

75‘

 

7. The expression "50" means "same consequent as the preceding
theorem or numbered theorem (or line in a proof)"

[<ii>[d<xi, waive] . (ii) W: V) was . (1*):in D M: -

XXII. 3 \L’Xi o (Pxi D \in o (PXi 3 \iyxi]] 3 E30 (LL), (LII. 1.0 (5)
.k .' n .
[(11) [d(xi, 333(1))“ . (fines, 3) >011] . (111‘) [(3, x) A

(xi, w)]] 3 so (5), Iaut and TII. 1.0 (e)

r—-\
P.
Hx'
r—:
O
N
H.
M
‘1

3':>>0 - an: E) 3x143, x)A(xi, :31] a e(xk,
(ex? a) xxk)x> O . (é), TII. 3.1, a; and 310.22

MAJ Tll. 3.2.0 might be called the law of least effort

for a single orranism (or a single 'rou: of organisms).

It is helpful in the sense tkat it snows clearly what ele—
ments are involved in that law without the added encumbrances
of a control group. If we let ’Wxi’ represent, ’X alleviates
his hunger’, ’nxi’ represent ’X eats dry bran mash’ and

’ represent ’x eats damp bran mash’, the above law so

,Xxi
interpreted reads: if during tne first k trials X defends
that he alleviate his hunger and X eats dry bran m.sn is

more effortful for X than x eats damp bran mash and X eats
dry bran mash and x eats wet bran mash are available to X
as means to alleviating hunger, then, on the kth trial X’S

knowledge (eXpectation) that x eats dry bran mash is more

eifortful than x eats danp bran mash is greater than 0.

. k, 3
311. 3.2.1 (11,[d(xi, :xi) = d(yi, 33100 . (PX: 13>)“: -

~ (cpyi E>Dyi) . ~(<pxi 3><pyi) . ~(<pyi E>oxi) . L‘yi E>XX1 .
(@, x) A (xi, w) . (o, D) A (Xi, ¢)] 3 [e(xk, xxk 3 ka)>

e(Yk: 33k 3 Wyk)]

.‘l‘ . .1 a“ .- Jr. u? "u:
"I
.-

160

Proof: prOp. TII. 3.2 and ill. 2.2
MS. This theorem, Ill. 3.2.1, seems to express part of the

meaning of the following proposition stated by Tolman on

pages e7-e5 of rurposive Eehaviorism

.u-n—I—

 

If different groups of animals, but with the same
physiological drive are run with different goal-
objects, the groups run with certain goal-objects
learn faster than the others.
I say "part of the meaning” because the expression "certain
goal-objects" could conceivably refer to the different val—
ences of tne goal-objects, the difference in efficiency of
one goal-object compared with another, or the difference
in effortfulness of one foal-Object compared wi h another.
It will be noticed that TII. 3.2.1 is concerned with :29
difference in effort only. the proof sketch shows that
this law is, in part, a direct product of the law of least
effort. Consequently, it may be sunmarized as follows:
Given the conditions prevailing in the antecedent of the
law of least effort (III. 3.2), then on the kth trial X’s

knowledge that xx leads to wx is greater than y’s know-

ledge that Dy leads to wy.

TII. 3.3 [(iEHB # D . cp 7‘ x . d(xi, Wxi) = d(yi, 31371)}0

0 (r(yi, B, Gyi)>0 . Eyi) 3 cpyi o (PB-Ti 1"in o (r(Yi, D: C137.)
(

 

-1"

E2:

1‘

ub, ill. 3.3 will be called the "disruption" theorem.

It seems to capture iolnan’s intentions concerninfi the
notion of disruption as the) are expressed in the follow-

ing remarks quoted from 93:9

7b of Purposive :ehaviorism.

 

Tolman writes:

find we shall suepose in peneral that in behavior
there is always immanent the expectation of some
more or less specific type of goal-object. If
such th oe of goal- object be not found, whether it

 

 

 

 

be because a better, anworse, or Here elV differ-
ent, {02 l -ooi ect has been substitute "d for it, then
the nintl s oestV1Cc will Show so~e sort of .is-

 

 

ruption such as hunting, startled speedin; up, or
what not.

 

 

 

Tll. 3.3 describes the conditions under which disruption
can be predicted where the means objects lead to the same
end. If we take the typical hunger situation, then Tll. 3.3
amounts to sa Jing that where two organisms (or two groups of
orfanis- us) have the same strer 3th of derrk nd for the allevia-
tion of hunger, if one orjanism or group of orcanis ms, that
is, the eXperimental group,is shifted from one goal-object
to another such that either goal-object leads to hunger
alleviation, while the other organism or group of organisms,
t‘nat is, the control group,does not experience the shift in
goal—objects though in fact either goal- object leads to
hunger alleviation, then at some trial; after the shift
(h+l) but before the end of the experiment (k), the ex-
peri1m ntal orgar ism’s knowledge that the path on which he

was trained (which led to tle origi1nal oal-object) leads

.071

to hunger alleviation will be less than the control or“an-

lsm’s knowledge that that same path leads to hunfer allevi-

162

ation. hotice that this theorem shows the "substitution"
as taking place only with respect to means objects. The
experiment of filliot’s which Tolman cites on panes 72-7h

)

Ch
9)

of Purposive Behaviorism shows tre Chang 3 taking place
both with respect to means-objects 32d final goal-objects.
This situation is easily deduced by substituting in post-
ulate TII. 2.7 [1% . Zecause of its sinilaritv to TII. 3.3

J

the theorem will not be produced here.

fi—nac. «MA—nu c-x-m-‘e-fi’

TII. 3.3.0 5A 3 [[d(x. wx.) = d(y., wy.))'0 . (G)Re
J

TII. 3.3.00 [(1 ) [E f D . v # x . d(xi, wxi) = d(Yi: in)

. we .

)c>. (bin-(Xi, yi) - (r(yi, E, CV1).>C>- Eyi) D wyi . wyi

D wyi o (r(yi, D, Gyi)>o o Dyi) D Xyi o Xyi D wyj-] O

ql-h-k i l ‘ fl ,

bx [(5, U: (I): (’4): X): “3):” D [r(yj: 13: Gyj)>r(xj, E: ij)]
TII. 103, Irflpo and Tauto TIIOBOBOO

h7. TII. 3.3.00 affirms nearly the same thing as TII. 3.3.
The difference is that now (provided the stimulus is sensor-
ily received) we are predicting the advantage of y’s tendency

h

to respond over X’s tendency to respond on the jt trial in

the disruption situation and not merely the animal’s (y’s)
greater knowledge (or expectation). In short, in this theo-
rem we have gone from learning as acquisition to learninw

L}

as exhibited in performance. We have gotten Tolman’s learner

.-
I o a
r ’ ‘
" o O 0
o
« ' r r
r i P f
.- a v r
u o I |
\ o f '

 

 

into "action". lhis should, in part, satisfy Guthrie’s
complaint that Tolman leaves the learner "buried in
thought". Furthermore it seems appropriate to point out
that the notion of response tendency used here seems con-

sonant with lolman’s "Erinciples of Performance" which

 

was published in the Psgcnclogical heview in beptember
of 1955.

k
T110 30” [(11) [E # D 0 ¢ # X d(xi: WXi) = d(yi, Wyi)> O

 

. d(X1, XXi, vxi>>d(yi, «9:11, mm) . (G)Re(xi, :71) -

'tflnfi ‘

(r(yi, i3, Gyi) >0 . Byi) D ‘Pyi . (PYi 3 ‘Wi . (r(yi, D: GY1)>O
- Dyi) 3 Xyi 0 .

XYi D vyi] . 8X ‘ [(E, D, G), (e, x), (v)]] D

[e(xk, ka 3 (ka D WK k));>e(yk, Gyk 3 (Eyk 3 wyk))]

TII. 2. e [‘i ,g], Sinp, TII. 1.2, TII. 1.3, laut and Exp.

- .k . . , -
TII. 3.4.0 [(1l)[B ,é D . <9 F x.0(xi, viii) = d(ifi, WiDC -

‘l

Q(Xi, xxi, WXLi )‘>Cdyi, wyi, wyi) . (G)He(xi, Y1) . (r(yi, E: Gyi)
‘>O . Eyi) 3 eyi .

wi 3 W1 . (r(yi, 13, Gyi)>0 . Dyi) 3 xvi . X‘Ji 3 Mi] .

(131) “r(xi, g, Gxi)>0 . Exi) 3 Mi - Mi 3 Mi -

(mi, D, ex. >0 . D‘x. ) 3 Xxi . xxi a up . (11151) maxi,
B,G l))O . “X1 3 Xxi . Xxi 3 Wxio

r(xi;L D, Gxi ))O . UK 3 LpXi . cpxi 3 ‘3,Xi]] 3 SC TII. 3.2.; and

i) TII. 2.2

TII. 3.u.oo SA 3 [d(xk, Bxk)>d(yk, Eyk] TII. 3.14.0 and T11. 2.3
E 2
[-,M]
cp x

 

k
(III. 30b.-o(;'!vc [(11) E 1% D o {P # X o C(Xi, \I’Xo) = d(yi, \ilyi)> O

o d(xi9 Xxi: \L’Xi)>d(yi: $0371: “5331) o (G)Re(xig 371) 0 (r(Yi: E:

G-yi)>0 . Eyi) D cpyi . @311 3 Mi - r(yi, 13', GyiDO 3 "3'in -

h - a w
-Xyi] , (il)[(r(xi, .3, exi)>0 . :xi) 3 exi . (0x1 3 (5X1 .
k

r(xi, D, Gxi)>0 3 ~ Dxi . ~Xxi] . (ih+1)[r(xi, B, 62(1))0

. bxi) 3 xxi . xxi 3 ¢xi . r(xi, D, Gxi)>'0 3 ~ Dxi . ~¢xi]] D

d(xk, Exk)>d(yk’ Eyk) TII. 3.1900 and 692.21

48. TII. 3.h.OOC seems to express Tolman’s meaning in the

following passare on paje ca of Purposive Eehaviorism.

 

(b) If a relatively "good” goal-object be sub-
stituted during the course of learning for a
relatively "poor" goal-object, the rat’s per—
formance shows a sudden improvement. (c) Con-
versely, if a "bad" goal-object be substituted
during the course of learninc for a ”good" one,
the animal’s performance shows a sudden defene-
ration.

"sudden" in the above passage is

The use of the word
extremely vague. it has therefore been ignored in theo-
rem Tll. 3.h.GOO. In a moment, I shall make certain re-
marks concernini the above quotation in relation to the

‘" experiment of hlodgett’s. The above

5...
\-

"latent learnin
quotation expresses two sides of the same coin. hence
a single theorem seems to adequately express both (b)
and (c) in that quotation. Row where we understand.
"better goal-object" to mean, essentially, that one is
more demanded than the other -in the theorem, this is
symbolized as ’d(xi, XXi: xyxi)>d(yi, (py’i, ayyi)’- and

also interpret "improvement in learning' to mean, in this

Case, an advantage in demand for the "route" leading to the

 

 

 

 

 

 

 

165

substituted better goal-object -whicr is the consequent
of the theorem TII. 3.h.CQC- we may read the above theo-
rem as follows: If during the trial series 1 to k, E is
not identical with D and Q is not identical with x and x
and y have the same demand strength (above C) for the
same type of goal-object W and xx is a better goal-object If
for x than is my for y and (the stimulus) G is sensorily
received by both x and y and y’s response by E to Gy

always leads to my which leads to wy and if during the ‘

trial series l-h-k, xx is substituted for ex at h+l
th

 

1.

relative to x’s response by B to fix, then on the k

trial x’s demand for fix is greater than y’s demand for By.

M9. The Elodfett latent learning experiment is simply
a version of this principle. however, Tolman’s neglect

of the vagueness of term "sudden" does not make the Elodfett
study a very good test of the latent learning issue. The
present author’s objection to the vagueness found in the
above quotation must not be taken as a denial that the
Blodgett version of the latent learniné principle is de-
ducible from TII. Cn the contrary, if and when Tolman makes
clear the limits of sudden improvement (or degeneration),

a ramification of TII. 3.u.OCO suited to the new require-
ments will altomatically permit a deduction of the Elodjett
latent learning principle.

E

8. The Elodgett experiment is discussed on pages h8-SO of
Purposive iehaviorism.

 

 

an ill. 3-h and TIT. 2.5

III. 3.h.lO Same as TII. 3.h.l except that ’d(xk, xxi, Qxi)>

I' ’ o ,-. - .
0(Yi: @Yi, QYi) 1n III. 3.3.1 is replaced by’ (Qoxi 3:) XXi .

a1-%> xyi . oyi )g) XXi . xyi D Qyi . d(xi, Qxi) = d(yi, Qyi)> C

t(X XXi, QdX >QY. TII. 3.h.l and TII 2.6

i,

. . ,- .k~ fl W
r111. 30);.on [(11) [5 ii U o (p 7! X . d(xi’ ‘J’Ixi) ..":
d(yi’ wi))0 ' Mi E) Xxi ° ‘931 E) X371 - (92/1 E XX: . (9)11

(Xi: yi) - (r(yi: 5: Gyi)>>0 . Eyi) 3 @Y1 . @Yi 3 Wyi .
“ P- ‘.\ l‘Il'l
(r(yi, b, uyi)>>0 . in) 3 Xyi . Xyi 3 Qyi] . Sx [(n, D,

G), (<9, )0, (QHJ Hill-(HM):- xxi, ‘5’X1)>O D [r(yj, 3, Gij

l,

U

r(xj, 15, ij) . r(xk, ii, (:xk)>r(yk, E, 0.ka TII. 3.21.10,

Simp, TII. 3.3.00, hi and Taut.

.k .
TII. 3.h.lCCO SA 3 [(ll)(t(xi’ xxi, ¢X1))>O) = [r(yj, E,

Gyj)>r(x,o, E, ij.) . r(xk, 1i, ka)>r(yi{, E, (4ka TII. 3.}1.lCO
” “ and TII. 2.9

\ft

0. This theorem, TII. 3.u.lCCC, has the form of Carnap’s
bilateral reduction sentence. It may thus be construed as
an "operational definition" of docility, that is, "teach-
ability". lt possesses cer vain interestin; ieatures. The
only intervening variable except that of demand —which here
may be taken as "drive" (that is, (Q)U(X, V) -w is an
ultimate goal-object of x and y-) is teac_t ability. All
other terms are either in wnat the psychologists call a

"data language", for example, "oyi 3 Qyi", or are in a

 

.
a
' I
.
u
i r
I . .
. . . .
. I
a u .
an 0 5
n 9 .
e .
. n M
,.
l - o O

 

langua;e which is immediately reducible to the data language,

i"° Afain

:4-

P.

for eX'fiple, "(r(xi, b, Gx-)>’C . ?x-) 3 x t

1 S:

43

in part, a consequence of tFe law of least effort. how it
is true that Tolman couches docilitf in terms of efficiency.

But the above operational eefinition —what lolman calls an

J
H.
(.1.
H.
O
:3

objective defiL - finds nuch support in Purposive

 

H
(D
F‘
m
<:
H-
O
O
F.)
03
H

-rism, espe ly in chapter 17. tor it will be

 

noticed that teachability, in the above theorer, is, in
part, couched in terns of disruption -or more precise y,

recovery from disruption.

 

ine doctrine we here contend for is, in short,
that wnerever a response shows decilit; relative
to some end -- wherever a response is ready 32
break out into trial and error and (b) to select
gradually, or suddenly, t1e more efficient of
such trials and errors with respect to getting
to that end, such a reaponse expresses .... a
purpose.

 

 

[his passaae on page lg of Purposive Eehaviorism is made

V

 

H

a bit more clear if we substitute the expression an

organism" for the expression ”a response" in all but

the last occurrence of the latter expression in the
quoted passage. The point I wish to make is that the

italicized hrase in the above passa e describes a con-

’13

dition which is the product of disrupt1cn in preciself
he sense in which the latter term is eXilained in TII. 3.3.

How Tolman, in the Glossary of Purposive Pehaviorism, by

 

no means limits the selection (which takes place before
or after disruption) of "better” goal-objects to merely
the more efficient ones-- where we may assume that effi-

ciency and effort are not reducible one to the other.

Renee, it seens perfectly prOper to couch one operational

definition of docility partly in terms of effo't. Given
tnese cons ioeratio1b what Ti]. 3.L.l£ C amounts to is

this: If the organism has a drive and is presented with

certain goal-objects (natns) one of which involves the
least amount of effort in its exe C1tion (in relation to
the others) and at some time in tte ex eriment t1e least

effortful goal—object is substituted for a more effortful

.M a.“ fi_..€ 3-. .'= g

woal Woo ect as a me

(‘3

ns to alleviating the drive state,

tnen tnrourl iout t e experin ent t1e organism is docile

.fi ...u“. ..-Id

(is teactable) with respect to the ”better" (i.e., least
effortful) goal-object if ano onlg if at some time after
substitution but before tne end of the eVpcrirert tnere
is dis rurtion relative to the regns to getting to the
substituted "better” goal-object and later there is re—

covery in favor of a greater selectivity for tie neans

leading to the substituted "better" al- Wobje .

51. ibis theorem seems to ex_press Tolman’s meaning in

the following passage on page Yd of Purposive :eiaviorism.

 

And it would undoubtedly also be
eve 1 wten t*e new goal-object was
tir1ru1srorlc and aid at first cause 01s ruption
sucr a disruption would after enouph experiences
disappear. inat is, it would undorbtedly be found
that tne behavior was docile with respect to the
new goal-object. '1ne rats would never, perhaps,
run as well for t“e new goal, if it were less
desirable, as tney did for tno old, but the dis—
ruption in tneir behavior, qua disruption, would
disappear.

H
O\
\O

1’ 1
3 (1(2):, xz.) = r)0 . £21 3 ((r(zi, Lp, ~zi))O , 'Pzi) 3
bzi,a) . 1:21 3 ((r(z., Q! :zi)>0 . Q12.) 3 G2 ,b) . (tzi .

d (Xi , i'LXi) — d(yi ’ . b
\ . f_+2 . k _
yXiJ> 0] O (lb-fl) [Ja . Lb] ( 11+2) [£18. . Lb , Xi . f;
E‘Ti . d (xi , &.Xi) = d(Eri , ELI/”1) : S) I“ . (1T8. . -,Xi ,a) D 1-x]: . E

TII. 3.5 expresses the weak drive, irrelevant incentive
version of latent learning. Let ’Ez’ be ’2 alleviates
his thirst’, ’xz’ be ’2 satisfies his curiosity’, ’Ez’
be ’2 is in the starting box’, ’o’ be ’takinp the right
route’, ’Dz,a’ be ’2 gets to goal—box a’, ’w’ be ’taking

the left route’, ’Gz,b’ be ’2 gets to goal-box b’, ’Ja’

be ’a contains food’, ’Lb’ be ’b contains water’ and

’hx (and y)’ be ’x (and y) alleviates his hunger’. TII. 3.5
when thus applied, in effect, reads: during k trials for

every 2 if the fact twat 2 does not demand that he alleviate

his thirst iMJliSS that he demands that he satisfy his

He

curiosity and f z is in the starting box then if he res-
ponds by talcinfjj the right route to the fact that he is in
be starting box then he gets to goal-box a and if he is
in the starting box then if he:responos by taking the left

route to tae fact teat he is in the starting box, then he

gets to goal-box b and when he is in the starting box and

170

takes t1e right route then is does not <et to goal-box b
and when he is in the starting box and takes the left
route then he does not get to goal-box a and during the
first n trials x is put in tte startinj box and 7 isn’t
and x’s demand that he alleviate his hunéer is equal to
y’s that y alleviate his nun er which is equal to t which
in turn is equal to 0 and foal-box a contains food and
goal-box b contains water and x has been taught taking
the right alley leads to satisfyinr his curiosity and
during the trials h+l to n+2 goal-box a contains food

and goal-box b contains water but iron trial h+2 to k
both x and y are put in the starting box and their crive
for alleviating hunger is greater than r which is greater
than 0 and if a contains food and x gets to a then x

‘I

alleviates his hun;cr and the same for v, tsen on the kth

I}

' 3

trial x’s expectation that il be (x) is in the starting

box then if he tat s the right route, he alleviates his
hunger, is greater than y’s that if he (y) is in the

starting box then if he takes the right route, he alle-

viates his hunger.

52. I shall make only one coxrent here concerniné the
proof of the above theorem. The elements Which were intro-

duced into TII. 2.10 so tlat Tll. 3.5 is the result are:
. .h , ,h+l+l
in (11), ’t = 0’, ’Ja’ and ’ b’; 1n (lh+l )’L8; in
k h
‘ ’ i )(z), ’J # L’.

1

(ih+l+l)’ ’Lb ; and finally in (

L .k, . L .
ill. 3.9.1 [(11,(z) [Q a m . e # D . J % L . e(zi, xzi) =

12>C). “21 D [(r(zi, e, 521)).0 . $21) 3 Bzi,a . (r(zi, w,
Ezi) >0 0 \LZi)

3
‘- 0h — - 1 ' --- _ 1 ~.- _
3 ~ bzi,a] . (11) [5x1 . ~Byi . 0(Xi, axi) — o(yi, Lyi) —
,h+2
t(r . ~ Ja . ~ LbotA(xi, oxi, xxi) )0] . (lh+l) [Ja . Pxi,a.
L i k aw ‘ .
o "fyi,a°~ Lb o "' {xi 0 "' Cyri] o (ih+2) [:Xi o Eyi o ”PXi,a .

Gzi,b] . (E'zi . $21) 3 ~Czi,b . (izi . $21)

1
~P¥1,a . d(Xi: iii-,1) = d(yi, 1N1) = S)? - Ja . " Lb - Pa

(Ja . Dxi,a) 3 hxi . (Ja . Dyi,a) D Fyi]] 3 [SC (T11. 2.10)]

..._ ——-_.

TII. 2.1C, *2.02, Simp, laut.

—1

.fi, .
5:".— :

 

TII. 3.5.1 represents a modified version of the Luxton—
beward free exploration type of latent learning. Given
the replacements for the variables listed in the discussion
of the preceding theorem with the addition of ’x is put

’

’Px.,a , this claim may be supported

. 2
in goal-box a for

unoer the approoriate interpretation for T11. 3.5.1.

k ,
111. 3.5.2 [(il)(z) [same as in T11. 3.5.1] . (11) [Ex

u
d
.
d
n
O
.
d
/\
H

~Eyi . d(xi, hxi) = d(yi, hyi)
d(xi, hxi) = d(yi, hyi)‘=fi>1‘o 33 . ' Lb . tA(Xi: ¢x1.J

)(Xi)>0] . (iiii) [Ja .

l
I?"
O"
O
H
a
N

d(xi, 1X1) = d(yi, 1:371) : s)r o d(Xi, HXi) = d(yi, Eyi) =
O . Ja . ~ Lb . (Ja . Dxi,a) D in . (Ja . Dyi,a) D hyi]]

3 [SC] (111. 2.10)] TII. 2.10, *2.02, RE, Simp and Taut.

TII. 3.5.2 represents the strono drive, irrelevant incent-
ive version of latent learning. heplacement of the vari-

ables by the values given in the discussion of the pre-

will]

I ' Ii' Ill-I‘d

cedina theorem 111. .5 rill confirm tnis claim.
5)

53. One final note: the latent learninj principle
should probably be much more general in character. I

have decided on this more specific handliny for two

reasons. :irst, the theorems represent fairly closely

to Show that the latent learnin» studies, as represented
by the various types of experimental desifin in contempo-
rary psycholoiy, are deoucible from folman’s system and,

hence, constitute a prediction from that system.

l72

u-r W sun .‘MIJA 1 am
a. -

173

CHAPTER V

 

 

 

LEE—FDLALCILIEPICN% Cu“ 31 {I Fthfiftfi71‘ SVTSTFT7
1. This final chapter has two main objectives. First,

there will be put forth some general remarks concerning

the system presented in this essay and some speculation on
wnat can be done in a future deveIOpment of Tolman’s system
in terms of the present symbolism. Secondly, there will

be a discussion of that in Tolman’s system which cannot be
formulated in terms of the present symbolism. here, again,
some speculation as to the future development of Tolman’s
system in terms of a different but perhaps more apprOpriate
symbolism will be set forth. In short, the first part deals

with the strong points of the present symbolism; the second,

with its weaknesses.
PART I
The "Core" System and the "Courtesy" §ystem

2. The system presented in T1 and T11 is what I shall
call the "core" system of purposive behaviorism. By

"core system", I mean the part of the "System" called

"Purposive Eehaviorism" which constitutes the fundamental
basis - the rock-bottom — of hat system. The "courtesy"
system is that part of "Purposive Eehaviorism" which con-
sists in certain statements which are merely repetitions,

using slightly different terminology, of statements in the

1m

core system and also in statements which can be abstracted

aw

(1‘)

y by definition from the core system. Clearly the determ-
ination of the core system is somewhat arbitrary; but not

completely so. lhe core system in this essay, that is, the

a}

system compri31ng TI and 111, is partly determined by wha

has been presumed to be fundamental in Tolman’s thought,

 

F“
by conditions of generality, and, of course, by certain 5
xternal considerations. Eor example, the present author f
talks about expectations because most psychologists talk E
4

about eXpectations rather than sign-gestalt expectations. E.

by

It should be clear that the system presented in this essay
is only a part of what has been called the core system.

To use a current psychological cliche, this enterprise

has been 'programmatic” --but, it is hoped, a little less

so than current examples (for ex_mple Tolman’s own recent

.5

Principles of Performance) of psychological theorizing

 

which are often, in part, justified by this term. For
example, the notion of expectation is dealt with only in

a very general ay in the present system. It has not con-
sidered its various particular manifestations, namely, per-
ceptual expectation, memory expectation, and inferential
expectation. It is assumed that however one construes
these concepts inside Tolman’s theory of learning, state-
ments about them will not falsify any of the laws of ex-
pectation in T1 and T11. Again, in T11, there are no laws
having to do with the frequency and recency of stimulation

presentation in relation to expectations and demand, and

175

so on. It should be understood that these laws were left
out because of time and space considerations and not bec-

ause they are not formulable in the present system.

3. The core system in this essay is largely concerned

with the two intervenin; variables of expectation and

 

p.

demand. It is the Opinion of the present author that from 2'
this core system it may be possible to abstract away that :
entire part of Tolman’s system having to do with sign— f
E
gestalt expectations, sisn-cbyects, Sign-Significate re- i
_ ' 4.

a v

a?

lations, etc. (which corprises about one-third of Purpos-

n
I.

ive iehaviorism). This supposition is based largely on

 

OJ

the discussion of the concepts of rea iness, expectation,

sign-gestalt-readiness, means-object, etc. in the Glossary

 

of Purposive Lehaviorism. For example, lolman defines

 

"sign-gestalt-readiness" as "the same as means-end-readi-
ness". Given this knowledge, plus the convention that
expectation and readiness are to be treated in the same
way in the present essay, then, in the languafe of TI,
we can define a sign-object as:

pSnx = Df [pilex . (3Q)(e(x, p 3 q) )0)],
that is, ’p is a sign—object of x’ means ’p is sensorily
received and some q is the end toward which x expects that
P leads’. He can define the signified—object as:

ad. __ --.e
qs x — Df(3p)[pn X . e(x, p 3 q)) 0],

that is, ’q is a signified-Object of x’ means ’some p is

sensorily received and is the means which x expects leads

176

in qfi Hmemadefinitions represent a fair trarslation
cfiohwn’snwaning oi sign-object, signif'ed object,

andsigigesmdt readiness. It will be noticed that in
themaexmqfles, the notion on the right hand si<e of the

f“

defhflifion Hie definiens) is a notion in the core system.)
Agann in Umaooinion of the present author, Tolman’s list
of.hfimrvemnn variables map be significantly reduced by

For ex-

rd ax ectation.

('3

'- dGflEHl

defin
ample, consider the notion of
"cathexis")vddch.is a nenber in the list of intervening

ition in terms of
" (or, later on,

variables ex licitly enunciated by Tolman in his 1937
presidential address before the American Psychological

 

but only implicitly enunciated in Purposive

Association,
Glossar: characterization of

 

‘ebaviorism. Consider the

rm

(1 .
0

CD

the term appetite. Tolman writ
An appetite arises out of a cyclically appear-

ing, metabolically conditioned, initiating physio-
And it con-

logixurl state, or excitement (q.v.).

sists in.a resultant demaid for a certain comple—
xnentalflf type of physiological quiescence (q.v.)
lilus 21 set of partly innate, partly acquired, more
or lfixss definite, means-end-readin sses (q.v.) as
to tree types of means-objects and goal-objects to
be Iifli conmerce-tith (q.v.) in order to reach this
deaf; typical appetites are hunger
and sex.

Iuied.quiescence.

.HOhrjlet; {XAifiJ’ mean ’X has an appetite for (or with res-
ccor ance uith the above quotation,

pect to) p’. lhenin.a

we can define
t r
)Qfl , ==33f(3p)(qox . e(x, p D q)) C)
’x expects (or

’2; kuas an.appetite for q’ means

4|";

‘1‘.

 

‘ -l:'

. .

177

mate a

-,.
\a’

mflrobjcct’. similarlj, we might define "aversion”
as fdflows. Let ’xnvq’ mean ’x has an aversion for q’.

lhen wenmq write:
V ._ “"1 "'.‘ .
xAcl— Uf(:p)((~q)tx . e(x, p 3 q))<3)
lanthenmne, it seems that concepts like "difierentiation",
I

'“dase§Y,"drive discrimination‘, etc. are capable of re-

k.’

ductflnlby definition in terms of demand and expectation.1

a. It is one of the virtues of the present symbolism
tnat it permits notions like "commerce—with" in its relat-
ions to thin;s to be abstracted out, by definition, from
the core system in ii. lne present system, therefore,
presents a special set of laws which include certain laws

pertaining to notions like ”commerce with" as abstractable
(and thus derivable) elements. For example, consider the
notion of confirmation. Let ’p’ mean ’X runs down alley A’.
now this proposition may be analyzed further in the follow-
in; way. Let ’E’ mean ’runs down alley A’. Then ’X runs
down alley A’ may be written as:
EX 0

This Imngnt be written in terns of confirmation as ’XC(EX)’;
’XC(r3c)’ is thus a substitution instance of ’XCp’. again,

inore gflnrerally, ’xCp’ might also be analyzed as ’xC(oX, y)

wherfa'fip’ is a.predicate variable and ’y’ is an arcument

 

1. {IO aiczertain extent, thi

s
alni immflSorquodale. Ci. Lode n ;'

 

 

i ". NJ «I;
' . r

.v"

 

Lib—‘1‘ I'd!" ‘
S

u‘.

'1;

"'1“

 

178

for example, (alley A).

altes,

0)
<1
’1‘)

i . ,.
11'} A R 8.

hence, 5$(e X,y)’ can be taken as a substitution instance
of ingfl; but, of course, tne converse does not hold. Ac—

cordhnflgg we might easily define "comLerce with" in terms

of Wxnuirmation". nor example, where ’CW’ means "commerce—

 

 

the above definition

with", we can write:
JN(X, y) = T143(9) . KC(QX, y). r!
*" I ii
that is, {x has cornerce-with y’ means ’There is a e such
that X has confirmed tlat x stands in the relation o to y’.

If one substitutes ’alle; A’ for ’y’,
reads x has commerce-with alley A’ means ’X has confirmed
something with respect to alley A’. the sane kind
7 u” this means,

ive i eas. a,

\

can be done for tne other prinit
it would be possible to deduce a great number of laws about
certain relations between oréanisms and thin s from El.

This discussion then demonstrates the greater power

generality of the core system in El.

5. Other interesting courtesy system concepts which

ndmfirt'be<iefined in terms of the ideas in ii are the notions
<15 satisfaction, frustration and conflictinfi expectations.

To sagric is frustrated is to say he has conflicting demands.

herune, mmaznight define frustration thusly. Let ’Xfirp’ mean

{x is inflistrated with respect to the state-of—affairs p’;

then we get the definition:
Xfiflfip = bf(31C) [d(x, n) = d(x, ~p) ==LI)C]
tnai:.is, {X is frustrated with respect to p’ means X demands
txdth.33 arxi ~p at the same strength which is above 0. Few

 

179

 

all 0 . o :1 o a a
let Um p’rman ’x 18 satislied with respect to p’.

xSAp = Elf ~xr‘rp
is satisfied with respect to p’means ’x is

y, conflicting expecta-

’x

that is,
frusmxfled with respect to p’. finall
tionszmhfifl>be defined thusly. Let ’xflp’ mean ’x has con-
Then

0.

flictnxgexpectations relative to p’.

K3? = ;,f[e(x, M) C‘ - e(x, ~p)) 0]

Ifdch memnsthat he expects both p and not p. These defin—

itions are interesting because they serve to make a connect-

ion - however small it may be - between iolman’s theory of
Their examination

learning and the a

would be interesting a;.

ihe examples of reduction and abstraction considered

r-C-.

6.
in paragra h 3 and h are to be found in the courtesy system.
S TIS —

ihey reduce to (or are abstracted away from) the core
of redundant statements

tem. ‘irhere remains only the
in the courtesy‘system. I will now provide examples of
this case. Consider wbat Tolman calls a "first-order drive".
Lalzxige 2d oi‘Purposive Eehaviorism, he writes:
lit is such demanded physiological states of quies—
oerxne and disturbance which constitute the final

gcan-objects which the rat, and all other animals,

arwz'to be conceived as persistinfi to or from.
a demand for an ulti-

CL

It is clear from this statement that
anite gran-object, for example, hunger—satiation, is a first-
cxrde1° ditive. Let ’xlp’ mean ’x has a first order drive for

linen ans may write the following definition:

13’.

xlp = Df pUx .

 

 

 

but<fleafib’the notion or first order drive is redundant.

(H‘CORSMXH‘the case of goal-object. Let ’pGx’ mean ’p is

a goal-object of x’, tren we may write:

- J
P3X " Df d(x: 9) r C'-
good example of redundancy.

4".

Iere again, we have 0.

”he courtesy system is not useless. Undoubtedly it

7.

Ins certain psychological a antages in the sense that it

3V5

perhaps conveys to the reader a more intuitive grasp of
Indeed, this is part

what the system as a whole is about.
of the reason why it is called a courtesy system. but from
a loaical point of View, it is unnecessary. This discussion

of the core system and the courtesy system of purposive

behaviorism indicates one of the main advantages of the

system presented in this essay, namely, that it is more
economical than the original system in Purposive Eehavior-

"a It is more economical in the sense that it attempts

to present only the indispensable, rock-bottom elements of

.purposive behaviorism. Surely progress toward this end has

 

C‘TT

2. fl concemit in the courted, system based on the ideas in
TII jJB "better goal-object". Let ’(e, w) (x, y)’mean
fin is 21 better goal-object for x than W is for y’.
Theni'we have the definition:

((P, \l’)(x: y) =7"-f(3x) [d(x, (PX, XX)>d(f], Wy: Xy)]

lhijazis, ’o is a better goal-object for x than w is for
y” Ineains ’there is a x such that X’s demand for ex as
a.rnearu3 to XX is greater than y’s demand for ex as a

From this definition, substituting X

the concept that ’m is a better

means to xx’.
x’. That is, we could get the

for y, we would obtain
goal-objectiflan\yfor

biconditional formula:
(<9, eh: E (3x)[d(x‘, CPX, XX)>d(X, tX, xxH.

 

 

181

lxmn mxieved to some degree. Te have thus a concrete

exmqfle dfone of the benefits which results from formal

 

ogxmdzation. Secondly, the system in.this essay is

shnfler1h1the sense that it involves fewer and less con-

fl

plex'findnitive" ideas than are found in the original

but let us not mis- r}

claimed that a

"systrfl'in Vurpcsive Eekaviorism.

understand this matteru 2ft is not beirnj

furfinn°reduction cannot be made in the list of primitive

ideas (by definitions) nor that the postulate set is not
Again, it is

 

1|.“ '3‘; ‘
Cs"
m

‘

susceptible of reduction to a smaller set.

a most alluring possibility that many of the postulates
in II may be deducible from the set found in Til. This
speculation is based on the fact that, except for a more

elaborate form, some of the postulates of TI are quite

similar to certain postulates in TII. (Of course, this
would mean abandonment of the prOpositional variable ’p’

’QX’

in TI in favor of the prOpositional function variable
because all of the postulates and theorems of TII are

couched in.terns of prepositional function variables.)

10 recaqxitulate, the economy and simplicity of the present

systmnn is to be seen only in comparison with the original

systeni:in Purposive Behaviorism. It was not the purpose

of iniis ewssay'to find the smallest postulate set or the
smallemytjpossible list of primitive ideas; that is, it

did Inst sitrive for logical economy and legical simplicity.

182

Furflmr Advantages of the Present system

b. nedfl.and nacCorquodale write:3

exmndnents which purport to be support for
fobuufis theory}. It does seem as if these
results might flow as consequences from "some

suct theory",...
Again,:hiconnection witn the preliminary discussion of
latent learning as offerin; support for Tolman’s View,
they writezur

....one could note tn actual "derivation"
of latent learninp from Tolman’s theory
here is simply not

9. The present system includes derivation of at least

some versions of latent learninf from Tolman’s heory.

Possibly, the critical comment nere will be that something
has been put into iolman}s system which was not there

originally'and which allows one to get, as theorems, certain
of latent learning. This objection is fostered by

the \nyiue use of the expression "the system” or "the theory".

(111 the aflmave quotations neehl and LacCorquodale are not at
all cfihear as tx>vtat they mean by "folman’s theory"). The

equwessicml "the system" may be used to refer to a certain
exgflLicitflqr stated set of statements -and no more. Eowever,
" bit more indefinite

it Iuay'enlso lae used in a way which is a

tuit (woes ruat lead to any inconsistency with the first use.

 

3. C33. cxit. , modern Theories of Learning, p. 196.

1+. Ibid., p. 195.

 

 

 

.Lq:
—_ .

 

 

U)
(D
C1-

Ulat is,it may refer to a certain exnlicitly stated

cfl‘stamnents plus any others wric3 Wight be added but

" nsistent.

U)
U)
Ft
9
Ho
6
O

which do not serve to>rmdu3 tne

lhegnwwent objection construes the expression "the sys-

tem":h1the first way. This is an unwise use. for it

prohibits tne jrowtn of a system.
nich can be

ly wonder whetger tiere is, in fact, anyttirf
{is first sense of the expression.

#14

called ”the system” in t
tainly true t;“t psycholorical theorists,

for, it is car
for eXample, hull, are constantly expandinj their theories

by the addition of new postulates. however, suppose that
tne first sense of the expression ”the system” has justi-

that even in this narrower

fication. I wish now to argue
sense of the expression, "the system" of Purposive lebav-
iorism permits the derivation of the latent learning theo-
rems found in TII. This would confirm, in the stronfest

,ossible wa", ueebl’s and pacCorquodale’s feelinf ttat the

variations of latent learning do "flow as consequences"

from Tolman3s theory -or, at least, from a close replica

of it.
lies in the

10. ‘Lne final :round for latent learnin:

ciiscussixni of transfer and docility found on pares 32 to

3a-<1f Elufiposivo tehaviorism.
"eloratory activity

A’Liy _._

himflater imms shown that general e of the
Iwrt occruns in cycles corresponding to the cpcles in tbe
coniawxytive activity And, furtner, if
‘tnerna be erttacned to the case a small
00513 iri'wnixna tnere is food, ne found tlat it is at the
lieigjit on? each.activity cycle trat tte rat passes into
thea.focxi—canye and eats, after wrich the animal returns
‘to ixae :Livdaig cage, cleans himself and then subsides .....

of the stomach.
rat’s main livini

 

J V
W

 

 

15h

n< give rise

10 quote:
t t’e small contractions

Thus we see tia tie
to we di11use activity in t;e large cage. lbs
and

mnmal seems at Iir 13 to be annoyed
tmnomes more and more restless as the contractions
gitw larger, until t1e ’main’ contractions set in
muitbe general discomfort becomes centralized in
tne1mn er sensation. Enis stimulus cominates the
ixxavicr of tne orfanisn and it enters the food-box
hben its avpetite has been satisfied, it
lasts until

st sign

to ea'. -.
gumsos into a perio cd 01 quiescence which
t1e stomach has beco:nc eupty and tne contractions
Have started up ajai1.
It apoears, in short, teat it is the Lunary, or satiation-
oema-Oin ,1et who is tne exploration- detandin“ rat. And
furtner it also apnears tbat a‘ t1e Teijrt of nun er, the
is speci11ca113 oire 'cted toward iood.

exnloratorin
now wisn to nake is that such explora-
relative to the actual finding
an an'nal’s exploratoriness
c*aracter,

The furtncr point we
toriness will prove docile
of food. We want to sycw tLCb
embodies a neans-end-readincss, 'udfnental in
to t1e e11tct tlat certain t Tes o1 ex;loration (exploratorv
object) are more likel3 to lead to 1ood tnan are others.
And, in fact, feneral evi_(enc e 01 t11is is to be seen, at
once, in certain general 1indin§s as regards Noze-uoajation.
quite as likely

.A "naive" rat, Laxni first run in a maze, is
to try to ousn 'ble crevices or to run upside

tnrougg iflQOSSl,
dow11cn1'U1e wire cover as 1e is to run in tne alleys prooer.
A "maze-wise" rat on the

-s become ready for

otn er rand, be
general t3pes of

9
alle3-ex lo ations onlf, i.e., 1cr those
eziploration wnicn 1e ras actually found tend to lead to
food.
Cr ageiji it is to be observed t at 11 a rat is s learned in
Maze alwa3s to ta e, a3, a rian t-turn to a

a given simple1_.

T, Emaxaill tend.to prefer such a rignt- tt rn wnen transferred

tx>za second maze which presents anotner 1' under somewbat,

knit b3 rm>11ean1s exactl3 , siflilar conditions to those of the

fiITHSIHaZG. A. rat will ”abstract” the goodness of rijht-

turn11r_j;from.lis first maze. This nas recentl3 been demon-
no

straixai speciiic all3 and very prettily b3 Genqerelli, w.
aroun of rats w'o most clearly carried over

reports tnat tnekJ _
the 'Rgenerugli cd habit”, or what we are calling the neens-
end-qreadilness, from the one situation to the other were not
actirr: in arnrrwilex ‘asnion. 2e describes one of the most
strsjjln czases of such "transfer" as follovs:

1113 rats by this time did not run the maze as if

itLIdePe a stereot3ped habit. The continual cnang-
to day rad caused

ira; oi’rmze patterns from day
tfi1er1 to adOpt a more circumspect poise in their
LrUIuiingg £3 tnis tire there was very little, if
argf, burpin; of noses at bifurcations and elbows.
itie anainals d become more exploratory in their
:ruruiingjattitude. ibe; invariably slowed up or
t'18 t 1 0101 8d

peniseolas they aporoacned an3tb1n3

Lfle a turn in the Laze.

Eductically all of the animals, therefore, approa ched
'He bifurcation in the naze pattern used in th is ex-

and deliterately. There was, acc ord-
at the cross-roads, and a

pmriment slowly
to side before the

infly, some hesitation
:_re£t deal 01 loogin; Lrom side
choi.ce was made.
And getixeyc carried the right (or the left) turnin —readi-
rwss owasirom the previous training.

oroins to us all so-called

d be evidence of tne formation
eumicarryin; over o1 specific (judgmental) neans-end-readi-
nesses. inus Vincent’s demonsrrcticn, of the formation and
transfer of the choice of white alle 3 rather than black
from.discrininaticn to" to "white-black" maze and vice versa
would similarlv be d‘GZ‘ ens tration of an acquired and truly
docile to the effect that white alleys

are better tea n ela “Uleadin: on to food.

Indeed it is obvious that ace
"transfer" e31periznents woul

1hat has been said here mi;ht be summed up, in part,

ll.
expectation acquired under

in the iollcwin; statement; any
7ole in

one se et oi ClPCUIWSt ances or drive is potentially usac
another set of circurstances or drive (even thoueh this
latter set of circuwstarces may involve diss ir1ilar con-
ditions) provided t1:at t1e learner is oocile. This state-
the well-known lolmanian

ment taken in conjunction with

View (51}1roviso emphasized again er:d 0{gain in Purposive
Zmfiuiviorism) that an.expectation,may be acquired in the
absencezcxf reinforcement- a condition which is implicit

ill the Ixostulate set in this essay- constitutes the
thecuwatical,tesis Lor the latent learning principle.
”hese cumnditions are summed up in postulate ill. 2.10.

11u3 orflgy;problem, so far as the present aithor was

concerned, was to construct a sym-

bolic t

have to

12.

expression

strue '

system"
a class

creases still does ruit

'tMBsgsten

ItnMLtion Cf
invent 111.11:

Let us return to t-.-e question of the use of tie
1 us con-

"the sdvstem” (or' 't1;e t1eor1’"). Let
W" in t1e wider se1se. lhis Use of "the

is analogous to constrain; ”t :e corporati on" as
of individuals whose membership thougn it in-

change tne weaning of the "the

lnere are food reasons for this

corporation".
H H

'"er twe possibility

her exanple, cons1os

ples or laws from

a personal COuLUhiCQ

tie present system in

1io11, Profess
Actually, however, in n, l have
merely used up words as s rin boards for covert
phenomenologizing which led we to believe that
such and such further er periments would be inter—
esting. And I gave a suspicion that no new ex-
periments can really be derived Iron my system
in a icimal wav t1at are not already inplied in
the initial deiinitions.
I tend now to believe t1" at the i’utu ure of
psychology ies in t1e lindin; of inde 3e11dcnt
euncirical facts (probablv physiolo: cal) whicq
wild- then lead to new inollcet ons. I do not
beJLieve in.short that my s;stem is a system in
the> true logical sense from which anytiin: verv
an be derived.

m" own thinking,

nevz<or interesting

 

5.

tLat the latent learn—

Time prwesent author does not cLanu
' corollaries, as pre-

irm:
sented inifll,a
Iiot; be>.false. lhess are matters for the experimerter

'to

t 11 6
bgf
11151
0343
1212
lkol.

Iqrienciple, TII. 2.10, and its

are bevond criticism; nor that ttev may
__.L._.___ .

okecixie - not the logician It is claimed onl' that

\ncrusions of latent leernin: which are formul;.ble
rhea me; 01 t1e present symbolism can be put in post-
te— tineor- cm orcier in iolman’ s svstem, that is, it is
:inued. that the versions of latent lc‘ arnino as catego-
eci 133"I11stlet1waite are deducible as theorems in
man ’ 8 sys tem.

 

Friar. . -.~

187

13. inst, -rofessor lolman’s use of the expression
mesyshmfl is aubiguous in tne way in which this partic-
ularckninite description tas been snown to be ambiguous
above. let us consider lis comment in relation to the
Innibwerxflew of the expression ”my system”.

la. Concerning tne "suspicion that no new experiments

can.really be derived from, [iolnan’s sgstem] in a formal

way that are not already implied in the initial definit-

ions", the following point can be mace. Tolman is correct

- in a certain sense. Logicslly speaking, one cannot

derive ”experimental" conclusions which are not implied
by the definitions an? the postulates. but notice this
” these implications are known -

does not mean that al Oi

nor that they have yet

been teased out of the system.
nenoe, there is a very good chance that there are "new"
experimental conclusions to be derived from Tolman’s

system. but now let us assume tLat Iolman’s system —
has exhausted all of

I -
I.

say, as it s ands up until l1flfl
its irqilioations for new laws. There is, nevertheless,
ancflflier vnfiy in which new laws may be discovered. The

systxxn caui be extended by the addition of new postulates,
y of inde-

‘40

m

"find n

1’.

it”? eXBBHXLe, those resulting from the

.permkmat ergxirical facts (probably phJSiOlOQlCfil)" and so

armi newv experimental conclusions can thus be deduced.

on,
Arui, ill facyt, iolman does this very thing in his paper in

1‘"e Principles

1.: .,

 

 

'tae ffisyckuilOSical neview, Vol. 62, NO. 5 - 1

oi‘jPeILformnance. On page 319, using almost the same termin-

 

188

ology as a pre—1955 Tolmanite with the addition of the no-
tion of "performance vector”, iolman writes:
The greater tne valence of the expected food, the
greater tee food need—push, and tre Preater the
expectancy tnat tge food will result, the freater
the magnitude of tne performance vector toward
actually pressing the lever.
in effect, tnis is a new postulate. That is, in the Opinion
of the present author, it is independent of the other post-
ulates in El and TII - becaLs of tne idea or ”performance

vector". In other words, neither it nor its nefate is

deducible from tge postulates of TI and TII. And certain-

system have yet to be discovered. hence the possibility
of new laws and also new experimental issues. This behav-
ior is appropriate to the wider use of the expression

/

"the system".0 Indeed, it seems to betray the fact that
TOlman.Limself implicitly construes the term "my system"

in the wider sense. If this is true, then the second
sentence in the cited coywunication above, is a bit mis-
leading. it is on such grounds as these that the present
writer defends the wider use of tLe term "tne system",

that is, the use which permits one to construe "the system"
as embodying a consistent set of postulates, staed and un—

stated, but nich employ the terms expectation, demand,

 

{r

b. The use of the term "the system" in .his wider sense
does have pitfalls. For exmnple, ima_ine two peeple
to supplement a shared set of postulates with one
postulate each, but that their supplements are mutu—
ally inconsistent. thich person has "the system”?

\-.

and so on, in a manner consonant with Iolman’s own use.
System building is a dynamic process. The system of
Newtonian physics as taught in contemporary textbooks

is not merely the physics of Isaac iewton.

 

 

.T‘,’ TL“ \ 3‘ “ T‘ “ I' CT-1"“‘AT
15, Se conclude the Lirst part of this final chapter

by suggesting certain ways in which the present system
(in tne narrow sense of tse expression "the system") may
beéaxtended. lhe concern here is to show what is poss-
ible in this line within the context of the adepted mode
of symbolism. (The present suggestions are more con-
cerned with TII than with TI. Previous considerations
in this chapter were largely concerned with TI.) The
first problem to be dealt with concerns the use of the
time arg tent i in the formulae of TII. here the con-
cern is with an elaboration of the present symbolism as

a wav of extending the system.

‘ o 1 ‘ o 01’ o k
10. Gons1eer the series (if) . . . (1r+1) where l

designates the first number of the series and k the end

of the series. In accordance with the conventions adopt-
ed in III, the above series indicates a series of trials.
’h’ and ’k’ are variables. ihej designate respectively a
point in the series (i?) and the end of that series. lhe
length of the series is undetermined. hence, if the series

is 20 trials long, k = 20. but even then, we do not know

what value h is; lb trials, the let trial, and so on.

1.

 

 

 

190

Again, h+l only indicates the first trial after h xd1atever
h may be. fhe pr sent symbolism does not say what a trial

8; that is, whether a trial is 16 minutes long or 15

P0

minutes long; 2 days or 3 days long, and so on. Shis latter
problem is more empirical than logical since it involves a
problem of neasurexent. Ebat is, it involves a question of

assigning numbers to certain predetermined units of time
called tria s. Again, a given tria lr mags, (in terms of
time) be longer or shcrter tpan another — especially where

a trial is determined by conplet ion of a certain activity.

iresent symbolism does not reflect differences

I
.L

k)

hence, the

in trial times and ther~bv fail to disti41’:uish between

(I

C"

0)

longer and shorter trials.

17. dome of the above postulates and theorems in TII
might be false because, in the cont e Kt of the present

rough dating apparatus, we may be able to infer certain
false theorems. Eor exem;le, supnose the difference in
effort between two actions is very slinht. Cne would ex-
pect that in certain circumstances, more than one "trial"
of training would be required to enable the learner to
build up an expectation of such differences. The postul-
ate TII. 2.h does not allow for such circumstances. In
terms of the present handling of time, it would be possible
to deduce from that postulate that the learner in one trial
could have built up the ap prOJriate‘exeect tions necessary
to distinguish between tne effortfulness of the two activ-

:ities. This seems quite unlikely. hence, it is important

n , ~ ,- :3! M: a 2 o- r
to such Wnat n anc k are in an.

U

rial series. but

('1'

again, these are matters which are more empirical than

logical.

18. Ebe handlinr or the time series in this essay does

(~—
"5
H.
(D
H

not allow for tre beginnin; or the ending of a given

 

(assuming that tris is car unit of measure, that is, each
positive whole nunber desifnates one trial). And, of
course, tnis is a very importan' problem. to illustrate,
consider the case of sudden inprovement after substitut-
ion of a ”better” Heal object. Cur units are aaain trials
(nowever tnese may be determined). bun-ose tiat iolnan
claims, in a given situation, that improvement is sudden
when it begins to appear exactly 2 trials after substi-
tution, tnat is, say, after h+l. the present symbolism

cannot record this fact: Improvement will "becin to

 

annear exactl; 2 trials after substitution". All the pre-
sent symbolism records is that improvement occurs, in this
case, at n+3. It does not record possible increasing im—
provement over a certain span of time, say from h+l to n+6;
it does not tell us whether n+3 is the beginniné, middle,
or end of tie trial or series Ci trials in which improve-
ment occurs. This problem is nore a logical problem than
a problem or measurement. A more detailed handling of the
time series could eliminate this problem within the con-
text of the present symbolism. This, of course, raises
the question c: over—laggin; time series. These matters

Imight be dealt witn after tie tecnnique of J. b. poodacr

192

I

in his monograph on tne ’iecnnique Cl theory Sonstruction”

in ”Rne International Tncyclopedia of tnified Science"

series.

19. Lowever, the KCSt serious difiioulty, with the

(0

present symbolism is it ’nabilit; to deal with cnanfies

happening witnin the course of a trial, or a riven series
oi“tri£fils. .Jor' exariple, :it :.ipi:t 1x3 i;gH3r gait tn) krmnq

tnat a rat turned :is been left ano right in the course

of

to

trial, for example, as in the VLE experiments of
inienziirper. zagairi, ii,; i in; be i;qn3rt£11t tc>1xnov1iiow

eat an animal moved to a so=cific part of a maze at a

‘

H

specific time in a Liven trial, or in a eiven series of
trials, to know whether tbe experixenter, say, puts in
(or takes out) hurdles, mirrors, or tLe like durinfi a

fiven trial or a jiv-

\—

3

i series of trials, and so on.

I’

inese circumstances cannot be recorded in the present

(D

symbolism for tne simpl reason that there is no pay of

Ho
Ho
3

expressing the situat o* "at snob and such a time, in or

k
)—

durinq trial k so and so happened". wowever, there is no
reason why the present symbolism cannot be extended so

that situations of the sort just described can be expressed.

p.)
c— L-
O
O J
O
(4
(a
}— o
(‘1

1 we re 1'3! t}; e

#-

summing up, those problems bav
logical cnaracter of time series night be handled, within
tne contegt of the present symbolism, by a more detailed

account of time. It is not being srfgested tiat the pro-

blems jrst cited in relation to the Hatter of time S‘ries

(1‘

are tne only ones. out tneb are representative and are

193

the Linc oi problems which most inrsdiately cone to mind
when one examines tne present system. hence, it is con-

cluded that a more detailed analySis of time will result

in

31')

certain sense, in an extenSion of the present sTstem;

a will ”correct” the present

Ft:
0
E
.2:
,C
H
9‘)
(D
9)
F.
i -’
.0:
m
O
O
(D
J
(”+-
m
[.40
H4
, J
H-
L \

anlicit assumptions explicit.

20. It will be renenbered that toe convention was

the con-

Ho
:3
6
F1
F_
v
s
a
(‘7'
3:9
l.._.|
H
d
a
|,__J
CD
5-:
0)
.J
‘J
<
O
H
<:
H o
D

adopted (

cent of least effort assumed tLat the conditions of

-

4

valence and efficiency were held constant. Clearli

D

-.

1..

another war o1 extending the present system (within the
context of tne iresent symbolism) is to oevelOp certain

laws about tne interrelations between effort, efficiency
and valence. 1e speculate nere only on a possible relation-

J

ship between effort and efficien 3-

21. Tolman is very cautious in fur osive Behaviorism
about assimilatinj ef“iciency to effort as has been done
by certain psycnolo;ists. I think his caution is well
founded, Fecause there is an essential differerce between
icien 3. ins latter can only be determined
in relation to a given end or goal; determination of the
former requires no snob restriction. Let me illustrate.
Consider a maze with two alleys one longer and more cir-
cuitous than the other. She lonfer we shall call "L";

the snorter ’d’. fl is a straight alley to a goal box.

goth alleys lead to the same goal-box. Kow it seems

19M

plausible to say that runnin; down L involves more effort
than runnin_ down B because runnin; down L requires a
greater expenditure of energy. Low consider the case
where animals are put in such a naze and wove about under
the impulsion of curiosity. It seems plausible to claim

that tne longer alley, L, is nore efficient as a means

L/

(D

to satisfyin; curiosity, tlat is, curiosity seti

J“.
_tion,

 

tnan is d. tut suppose we consider L and H in relation

:1
to tne lunyer drive. Inen tee shorter alley R is more ‘
efficient tLan L as a ncans to nun er alleviation. [nus r

we see that in one case tye more effortful alley L is
more efficient tian the less effortful alley A, but, in
the other case Davin? to do with hunger, the more effort-

ful alley L is less efficient than the less effortful

Ct

22. Assuminj that no distinction between effort and

efficiency is legitimate, we are in a position to lay

DJ
9
f;
P
O

ertain laws concerninf their interrelations.
Tolman seems to su fest in Eurgosive febavicrism,
given tne two conditions of efficiency and effort (other
conditions being equal) efficiency is dominant. As a
result we may lay down the law that of any two actions
ex and WK where ex is more effortful than ex but ex is
more efficient than ex, as a means to satisfying a given
drive, tnen the organism will respond more frequently by
w than he will by e. Indeed, we might tentatively pro-

pose the following postulate (which Las the form of an

19S

oxerational definition) for efiiciencv. Let ’Efi)’ mean

.k _
XXi - ~F Xi: $11, xxi)] 3 [(11)(wxi Va) exl, xxi) :

iiis preposition reads: durin: each of k trials if x
demands that x and E and e are availUI ale to x as means
to X and * and e are available to x as means to X and

i is false t} t x.is fixated on ex s a_neans to vx,

pa

 

 

tnen throughout each of k trials ex is more efficient

than ex as a means to yx if ans only if on the kth trial

X's tendency to respond by W to fix is greater than his
tendency to respond by e to Ex. fine italicized part in

the above translation emphas1zss that efficiency is only

Opel ative wnen tile ani1al is net fixated on the poorer

or wiat proves to be the less efficient action. for, as

fixation is defined, in chapter II of this essay here is
a rigid condition in the organism’s behavior in the sense
that there is no confirmation of possible alternatives;

--which amounts to sagdiny must there are no alternatives,

better or poorer, for the fixated animal.

23. The relationship between efficiency and effort dis-

cussed at the beginning of the last parafraph crn be de-

(‘0

duced ea silyr from the above postulate. fence we get the
follo owing preposition:

.k . i l
(11) [d(Xi, XX1)>O . (exi . (P311) 3 XXi . (bxi . wxi) 3 XXi -

”3(Xi, (9X1: XXII) . 901x11 .3.‘.> Q'Xi . wxi 7) (pxi, xxi] D

r(xk, v, 1?X1—:)>1‘(‘Jk: (P: Wk)

2;. Hith respect to the above described situation in-
volving alley L and alley n we might try to speculate on
the implications of tne concept of efficiency for latent
learning. The supposition above is that when the organism up

is shifted from the exploration drive to the hunger drive

('t

there is a corresponding snift in efficiency fac or, that
is, the formerly less efficient alley R as a means to

alleviation of curiosity becomes the rore efficient alley

 

ll'?-'-O' ..

under the hunfer drive. Te might use this hint in the
confirmation of latent learning. ior example, the latent
learninf principle claims that during the exploration
period the organism is allowed to build up "knowledge"

of the various routes to the foal—box. Then when the

food drive is introduced we should expect, in the above
situation, provided the organism is docile, that the
organism, in accordance with the shift in efficiency to
alley R, will pick that alley h more frequently than he
would alley L. So far we have not differed too much from
the customary experimental latent learning situation. But
now suppose we block, at some point in alley R, the organ-
ism from going to food. then it would follow from the
avoidance principles in TI and the efficiency hypothesis
presented above, that the organism would immediately stOp

runninfi down alley H and pick the now more efficient alley

L (which also is now the less effortful) as a reans to

 

197

7

food. And thus we have an exagple of row the present
system rat bee;xtended in tfis latter sense. Jinally,
it might be noted tkat, in tge same vein, Tolman’s re-

marks on avoidance in his recent Lne Principles

C
6
n-I.
(D
.1

c .' - .,., n "I“: ,,‘r_‘ ‘1. ‘\ _‘ A - r 3-, V‘. V " .
OJ. reI‘fCI‘ua-DCG saint we heed LC (Jo-1811:8563 111 tile ex-

tersion of tLe present sistem.

 

 

Inadeqpacies ‘f tue “resent sgnbolisn
25. ibis section has to do witn tne weaknesses of the

present symbolism. it is cirected to tne question of wnat

cannot be expressed in Lye context of the present symbol-

(W

aparaisal cencerns itself with the

.L

‘m. in general, tre

H.
U‘

notion of naterial or trutn-functional implication which

(I)

rmbol ’3’ in tLis system. the main

L

is expressed by tne
point to be mace is this: trovgh the lofic of material

implication —whien philosophers call an extensional logic-

 

is sufficient to exoress a great deal of what Tolman says
in nis system, it is too weak a relation to capture the
full meaning of certain concepts. For exam lo it is too

on to capture the full meanin: of means-end-

["10

week a relat

expectation.

 

7. It is important to note that in tee usual sixple T
maze type of apparatus used in the studies of latent
learninfi, due to equalized training procedures, no
errort factor is built up.

198

25, We have had a prelude to tLeso oiiriculties in tie
preceding pabes or this essay. Eie two nost era atic

cases were, respectively, (1) t_e dogonstration of tke

failure of tne grincipfa law

 

ween placed witiin tne context of tre pronositional atti-

(T)
A
r»:
‘0
A
O
U
"S
(7
III
CD
a
‘0
d
U
..Q
U
"S
v
v
C)

does not hold; (2) tie demonstration tEat t1e relation-
ship between ex and ’qx is Jeans-ent availability was
too weak. :ne iirst case iailed, tlat is

e(x, (p . q) 3 r)>C' :— e(;~:, p : (q 3 r)‘)>0
failed, because t;G trutn ”tnctional ”if, tnen" does not

capture a certain consecutivit; factor in the conception

means-end expectation. in ca

09
(D

of means—end availability,

q

we found tnat ex is a means to gx was better cescr'

r-SJ

.ed as
’Ihe nakin; true Oi @K is sufificient to bring about the

realizability of px’ rather tnan as merely ’If ex 18 true

CO

7 o , -_ 1' ,, J- o a ‘ -: ’0 n p o .
tnen so is ax , tnat l , as M8P813 a trutn lunctional "it,

then" relationship between (x and wx.

27. ihe ensuing discussion is limited to tte failures
of the naterial ”if, then” and the remedy thereof in the
case of expectation. heference will be made to the case
of means-end availability as a m‘ans of c woerison in
certain instances. Te begin witn a discussion of the

terms to tie relation ’3’ witnin the context of the pro—

positional attitude of expectation.

199

20. Consieer tale 1781‘€~.dig13:

(‘3

A

r

l-’°
I

Tnis ma; be read: tre strengtn of x s expectation (re.

'3

less, anticipation, belief, knowledre) that if p then L
is greater than C. sunaosetqe sntstitute ’x runs down
:- '1 a- 3 n 1 bx” ,“ ’ a \ P +_ -2 j ’ 4) ‘ 3 ’ , 733‘ l
alley L 101 p and A eats ioou lQl q . inen ( )
reads: x expects tnat if Le runs down alley L is true
then ’ne eats itxxl’ is true. inis e:xmnfih3 suggests a

ratLer strained interpretation of reans—end expectation.

Lhen an organism expects a certain state of affairs as a

r— G
(I)

§e§n§_to ano'ner state-of-affairs, LC not, in every

case, expecting that if the first state of affairs is true
then the second is also true. “at er he expects that if a
state of affairs ’p’ is true then it is possible that ’0’.

Eor example, as I sit at m1 desk I expect tpat if I walk

to the door, tnen i can open it.

 

Con

[\D
\O
0

C0

ider tne following postulate which is in T1:
(2) (xCp . e(x, p 3 q))C) 3 e(x, q))O

(2) says that (with appronriate substitutions), if X has

confi med tnat X runs down the alley L and Le expects

.1

tnat if he runs down alley L then re can get to food,

 

then he expects that ne can get to food. totice here
that tne word can makes all the difference. It is a

translation of the ”it is possible” used a few sentences

back.

3C. ine tse of tee expression ”it is possible" in the

precedin; oiscu sion is perhaps unfortunate. :0 tbs logic-

[0

ian it nas a diiierent meaniLf tgan the neanint ascribed

to it in tre precedinj paragraph. "It is possible" means
sinle "it is not incompatible (or it is not inconsistent)"
in contemporary lo;ic. In its formal employment it is

associated witn trose lchicial systems wiich are called

L:
O
C\
CD
H

I

I
C."
D'
(a
U)
C
5
(9-
Ho

was ”intensional”. after v. I. Lewis,
it is usually represented ; t' e diamond ’0’. In the

\v

ble",

H'

above discussion, we d

O

\ 1.- H- .0. --
not mean oj it is poss

 

it is not inconsistent (or irconnatible)". gather by
’x expects that if p teen it is possibks that q’, what

is meant is tnat X expects tLat if p then be can (or is

C'f

able to) 1.1ake q true, or to put it another way, the X
expects tLat if p is true tnen Le can (or is able to)
realize (or actualize) q --to use Carnap’s phras . In

short, formula (1) can be read: X expects tLat if p 18

realized tnen q can as realized, tnat is, is realizable.é

 

o. It may seem arbitrary to delimit ’p’in ’e(X, p 3 q))bO’
to being a realized predicate. for example, this ex-
: X

pression night witn equal justification be read
expects that if he is able to (or can) realize p then
he is able to (or can) realize q. however, it will be
renembered, that in the response postulate CI. 2.6 the
expression ’phex’ occurred. since tne only values

of p are realized states-of-affairs, it was accepted
as a tacit substitution rule in this system that the
values of tne first member in a means-end expectation
are realized states-of-affairs. Indeed, this comports
with our ordinary notion of ”stimulus situation” as an
actual state-of-affairs (of. footnote 5 on page 13h

of this essay).

201

31. iLe groblem or realizable states—of-affairs, that
is, or states-of-affairs which can be made true, as values
of tne prepositional variables also carries over to pro-
positiozal functitns. ire postulate El. 2.6 -tne response
postulate- is expressed part1, in terms of propositional
functions. lt will be ren3nbered ttat tbere was adOpted
tacitly a substitution rule to the effect twat the only
values wricn tne predicate ’ox’ (in the part of that post—
ulate which read ’e(x, p 3 (ex 3 q))) 0’. could take were

1

realizable predicates. ibis re-examinaticn requires that

we give a more Lull analysis of exnectation than has been
Liven. {or example, let ’K(z, o)’ wean ’2 can make o true
(or z is able to do o)’. Ihen, in terms of the above

ert ’X(Z, o) in formula (1) thus:

{17

appraisal, we might in
(3) e(x, p 3 Hz, <0))>C,

that is, x’s expectation that if p then 2 is able to do a

let ’o be ’x brinfs

is greater than C. To illustrate:

apples to z’ and ’o’ be make an apple pie’. Eben (3)

reads: x expects tgat if he brings apples to 2 then 2
can make an apple pie. Again by substituting ’x’ for

’z’ in (3) we get tne typical expectation situation as
viewed from the experimenter’s position. Let ’p’ be

’the wnite card is present before x’ and o ’junps to be
white card’.

then (3), with ubstitutions, reads: x

expects tnat if the wnite card is present before him then

9

he can jump to the white card.

 

9. Cu these same matters see also paradrapbs lb-2l in the

discussion of means-end-availabilit“ in chapter 2U! of

\.
Q)
l ‘ O
u > 0“"
C7.r.|.1LS 6330.”.

 

2C2
32. having oealt wit: the terms to tie relation ’3’
witnin the context of expectation, we may new direct
our attention to the relation itself. mne translations
of (l), (2) and (3) have all been put in tne indicative
form. Bowever, these translations are a bit misleading
in tne sense trat tne, do not capture a certain con-
dition of necessity obtaining between ’p’ and ’q’ (or 3‘?
between ’p’ and ’h(z, o)’). Leans-end expectations are :
often expressive of a more ngpotnetical or provisional y
character in tbe meanin, of ”is a means to”. Let us i J
consider tne interplad of neans-end-relationsbips in the '
rat who "debates" witn timseli at the choice point in a
maze. ine experimental phenomena wnicn are the basis of
this account are the so-called Vicarious Trial-and-Error
phenomena discovered by fluenzinger and the "hypothesis"
phenomena discovered b5 Lrech(evsky). sqain, support
may be found in Iolman’s account of inferential expecta-

tions (Gf., pages 97 and lbO-lul of Purposive hehaviorism).

 

[his condition of necessity is much better expressed in
the subjunctive ratner tgan in the indicative. inat is,
wnen we say that an organism expects that something is

a means to sometnin; else we might better translate this
in tbe lollowin; way: x expects that if he wer§_to run
down alley L, tnen he would be able to get to food. Thus

' with

wnat was meant by saying that the rat was "debating'
himself at the choice point is simply that tne rat is en-
aaging in an expectation of this provisional sort. The

L.«

203

1 O ‘I

point is that subjunctive cono tionals (such as that whicn
comes arter the word "expects" in tre rephrased account of
expectation above) are n£t_truth functional.lo Indeed, it
has been suppested trat trere is a certain necessity fac-
tor involved in subjunctive conditionals which prohibits
that conditional from being truth functional. This nec-
essity factor is not the necessity which contrasts with

1

possioility in tre logical sense of possibility discussed

above. what i

(I)

intended here might better be called
"natural necessity". As a result, we might aiain re-
phrase our notion of expectation; x expects that p natur-
ally necessitates q (or p naturally necessitates K(Z, ¢)).
Take our "apple pie" translation above. That situation
is now rephrased as x expects that x’s bringing home
apples naturally necessitates that 2 can make an apple
pie. That is, ’x’s br'nging home apples’ contributes

to his wife’s being able to make an apple pie. This is
just another meaning of "if, then". Quite generally,

the revised version of expectation might read: x expects
that p naturally necessitates the realizability of q.

the remainder of this essay is concerned with a discus ion

U)

of the concept of natu‘al necessity and its relationship

to expectation.

 

1C. Quine, K. V., gethods f LOCic felt, 1950, pp. l2-18.

——- ——*——-, l

20h

ihe leture of Latural becessit:

 

 

33. S nsider tne prepositions

\

(a) e(x, (p . q) D r))O E e(x, p 3 (q 3 r))>O
and

(5) e(X, ~p 3 (p D q)))C‘.
(a) and (S) are sometimes false. (u) is sometimes false
because it does not capture a certain consecutivity char—
acteristic of means-end expectation. out it is also false
because it overlooks a certain stronger View of the con-

, ’

junction p . q in the antecedent of (A) than is pre-
sented by the ordinary truth functional conjunction

’p . q’. ror example, substitute ’x lifts his paw’ for
’p’, ’x lean a“ainst the lever’ for ’q’ and ’x nets a
food pellet’ for ’r’. Lnder tlese substitutions, the
antecedent of (4) reads: x expects that when he lifts
his paw apg_lean‘ against tlc lever then ie fots to food.
Suppose that the experiment is so I’l'fCSd twat tie animal
must do botr actions in a certain consecutive manner

before he does get tne pellet of food. Under these con-

ditions, the consequent of (a) under the above substitu-

tions could be false. that is "x expects that when ’he

, o

lifts his paw is true then it 18 also true that ’x leans

against the bar’ implies that ’x gets food’ is true”,

could be false. ihe point is this: X’s expectation of

the conjunction of ’p’ and ’q’ implyiny ’r’ is an expecta-

’ 3

tion that the conjunction of p and ’q’contributes to

the bringin: about of ’r’ - ’r’ is the result of the con-

205

junction of ’p’ and ’q’. Indeed, it me: be put more strongly;

(J

9 1 3

x expects that the world seinj what it is, ’p and q are suf-

ficient to the brinping about of ’r’. The consequent of (b),
so interpreted, fails precisely at this point. For it allows

(1) that ’p’ i sufficient to bring about the conditional

(Q

’q D r’ - which could be false - and (2) granting ’p’ is suf-
ficient to bring about ’q 3 r’, that ’q’ is sufficient to bring ; a

about ’r’ - wnicn seeps higth duoious in relation to X’s ex-

pectation that it is the conjunction of ’p’ and ’q’, and not

 

either alone, which is sufficient to the bringing about of ’r’. J

 

erhfi.“ - -

This characteristic of means-end eXpectations will be called

the "efficacity" cneracteristic of expectation.

3h. It is interesting to note that the same kind of relation
obtains in the idea of means-end availability. :his was recog-
nized when we rewrote this relation as ’phq’ which means ’the
world being what it is, the occurrence p is sufficient to bring
a ., 9 ll ~~ . - -- n
about tne occurrence of q . Our argument in the case 01
means—end availability proceeds as follows: ’finen we affirm
that certain states of affairs are available as means to
others, are we merely saying that when a given state-of-
affairs is true so is another given state-of-affairs?’
The answer must be no. We are reluctant to claim that
something is available as a neans to something else unless
we have perceived that in the past (or realize that in
the present) a given state—of-affairs - (perhaps, most

C

commoan, an action) leads to or contributes to the brine-

V
U \.

 

11. Of. Chapter IV, paragraph 20.

2C6

ing about or an end. for exanole, tne lollowinfi two pro—

Lambert scratcned his ankle

‘0
O
U)
*— o
(‘t
H.
O
D
If:
f‘fi
*-
(n
C
0
(Hf.
,_
c1
*3
(D
u o

wit; his left hand at 9:1; on Lngugt ll, 1956, and LaKCert

iinisnea writinc a sente rxce witn his right haxid a t9: 15
on AuLLCU t l! leo. the first preposition normally would

not Ce consicel ed as tne kind of proposition which was

available as a means to the second. the point is this:

9' “Hf;
r.

tnile it is a necessary condition tnat two prOposition

one of whicn is consioered as available a a means to the

(o

otLer are both true or coulc he true, it is not a suffi-

g4--

 

cient conciition ior one beinj availatle as a Keans to tne

._'_ -.

other; not an? old pair o; urue propositions can an in

CW-
,C

an available-as—a-Kec 1-s- to relation one with the other.

Lence, tnere is an iuqortant c,:racteristic oi w}; we

0

mean by availabilitv-as-a—ueens to" wnich is not express—

0.]

ible in terns of the Katerial "if, then . ibis pronerty

 

 

 

 

iew lnternationa Iictiorer‘ Ceccno ‘d1tion here
"availabilit;" inalies that soretnin is " iliCcClOUS
01 its oogec+" inat is, or l° e: Wic cicus Cl hX' col-

35. Consider prOposi M10 (5). (3) is sometimes I lse.

m

for it prOposes tr1at x expects that a non existent state-

-affairs o 18 as a flea ns to (that 18, contributes to

.L

w

tne bringing about of) an existent state-of—affairs if p
tnen any old state—of—affairs q. hut we noticed earlic

in tnis essay that ’q’, in general, had to be something

realizable by x - something wnich x can make true. but
even if we adept tnis convention the prOiosition would
not be true. ior organisms do not, generally, expect
that non-existent or non-realizable states-of-afiairs
contribute to tte bringing about of anything. flor ex—

J

ample, (5) under appropriate substitutions mignt read:

u

x believes test if ’ne does not light a match’ is true

 

then also tne conditional state-oL—aiia'rs ’ii he lights
a match, tLe room will blow up’ is true; tnat is, he

believes tnat not lighting a match contributes to the

 

existence of the above conditional. This preposition

could easily be Lalse.
35. It ma; have occurred to the reader tEat what is

involved in the "ii, tnen” relationship between ’p and

’q’ in twe means-end expectation is more aperOpriately

rendered by the verb "can—cs”. Ibis is not quite true.

C)

Her consider tre animal wno debates with himself at the

choice-point. his provisional expectation (or hypotbes s)

are better expressed in the suojunctive; tbat is, they

have the form ’x expects tgat if x were ... then x would

...’. In such a case, tne organism does not expect that

tne ”if” condition exists and probably doesn’t expect
tnat the "then" condition exists. But the expectation

that p causes q, that is, the non-provisional expectation,
includes both x’s expectation that p exists and p contri—
outes to (is sufficient to, the world being what it is)

the bringin_

r‘.
_‘

about of q. Eor example, consider the follow—

 

208
ing preposition: (Lxuerimenter) y unprovisionally ex-
pects tnat if (animal) x 0083 not demand that x be
hunger-alleviated, x ~xpects tnat when he eats food,

he can alleviate nis hunger. :rmbolically tLis is:

where ’nx’ MEBDS ’x alleviates ’is hunfer’ ’fx’ means
x eats iood’ and ’1(x, fi)’ neans
his nun er’. accordiné tLe TI. 2.b, if

(7) 373 (~d(x, sz)>C)
tlierl Vie {Cit

(t) eh", d(x, l'lx))0 3 (e(x, i‘x 315(X, 2~i))>0])0
Under conditions (o) and (Y), it is the present author’s
belief that (b) is seldom, if ever drawn as a result of
thOse conditions. Ine reason is this: the investigator
construes (o) and (7) as causing (b). but (5) would
surely be regarded as false where tne material "if, then"
is replaced by a causal "if, then". In an unprovisional
expectation, the experimental investigator expects that
tne antecedent of a conditional statement exists be ause

he conceives tnat it is the existence of that antecedent

 

which ”br‘nfs about", "influences", (or tie like) the

truth, tfat is, the existence, of the consequent.

 

37. ine causal "if, then" like the subjunctive "if,
'nen" contains the elements of consecutivity and effica-

city. rence it seem possible to define the causal re—

lation in terms of the relation of natural necessity.

 

209

3e shall discuss tnis point in a moment,

3'0. in general, where ’p,.q’ means the world rein") what
it is, p is sufficient to brin? about q,

piq 3 p 3 q
is true. LCRCS, if the laws of TI and ill were couched
in terms or tre:relation ’p q’ bot: inside and outside
or prepositional attitude contexts, the present laws
WOUlH nold. namiiicetion of tie present Sjstem in the
above terms would ”correct" the present system in the
sense tnat laws of tne ioliowing sort would not follow:

('9) e(x, ~p 3(1) D q))>0

(lC) ~p 3 (p 3 q)

(ll) e(x, (p . q) 3 r))O E e(x, p 3 (q 3 r)))O
hence, certain tnings we regard as always true (though
suspect) in the present system in the ranified system
could not be ceduced. ibis ramification, in other words,
would have somewhat tne same effect on the present sys-

as arguments would

i—J-

tem as a more detailed analysis or t

have.

39. Let us now consider tie relations ’pig’ and ’p
r * n ’ X, ' ’ ”‘1“; , ’ (“l-p1 ’ 1 -:- ‘ ' . 0

Causes q tnat 18, pt q . pa q may be defined as

follows

“A _
pv q - Df[p . pnq]

I "A

that is ’pC“q’ means ’p is true and p is suificient to

bring

about q (or p naturally necessitates q)’. Renee,

the provisional expectation (or hypothesis) may be written:

 

210

e(x, p1q))'0;

O."

the unprovi ional expectation may be written:
e(x, p . -hq))> O;
and hence by tbe definition:

e(x, qu)))<>.

no. ihe above discussion of natural necessity sug-
ests tnat the following prepositions are apprOpriate:
i ~[(~p . p) sq]

ii [p . pliq] 3 q

Ho

Ho

H.
’U

5(q1r) 3 (p . q)hr

Al. Preposition i affirns that it

Iw

3 false that ~p
and p are sufficient to bring about the existence of q.
Because of this law the antecedent of the true conditional
[(~p . p) Nq] D [~p . p) 3 q]
cannot be asserted and hence we cannot deduce
(~p . p) 3 q,
though, of course, it is true in its own right. The
above conditional is the result of replacing ’p’ in post-
ulate ii by (~p . p) and exporting on postulate ii. In
accordance with tne preceding remarks, we also find that
e(X, ~[(~p . p) lq])>‘0

is true.

i

C3

M2. Prepositien ii re-ds

...,.)
*J

t, and if p necessitates

q, then q. treposition ii and the definition of cause

 

211

allow us to assert

fl
(‘1;
pv q 3 Q:

and also,

and hence,

pCAq 3 (p 3 q).

Ibis latter statem nt wEen imported a ves us
I" AAA ‘
(p . Inlci) 3 q
wbidiis an analogue of preposition ii. Again, by the
definition of cause, preposition i, and preposition ii
we get

~[(~p . p) CAq].

These formulae cemeert witn the remarks on causation above.

A}. frepesitien 'ii affirms that if p necessitates that
q necessitates r, than n and q necess?tate r. By this pro-
position and preposition i we get

~[~pfl (pmr)]
hence we cannot infer the truth-functional

"p D (p 3 q),
though, of course, it is true in its own right. The point
here is tnat we don’t get this law Mnere we don’t want it,
e.g., in expectations. lhe converse of this postulate
does not held. The converse is rejected on grounds found

in the preceding discussion of preposition (h).

an. Prepositien iv affirms that if p necessitates r

and q necessitates r then the conjunction of p and q

 

212

necessitates r. Erem it we can prove, with the help of

preposi‘ien i,

791561 3 ~(~p*‘q)-

4r

5. Brepesitien v reads: p necessitates the conjunct-
ion of q and r is equivalent to p necessitates q and p
necessitates r. Jrem it we get an interesting theorem
(with tne help or preposition ii) namely

plum . r) 3 (p a q . pm.

4.

he. the above prepositiens and their theorems help

to give the meaning of ’phq’ and also ’pCAq’. is con—
cluce this essay witn the following remarks. In general,
given

[popbqqu

where p is taken to be true, and p 3 q is a preposition

H-

in Er ncinia, we found that we could not infer q because

A.

3

C- ° .1.

p 3 q’ was ialse in certain prepes tional attitude cen-

texts. we therefore could not categorically say that

wLenever a preposition in Principia was imbedded in a

 

prepositienal attitude context it was true. however,
given

[p . IDs-q] 3 q
where p is taken to be true and ’puq’ is one of the above
postulates er a theorem deducible from the same, q can be
deduced. He can say this because whenever such preposit-
ions of the form phq are imbedded in prepositienal atti-

tude contexts they are valid. These remarks are of nec—

 

essitv onl; preliminary. hues work an» investigation 8

needed in order to determine the full meanin of ’pfiq’.

 

21h
BIBLIOGRAPHY

 

Note: The present bibliography lists only items that are
specifically mentioned in the present essay.

Bennett, A. A. and Bayles, C. A. Formal Logic. Prentice-
Hall Inc., 1939

 

Carnap, R. Logical Syntax of Language. Harcourt, Brace and
00., 1937

 

Carnap, R. Testability and Meaning. Yale University Press,
1955

Carnap, R. Foundations of Logic and Mathematics.
International Encyclopedia of Unified Science.
Vol. II, Number 7, 1952

 

 

Hilgard, E. LLTheories of Learning. Appleton—Century-Crofts,
l9 H

Koch, S. "Clark L. Hull" in Modern Learning Theory.
Appleton-Century—Crofts, 195M

 

MacCorquodale, K. and Meehl, P. "Edward C. Tolman" in
Modern Learninngheory. Appleton-Century-Crofts,
195k

Marx, M. Psychological Theories. MacMillan, 1951

Quine, W. V. Mathematical Logic. Norton, l9h0

Quine, w. v. Methods of Logic. Holt, 1950

Reichanbach, H. Elements of Symbolic Logic. MacMillan, 19h?

Russell, E. Human Knowledge; Its Scope and Limits. London,
l9u8

Tarski, A. Introduction to Logic. Oxford Press, l9hl

Thistlethwaite, D. "Critical Review of Latent Learning and
Related Experiments." Psychological Bulletin,
1951, ha: PP- 97-129 -

 

Tolman, E. C. Purposive Behavior in Animals and Men.
University of California Press,*19§?
(Reprinted in 1951)

Tolman, E. C. "The Determiners of Behavior at a Choice Point"
Psychological Review, 1938, AS, pp. l-ul

 

215

Tolman, E. C. "The Principles of Performance?
Psychological Review, 1951, 62, Pp. 315-325

Whitehead, A. and Russell, B. Principia Mathematics.
Cambridge University Press, Second Edition, 1950

Woodger, J. H. The Technique of Theory Construction.
International Encyclopedia of Unified Science.

Vol. II, Number 5, l9h7

Woodger, J. H. Biology and Language. Cambridge University
Press, l9Sh

“9