PRESUPPOSITION AND NEGATION
AS NONDISCRE'EE SEEIAIIC AND SYRIACTIC
VARIABLES

THESIS FOR THE DEGREE 0F ILA.
MICHIGAN STATE UNIVERSITY

GREGORY KARI. SHENAUT
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PRESUPPOSITION AND NEGATION
AS NONDISCRETE SEMANTIC AND SYNTACTIC VARIABLES

By

Gregory Kari Shenaut

A THESIS

Submitted to
Michigan State University
in partiai fuifiiiment of the requirements

for the degree of

MASTER OF ARTS

Department of Linguistics

and Oriental and African Languages

1975

ABSTRACT

The assumption that all presuppositions are of the
same strength and that internal and external negation are
discrete categories is examined empirically. Using evidence
from judgments of degree of contradiction resulting from
conjunction of a sentence and a denial of its
presuppositions, it is established that presuppositions
differ in strength depending upon the surface presupposer,
upon depth in the presuppositionai structure of the
sentence, and upon the surface negator of the sentence.
Also, it is shown that there is a range of negators along
the continuum from internal to external.

The exposition takes the form of positing certain
definitions for such commonly used semantic relations as
negation and semi-entailment, then producing evidence which
shows how the definitions must contain allowance for
nondiscreteness to account for intuitions about language,
and, finally, the definitions are altered to take such

considerations into account.

ii

LIST OF

Chapter

1.

TABLE OF CONTENTS

FIGURES O O O O O O O O O O O O O 0

INTRODUCTION . . . . . . . . . .

NOTES TO CHAPTER ONE . . . . .

SOME RELATIONS BETWEEN SENTENCES

SEMI-ENTAILMENT o o o o o o o o
INTERNAL AND EXTERNAL NEGATION

FULL ENTAILMENT AND PRESUPPOSITION

PRAGMATIC PRESUPPOSITION . . .
NOTES TO CHAPTER TWO . . . . .

VARIATION IN PRESUPPOSITION AND

NEGATION O O O O O O O O O O O
FUZZY CONTRADICTION . . . . . .
CAUSAL CONJUNCTION . . . . . .

DIFFERENCES IN TYPE OF
PRESUPPOSER . . . . . . . .

DIFFERENCES IN TYPE OF NEGATION
WILSON'S HYPOTHESIS . . . . . .

DIFFERENCES DUE TO DEPTH 0F
PRESUPPOSITION . . . . . . .

NOTES TO CHAPTER THREE . . . .

FUZZY RELATIONS BETWEEN SENTENCES

SEMI‘ENTAILMENT o o o o o o o o
NEGATION o o o o o o o o o o 0

iii

Page

13
1h
15
17
22
2h
27

29
30
33

36
39
an

A7
51
52
S3
55

Chapter

5.
APPENDIX
REFERENCES

SUMMARY AND DISCUSSION

PRESUPPOSITION AND FULL

NOTES TO CHAPTER

Page

ENTAILMENT . . 58

LIST OF FIGURES

Figure Page

1. Chart summarizing the relation of
negator and presupposer in terms
of strength of semi-entailment
under negation . . . . . . . . . . . . 61

2. Hypothetical routine for computing
the minimum truth for satisfaction
of the presuppositions of a
sentence T . . . . . . . . . . . . . . 63

Chapter One
iNTRODUCTiON

During the development of the transformational
approach to grammar, quite complicated arguments were often
based upon certain assumptions held to be true by those
involved. in more recent years, it has turned out that some
of these assumptions were open to empirical testing, and now
a large body of literature dedicated to their examination
has been brought forth. This is very important to
linguistic theory, since an immediate goal of endeavor is to
describe what an adequate grammar must look like, and a
grammar based upon false assumptions has no chance of
achieving adequacy.

in this chapter, several areas are briefly discussed
which indicate the shape this trend toward careful
examination of assumptions has taken. This provides an
orientation to the framework within which this thesis is
written.

First is the observation that only declarative
sentences have truth values. Sentences with other forces,
such as questions, requests, and promises, do have sincerity
conditions, but it is impossible to evaluate the truth of,

say, a question. This seems obvious, yet the implications

for grammar are important. For example, one of the most
common and most important tools used by grammarians in
determining the derivation of sentences is the test of
paraphrase. Chomsky (1965) characterizes this relation
(using the euphemism cognitively synonomous) as (p. 22):
"(Two sentences are mutual paraphrases if) one is true if
and only if the other is true." if this characterization is
adhered to in the grammar, then (1) and (2) would not be

paraphrases:
(1) Did Jack call up Mary?
(2) Did Jack call Mary up?

Yet, intuitively, it seems obvious that (1) and (2) are

related just as (3) and (h):
(3) Jack called up Mary.
(M) Jack called Mary up.

Most speakers agree that (3) and (u) are paraphrases
(ignoring for present purposes differences in pragmatic
information). Thus the grammar is weakened at the level of
descriptive adequacy by the assumption that all sentences
have truth values. Lakoff (1973b) has discussed a formal

means of accounting for paraphrase (and other truth-based

relations) in sentences with nonassertive forces. In his
system, the relevant value is felicity. That is, two
sentences are paraphrases of one another if one is
felicitous if and only if the other is felicitous. A
sentence is uttered felicitously only when it is uttered
sincerely and nondefectively. See Austin (1962) for an
introduction to the concepts "felicity," "defective," and
"sincere," as used by Lakoff.

Second, there are elements in the derivation of a
sentence which have to do with its linguistic and
noniinguistic context or environment. Examples of such
factors are: beliefs about the world on the part of the
speaker, Eocial class of the speaker,2age,3 perceived social
class of the addressee, formality of the situation, and so
on. in many of these cases, decisions about the
grammaticality of a sentence must be deferred until such
information is known. That is to say, grammaticality
judgments cannot be made (in some of these cases) on
sentences out of context. Thus the grammar would be
weakened at the level of descriptive adequacy if an
assumption were maintained that context free judgments were
sufficient.

Third, it is easy to demonstrate that not even all
sentences of declarative form have bivalent truth values.
Certain surface forms are conventionally used to indicate
that the speaker presupposes that certain material is true.

if it should be the case that these presuppasitions are no:

true, then it is impossible to evaluate the sentence for
truth. For example, (5) and (6) both indicate, through their
use of a proper name, that the speaker intends to mark (7)

as presupposed:

(S) The present King of France is bald.

(6) The present King of France is not bald.

(7) There is presently a King of France.

That is to say, if it should not be the case that (7) is
true, then clearly (5) is not true. A little reflection
will show that (6) cannot be true either. In a bivalent
logic, all propositions which are not true are false, and
the negation of a false prOposition is true. Thus if (7) is
not true, then it is impossible to uniquely determine the
truth of either (5) or (6). One way to remedy the problem
is to introduce a third value for truth such that
propositions with false presuppositions are neither true nor
false, but void. in any case, a bivalent logic is
inadequate to account for inuitions about the truth of
sentences with presuppositionai failure.

Fourth, John Robert Ross has been concerned with
evidence suggesting that grammatical categories such as NP
are nondiscrete. in Ross (1973), for example, evidence is

given that there is a continuum of noun-phrasiness from real

to fake NP's. He shows that certain rules which refer to
the category NP in their structural description result in
sentences which are more acceptable when the NP in the
sentence is more real than when the NP is more fake. One of
his examples involves the rule PROMOTION, which relates

sentences like

(8) Harpo's being willing to tune surprised me

to sentences like

(9) Harpo surprised me by being willing to tune.

Real NP's (like Harpo and other animates) allow PROMOTION to
operate freely, but as NP's get faker (less like animate,
concrete NP's), sentences produced by application of

PROMOTION get progressively less grammatical:

(10) a. My cat surprised me by knowing how to yodel.
b. The heat surprised me by making the tar soft.
c. The concert surprised me by lasting two weeks.

d. This tack surprised me by being taken infrequently.

if the facts reported by Ross accurately reflect his
intuitions, then this constitutes fairly strong evidence
against making the a priori assumption that grammatical

categories are discrete.

Another piece of evidence against the assumption of
discrete grammatical categories is that certain
generalizations about language usd‘ and also judgments of
grammaticalitis must Incorporate relative frequency in the
description of what has been called free variation in the
past. Changes in the frequency of such variation can be
correlated with such factors as style, social context, and
pragmatic conditions. A descriptively adequate grammar must
have some means to include indications of relative frequency
of use and grammaticality.

Both Ross (1973) and Labov (19723) among many others
have utilized the concept of serial implication to describe
this kind of generalization. This involves listing
sentences or other grammatical variables in order along some
continuum. For example, the sentences of (10) are arranged
along the continuum of grammaticality, such that each step
down the continuum corresponds to a lessening of
grammaticality. G. Lakoff (1973a) suggests a way to formally
Incorporate such generalizations into the theory of syntax.

G. Lakoff (1972) discusses another nondiscrete topic:
fuzzy truth and presuppositionai satisfaction values.
Suppose we are interested in the set of all tall men. It
seems clear that it is impossible to make a concrete
decision about membership in such a set, since men are tail
to different degrees. Thus the set TALL is a fuzzy set, a
set in which membership is to a degree. Suppose there are

three men, with the following height:

(11) John: 5'2"
Bill: 5'8"

Chet: B'h" .

Clearly, John is not a member of the set TALL to any
significant degree, in fact, John is rather short. Bill is
sort of a member, and Chet is definitely a member. This
seems obvious. However, the interesting result is when
membership in such a set is predicated upon individual

members (or nonmembers):

(12) a. John is tall.
b. Bill is tall.

c. Chet is tall.

How may we determine the truth of (12)? Suppose we decide
that (12a) is false and (12c) is true. (12b) is clearly
more true than (12a), but less true than (12c). To resolve
this dilemma, Lakoff postulates a scale of truth values,
from 0 (false) to 1 (true). Using this device, it is
possible to assign truth values in such a way that the
intuitive relations among the sentences in (12) are
preserved. This has interesting grammatical implications.
One of the surface forms alluded to above which

speakers use to indicate that they presuppose certain

material to be true is the factive verb, first discussed by
the Kiparskys (1971), and worked on since by many others,
including Karttunen (1970) and Givon (1972). Factive verbs
mark their complement as presupposed by the speaker of the
sentence. If sentences like those in (12) are embedded
under factive verbs, then two interesting things happen.
First, sentences in which the presuppositions are
relatively less true are relatively less grammatical.
Second, sentences which have relatively untrue
presuppositions have relatively lower maximum truth values.

For example, consider

(13) a. Sam knows that John is tall.
b. Sam knows that Bill is tall.

c. Sam knows that Chet is tall.

In (13), given the heights of John, Bill, and Chet listed In
(11), sentences are ordered along two implicational
continua. Example (a) has the lowest maximum truth value
and is the least grammatical, example (c) is the highest on
both scales, and (b) is in between.

To account for this observation, Lakoff postulates a
nonsense value, again varying from 1 (failure of
presuppositions) to 0 (presuppositions satisfied). The
degree of nonsense depends on the truth of the presupposed
proposition (nonsenses l-truth of presupposition). Once this

value is determined, the maximum value of true (or false) is

equal to 1 minus the nonsense value. A possible valuation
for (12) is given in (IA), where the first element of the
ordered pair is the truth value and the second is the

nonsense value:

(1h) a. (.1, 0)
b. (.5, 0)
c. (.9, 0).

Given these valuations, the range of valuations for (13) is

shown in

(15) a. (O to .1, .9)
b. (O to .5, .5)
c. (0 to .9, .1).

As the nonsense value increases, sentences are progressively
less grammatical, and vice-versa.

Labov (1972a) discusses the problem of using
uncontrolled intuitions in justification of a grammar. He
concedes that it would now be impossible to consider a
methodology which did not allow the use of linguists'
intuitions to treat the subtle distinctions and abstractions
which hold the central position in contemporary linguistics.
However, claims Labov, unless these intuitions are given
support from the speech community, they are meaningless. He

cites two studies in support of his position.

10

First, in a discussion of a paper by Grinder and
Postal, Labov notes that grammaticality judgments made by
two different groups of linguistics graduate students
depended upon the theoretical position prevelant in their
departments. This indicates that theoretical bias might
influence the data upon which the theory is to be based.

The second study is that of Spencer (1972), In which
150 example sentences taken from the literature were given
to 60 subjects: 20 graduate students in linguistics, 20
graduate students in other fields, and 20 non-university
community members. Subjects were asked to make judgments of
acceptability for the sentences. There was considerable
disagreement with the original authors of the studies from
which the sentences were taken: in an out of 150 cases, the
author failed to get a majority of the subjects to agree
with him. But when there was disagreement among the judges,
the non-linguist graduate students regularly sided with the
judges from town, leaving the linguistics students by
themselves.

Labov concludes, "As linguists become more deeply
involved in . . . theoretical issues, it is likely that
their intuitions will drift further and further away from
those of ordinary people and the reality of language as it
is used In ordinary life (p. 199)." This possibility is
strong reason to question any assumption that linguists may
base their analyses upon their intuitions alone, with no

reliable and valid means of outside verification. It seems

11

essential that linguists be trained in such methods, since
it is now uncommon to find support for intuitions in
theoretical papers in linguistics.

To sum up briefly, recent work in linguistics has
often centered on demonstrations that language cannot be
adequately described by a theory of grammar which assumes
any of the following: (a) all sentences have truth values
(and the paraphrase relation can be defined on the basis of
truth values), (b) sentences may be analyzed out of context,
(c) all declarative sentences have truth values, (d) truth
is bivalent, (e) grammatical categories are discrete, (f)
frequency data is irrelevant, (g) truth is discrete, (h)
pragmatic information is not part of grammar, and (i)
intuitions alone are an adequate source of basic data.
Hopefully this thesis makes none of these assumptions.

The aim of this thesis is to demonstrate yet another
area in which nondiscrete variation occurs: the interaction
of presupposition and negation. Evidence is given which
indicates that various of the surface markers of
presupposition result in relatively stronger or weaker
presuppositons. Also, evidence is given that different
surface markers of negation result in different degrees of
cancellation of presuppositions, and that strength of
presupposition depends in part upon complex presuppositionai
relations in the sentence. An attempt is made to integrate
the data into a descriptive (and hopefully explanatory)

model.

12

In the next chapter, certain basic terms are defined
in a way consistent with their current use. in later
chapters, evidence showing the necessity for changing this
usage (and the definitions) is given, and specific

suggestions for the changes are made.

13

NOTES TO CHAPTER ONE

1. Borkin (1971) shows that beliefs of the speaker
are necessary to account for the use of polarity items in
questions. R. Lakoff (1969, 1970a, 1970b, 1971, 1972a,
1972b, 1973) discusses beliefs of the speaker in such cases
as modality, politeness, questions, tense, polarity items,
and passives.

2. In Labov (1972a), the effects of social class are
discussed in many connections. One of the more interesting
was the study of the pronounciation of /r/ on the different
floors of Macy's department store in New York City. It was
found that there is a correlation between the social status
of a floor and the deletion of final /r/ by the people who
worked there.

3. Stokes (197k), in a study dealing with sentences
of the type discussed in Carden (1972), found that one
predictor of ability to see more than one reading in
potentially ambiguous sentences was age and educational
level. »
A. See Labov (1972a, b), Cedargren (1972), Cedargren
and Sankoff (197k), and Laberge (1972) for other examples.

5. The literature on quantifier negation abounds with
this. See Carden (1970, 1972) and Labov (1972b).

Chapter Two

SOME RELATIONS BETWEEN SENTENCES

If logic is the study of relations between sentences,
than natural logic is the study of relations between
sentences in natural language. This thesis is essentially an
exploratory essay in natural logic. in this chapter, an
orientation is given to some of the more important terms
currently used by natural logicians. Since one of the more
salient aspects of literature published in the field is the
confusing proliferation of terms often used to describe the
same (or very similar) concepts, the present chapter's aim
is to provide a coherent, integrated account of certain of
these concepts, rather than reviewing the literature per se.
Specifically, the terms to be discussed are semi-entailment,
internal and external negation, full entailment,
presupposition, and pragmatic presupposition. (Note:
throughout the thesis, "presupposition" means "logical
presupposition.") In the Appendix, a listing is given of a
large number of definitions for these terms, taken from the

linguistic and phil050phical literature.

1h

15

SEMI-ENTAILMENT

The basic relation between sentences is

semi-entailment:

(1) Sentence A semi-entails sentence B if and only if
for all speakers S who believe A to be true, 8

must believe 8 to be true, and B is synthetic.1

Some examples of sentences between which this relation

obtains are

(2) a. A: All men are mortal
B: Some men are mortal
b. A: John's wife has two apples

B John's wife has at least one apple
c. A: John's wife has two apples
B: John has a wife
d. A: John sincerely said "The cat is on the mat"

B: John believes that the cat is on the mat.
A sentence which is analytic is true by definition, that is,
it may, by valid rules of inference alone, be reduced to an

identity. An example of this is

(3) it is snowing or it is not snowing.

16

Regardless of the truth of "it is snowing," i.e., no matter
whether it is true or not true, (3) is true. Thus (3) is a
tautoiogy, and analytic.

This is not the case in

(A) Chicago is in illinois,

however. In order to determine the truth or untruth of (h),
it is necessary to have knowledge about the world. For
example, if the boundaries of the state of Illinois were
changed, (u) might become false. Synthetically true
sentences are different from analytic sentences, since (i)
knowledge about the world is necessary to determine the
truth value of the former, but not the latter, and (ii) the
former are falsifiable, but not the latter.

The reason for the inclusion of the constraint on
semi-entailment (that the semi-entailed sentence must be
synthetic) is to make the relation conform more closely to
intuitions about relatedness between sentences. As Katz
(1973) observes, in a discussion of presupposition (which,
as we shall see below, is a subset of semi-entailment), an
analytic sentence is implied (in the logical sense, which is
roughly equivalent to semi-entailment for present purposes,
but without the restriction on syntheticity) by every

sentence. Thus, if not for the restriction, (5) would be

17

included as a semi-entailment:

(5) A: John's wife has two apples

B: If someone is rich, then someone is rich.

In order to constrain relations in the natural logic so that
they correspond more closely to the intuition that the
sentences in (5) have no relation to one another, the
possibility that analytic sentences can be semi-entailed is
excluded.

The relation semi-entailment is of such a fundamental
nature that it may be used to define all of the other
relations in this chapter, with the inclusion of the

primitives true, false, and sincere.

INTERNAL AND EXTERNAL NEGATION

It is important to grasp the distinction between what
has been called internal and external negation. The terms

may be defined as

(6) Sentence A is the internal negation of sentence B if

and only if "A Is true" semi-entails "B is false"

(7) Sentence A Is the external negation of sentence B if

and only if "A is true" semi-entails "B is not true"

and "B is false" semi-entails "A is true."

18

An example of internal negation is

(8) A: John's wife doesn't have two apples

B: John's wife has two apples.

If one believes that A is true, then one must believe that B
is false. Thus "A is true" semi-entails "B is false."

An example of external negation is

(9) A: The sentence "John's wife has two apples" is
not true.

8: John's wife has two apples.

if someone believes A to be true, then he must believe 8 to
be not true, and if he believes B to be false, then he must
believe A to be true. The reason for the inclusion of the
second condition in internal negation is to exclude pairs

like the following:

(10) A: There is no present King of France

B: The King of France is bald.

In the case of (10), one who believes A to be true must
believe B to be not true, yet intuitively, while there is a

relation between A and B, it is not the same relation that

19

Is commonly thought of as negation. However, one who
believes B to be false needn't believe that A is true, and
this condition suffices to exclude such cases. This
possibility does not arise for internal negation, for
reasons which will become more clear after presupposition is
discussed.

There are various surface means of marking a sentence
as being internal or external negation. However, it should
be made clear that internal and external negation as I have
defined them here (and as they are usually defined
elsewhere) are semantic and/or pragmatic concepts, and it is
impossible to give an adequate surface-only characterization
of them. This will become even more clear during the
discussion of nondiscrete variation in negation. However,
internal negation is usually indicated at the surface level
by the presence of a negative particle (not, un-, in-, no,

etc.) within the negated sentence, as in

(11) a. [X I]
[N not i]

3288) internal Negation

20

b. Bill is a crook
Bill isn't a crook

Bill is no crook

c. Bill stole some money
Bill didn't steal any money

Bill stole no money

d. Bill is tall
Bill is not tall

Bill is short (lexical incorporation).

In (11b-c), the first sentence of each triple is to be
viewed as an "A" sentence in the definition, and each of the
others is to be viewed as a "B" sentence. (11d) shows that
in some cases the negative particle is incorporated at the
surface level in a lexical item with the meaning (roughly)
"not X."

External negation, on the other hand, is characterized
by the presence of a negative marker outside the negated
sentence, usually in a higher sentence with internal

negation:

21

(12) a. [x f)
N not Z [N i]

b. Bill is a crook

====> External Negation

It is not the case that Bill is a crook

The sentence "Bill is a crook" is not true

c. Bill stole some money
it is not true that Bill stole some money

The sentence "Bill stole some money" is false.

Notice that the external negations in (12bAc) can be

paraphrased as the internal negations of

(13) it is the case that ...
The sentence ... is true

It is true that ... .

This indicates that the relation is functional rather than

just syntactic.

22

FULL ENTAILMENT AND PRESUPPOSITION

The closest counterpart in the present system to the
traditional logical relation called "entailment" or

"implication" is full entailment:

(1h) Sentence A fully entails sentence 8 if and only if
A semi-entails B and the internal negation of B

33mia3ntails the Internal negation of A.

Although this relation will not be discussed in detail, some

examples are given in

(15) A: John's wife has three apples
B: John's wife has at least two apples
C: John's wife has at least one apple
-B: John's wife doesn't have at least two apples

-A: John's wife doesn't have three apples.

Notice that A semi-entails B, since a believer of A must
believe B as well, and also that the internal negation of B
(-B) semi-entails the internal negation of A, (-A). Also
notice that full entailment is transitive, since if A fully
entails B and 8 fully entails C, then A fully entails C.
Perhaps the most important of natural logic relations

for the present discussion Is presuppostion, which is

23

defined as

(16) Sentence A presupposes sentence B if and only if
A semi-entails B and the internal negation of A

semi-entails B.

An example of presupposition is

(17) A: John's wife has some apples
B: John has a wife

-A: John's wife has no apples.

If one believes A to be true, then one must believe 8 to be
true, and if one believes -A to be true, then one must also
believe that B is true.6

An important feature of presupposition is that
presuppositions may be presupposed by other presuppositions.

That is, presupposition is a transitive relation. This is

illustrated in

2h

(18) A: Bill knows that John's wife has two apples
B: John's wife has two apples

C: John has a wife.

An examination of (18) will show that A presupposes B, B
presupposes C, and A presupposes C, by way of B, so to

speak. This will be discussed in more detail in Chapter 3.

PRAGMATIC PRESUPPOSITION

It is failure to distinguish between presupposition of
the type defined in (16) and pragmatic presupposition which
results in much of the confusion about presupposition which
exists in the literature (see Katz 1973 for an example of
this confusion). Pragmatic presupposition may be defined as

in
(19) Sentence A pragmatically presupposes sentence B if
and only if "X sincerely says A" semi-entails "X

believes B" and B is synthetic. 7

Some examples of this relation are in

25

(20) a. Does John's wife have two apples?

John has a wife

b. Give John's wife an apple
John has a wife

c. John's wife is happy
John's wife is happy

d. The cat is on the mat
The cat is on the mat

e. Please give me an apple

I want an apple.

Notice that for declaratives, any sentence A pragmatically
presupposes itself (c and d). Of course, all of the
semi-entailments of A must be believed true for A to be
believed true, including trivially all full entailments and
presuppositions. Therefore, any sentence which is
semi-entailed by A is pragmatically presupposed by A.

In the other cases (questions, requests, etc.),
pragmatic presuppositions are what have been called
sincerity conditions by Austin (1962), Searie (1971a&b), and
Gordon and Lakoff (1971). Heringer (1971) makes use of this
fact in a different vein.

One thing which is apparent throughout the present
chapter is that all of the discussion has tacitly assumed
that truth is discrete, as is falsity, that the relation

presupposes is discrete, and that all negation is either

26

internal or external. Yet in the first chapter, much space
was devoted to Indicating that the trend in much of
linguistics is to question such assumptions. In fact, the
purpose of the present chapter was to set the stage for
further discussion, to include careful examination of such
assumptions. The terms introduced in the present chapter
have been explained in a manner consistent with their
present use in the literature. in the next chapter, an
attempt is made to go beyond this level, by examination of
facts which suggest that in an adequate natural logic, the
definitions and conceptualizations as given here must be

extended to account for nondiscrete variation.

27

NOTES TO CHAPTER TWO

" 1. For "must p" read "it is logically necessary that
g "or X is committed to the truth (belief In the truth) of

2. The idea of predicating "analytic" of a sentence
can be traced to Carnap in Meaning and Negesslty, Quine
(1960) discusses analytlcity and defines it interconnectedly
with synonymity:

Sentences are synonymous if and only if their
biconditionai (formed by joining them with a
biconditionai) is analytic, and a sentence is
analytic if and only If synonymous with
self-conditionals ("if p then p"). (p. 65)

Quine states that the intuitive notion of analyticity is
that a sentence is true (if analytic) purely by meaning and
independent of collateral information, and gives "no
bachelor is married" and "pigs are pigs" as examples.

3. As it happens, A must be synthetic as well, but it
is unnecessary to include this in the definition, since it
follows from the fact that if A is analytic, then all
speakers must believe it, but since B is synthetic, not all
speakers must believe it.

h. This condition may be too strong, since it blocks
pairs like

A: John knows that it is either snowing or not
snowing.
B: It is either snowing or not snowing.

There does seem to be some relation between A and B, at
least more of one than in (5) in the text. But since any
speaker must believe 8 regardless of his beliefs about A,
this is probably properly excluded.

5. I mean to use the terms true and false in a way
corresponding to the following tests:

a. if the sentence may be used to make a sincere
assertion, then it is believed true.

b. If a sincere answer of "no" may be given to
a simple yes-no question made of the sentence,
then it is believed false.

c. If a sentence cannot be used to make a sincere
assertion, and if a simple yes-no question made

28

of it cannot be answered sincerely with "no,"
then the sentence is not true and not false.

An example is the following story. Suppose there are two
people talking, John and Mary (who else?). John believes
that Bill doesn't have a wife. Mary believes that Bill's
wife is pregnant. The following statements are issued:

d. Bill's wife is pregnant
e. Bill's wife isn't pregnant
f. Bill isn't married

For Mary, sentences (e) and (f) are false, and (d) is true.
However, for John, (d) and (e) are not true, and (f) is
true. For him, neither (d) nor (e) are false, while for
her, both (e) and (f) are not true. Notice that to answer as
in

g. Q: Is Bill's wife pregnant? A: No.

is insincere for both, but in addition for Mary it would be
a lie. For a detailed discussion, see Shenaut (197k).

6. It may now be seen why it was unnecessary to
include a condition like "B is false" semi-entails "A is
true" in the definition of Internal negation. The reason a
similar condition was included for external negation is to
block pairs like

A: There is no King of France
B: The King of France is bald.

This type of pair is blocked for internal negation, since
whenever A is true, a presupposition of B is false, making B
not true and not false.

7. The condition on syntheticity is included for the
reasons mentioned during the discussion of semi-entailment.

Chapter Three

VARIATION iN PRESUPPOSITION
AND NEGATION

In the previous chapter, several concepts of much
current importance were introduced. in this chapter, two of
these concepts will be focused upon in more detail:
presupposition and negation. Obviously, these two concepts
are related, since it is necessary to refer to negation to
define presupposition. in fact, in much of the literature
(e.g. Horn 1972), the distinction between internal and

external negation is characterized as follows:

(1) Internal negation shares the presuppositions of the
unnegated sentence; external negation cancels the

presuppositions of the unnegated sentence.

Clearly, there is a very intimate connection between the two
relations.

This close interaction between the two has been
pointed out before, and has even caused some linguists to
question the usefulness of the notion "presupposition." One

such linguist is Wilson (1972). we will have more to say

29

30

about this approach later.

FUZZY CONTRADICTION

In Chapter One, G. Lakoff's (1972) description of a
fuzzy presuppositionai logic was briefly introduced. In
that system, truth and nonsense are nondiscrete, and vary
along a continuum from 0 to 1. Nonsense is the degree to
which the presuppositions of a sentence are not true. This
framework will be extended here to describe another
continuum, contradiction, which is dependent in part upon
truth and presupposition.

In Lakoff's paper, "hedges" are described as
predicates which decrease the degree of truth required of
some prOposition for some given degree of truth for the
assertion. An "intensifier" has the opposite effect. For

example:

(2) a. John is 5'2" tall.
Mack is 5'6" tall.

Jim is 6'h" tall.

31

b. John is tall.
John is very tall.
John is sort of tall.
c. Mack is tall.
Mack is very tall.
Mack is sort of tall.
d. Jim is tall.
Jim is very tall.

Jim is sort of tall.

Given the tallnesses of (2a), it can be seen that "sort of"
can act to increase the truth of a sentence which was not
very true, while "very" can serve to decrease the truth of
relatively true sentences. in Lakoff's terms, "sort of" is
a hedge and "very" is an intensifier.

Contradiction, in general, results from the

conjunction of some proposition and its negation:

(3) p and (not p) (or "p but (not p)").

For example, consider the following contradictions:

(h) a. it's snowing and it's not snowing.

b. John is a bachelor but he's married.

In (ha), the contradiction is direct, since the first

32

conjunct is a proposition and the second its negation. The
contradiction in (hb), however, is less direct, since the
first conjunct semi-entails a proposition, and the second
conjunct is the negation of the semi-entailed pr0position.
(hb) is contradictory due to application of modus ponens.
Now consider the effect of inclusion of hedges and

intensifiers:

(S) a. It's sort of snowing and not snowing.
it's snowing like a bitch and not snowing
at all.
b. John is sort of a bachelor, but technically
he's married.

John is a strict bachelor, but is very married.

It seems clear that when hedges like "sort of" and
"technically" are included, the previous contradiction is
improved; that is, it becomes less contradictory. On the
other hand, inclusion of intensifiers like "like a bitch,"
"at all," "strict," and "very" seems to increase the amount
of contradiction. In Lakoff's system, this might be
accounted for by simply adding the minimum degrees of truth
for the contradictory prepositions, so that the conjunction
is contradictory to the degree that the sum exceeds 1.
Using this measure, the scale of contradiction extends from
O to 1, as do the scales of truth and nonsense. This fact

can be used to examine the hypothesis that negation and

33

presupposition are not discrete.

CAUSAL CONJUNCTION

There is a test for presupposition involving
contradiction. The test involves conjoining some
proposition with some other pr0position, and also conjoining
the negation of the first prOposition with the other
proposition. If both of these conjunctions are
contradictory, then the first preposition presupposes the
second. (Note: although internal negation is used in the
usual version of this test, any negation can of course be
used if desired. However, failure to find contradiction
with an external negation does not mean that the first

proposition does not presuppose the second.) Here is an

example with the factive predicate "resent":

3:.
(6) A: Mary resented that Fred left.
B: Fred left.
AN‘B: Mary resented that Fred left, and Fred
didn't leave.
(‘A)&"B: Mary didn't resent that Fred left,

and Fred didn't leave.

in the example, both of the conjunctions are contradictory,
so A presupposes B.

We are concerned here with a subset of sentential
conjunctions, namely, the set of "causal" conjunctions. in
application of the above test, one of the causal
conjunctions is substituted for "and." A causal conjunction

may be defined as follows:
(7) A conjunction C is causal if and only if for all pairs
of sentences (A, B) such that C(A, B), B is a reasonfor

the truth of A, and C(A, B) semi-entails "A and B."

Some examples of this are:

3S

(8) a. Ford is president because Nixon appointed him and
then stepped down.
b. §lfl£§ all men are mortal and Socrates was a man,
Socrates was a mortal.
c. You've had too much to drink,_§g you should go

home now.

Notice that all of these conjunctions have the flavor of the
conditional in logic. In fact, there is some similarity,

but

(9) If p, then q

does not semi-entail

(10) p and q.

That is, while material implication may connect any two
well-formed sentences, causal conjunctions may only connect
sentences which the speaker intends to indicate that he
believes are true.

The interesting fact about this type of conjunction is
that in sentences of the form C(A', B'), where A' is the
negation of A, B' is the negation of B, and A presupposes B,
B' is a reason for A' when A' is an external negation, but

is not a reason (and is contradictory) if A' is an internal

36

negation of A. Example:

(11) a. Tom didn't marry Fred's sister, because Fred
doesn't have a sister.
b. The sentence "Tom married Fred's sister" is

not true, because Fred doesn't have a sister.

Example (11a), with internal negation, is contradictory, but
(11b), with external negation, seems quite reasonable. We
now turn to the use of this test to examine the discreteness

of presupposition and negation.

DIFFERENCES IN TYPE OF PRESUPPOSER

Suppose we hypothesize that different surface markers
of presupposition have different requirements for
satisfaction. That is, marker m1 requires that the
presupposed proposition be true to degree d1, and marker m2
requires that the presupposed proposition be true to degree
d2. if d1 is not equal to d2, then we would expect to find
a difference in the degree of contradiction resulting from
the causal conjunction test. in fact, this is what we find.

Consider the following sentence:

37
(12) a. Bill doesn't know that someone robbed the bank,

because no one robbed it.

b. Bill doesn't realize that someone robbed the bank,
because no one robbed it.

c. it wasn't Bill who robbed the bank, because no
one robbed it.

d. Bill isn't the one who robbed the bank,

because no one robbed it.

All of the above sentences are of the form

(13) A' because 8'
A presupposes B

A' is an internal negation of A.

The only difference is in the surface means of marking the
presupposition. (12a) uses a factive predicate, (12b) uses a
semi-factive,1(12c) uses a cleft sentence, and (12c) uses a
pseudocleft sentence. Most informants agree that for the
four surface markers of presupposition in (12), there is a
decreasing degree of contradiction from (a) to (d). This
may be seen as indicating that there are four different
degrees of truth required by the presupposers of the
presupposed proposition.

Another pair is seen in (IA):

38

(1h) Bill's wife isn't the one who wrecked my car, because
a. Bill doesn't have a wife.

b. my car hasn't been wrecked.

Again, most informants agree that possessives like (lha) are
less contradictory in the test than pseudoclefts like (lub).
This indicates that the surface possessive does not require
as great a degree of truth. To sum up, we have shown some
examples of presupposers which apparently demand different
degrees of truth of their presuppositions. The order in

terms of decreasing degree of truth required is:

(15) a. factive predicates
h. semi-factives
c. cleft sentences
d. pseudocleft sentences

e. possessives.

That is, there seem to be at least five different
levels of strength of presupposition shown by the results of
the contradiction test. This is strong evidence that the
relation "presupposition" obtains to a degree rather than
categorically. In the next section, we apply the

contradiction test to negation.

3'9

DIFFERENCES IN TYPES OF NEGATION

In Chapter Two, internal and external negation were
defined, and examples of some of the more common surface
markings of these categories were given. it was observed
that the distinction is actually semantic and/or pragmatic,
and that the surface form does not always match the
predicted meaning. In this section, evidence is given that
what may be going on Is that it is the categories which are
not useful, rather than the surface forms which are
inconsistent. But first we introduce some more terminology.

Karttunen (1973b) explored the effects of different
types of predicates on the presuppositions of complex
sentences. He classified all of the predicates into the

following categories:

(16) a. Plugs: predicates which block off (cancel) all
of the presuppositions of the complement sentence
b. Holes: predicates which let all of the
presuppositions of the complement sentence become

presuppositions of the matrix sentence

50

c. Filters: predicates which, under certain
conditions, cancel some of the presuppositions

of the complement. (p. 17h)

In this framework, internal negation is a hole, and external
negation is a plug.

if we hypothesize that some negators approach the
hole, and others approach the plug (rather than falling
discretely into either), then we would expect differing
results from the contradiction test depending on the negator
present in the sentence. There is some evidence that this
is indeed the case.

Consider the sentences of (17):

(17) No one kicked my dog, so
a. The sentence "It was Bill who kicked my dog"
is not true.
b. It is not the case that it was Bill who

kicked my dog.

c. it isn't Bill who kicked my dog.

In all of the sentences in (17), the form is

Al

(19) ”B, so A'
A presupposes B

A' is a negation of A.

All of the presupposers are the same (cleft), and the
presupposed proposition is the same. What varies is the
negator. Both (a) and (b) are what we identified before as
external negations, and (c) is an internal negation. As
predicted, (c) is more contradictory than either (a) or (b).
The unexpected result (if internal and external negations
are discrete categories and all negations fit into one or
the other) is that (b) is more contradictory than (a). That
is, there are three levels of negation (in terms of
cancellation of presuppositions) in (17) where there should
be only two under the old classification.

Another example is shown in

(19) Bill isn't married, so
a. it's not the case that Bill's wife has a Swiss
bank account.
b. Bill'swife doesn't have a Swiss bank account.

c. Bill's wife has no Swiss bank account.

This time, (b) and (c) are internal negation and (a) is
external negation. As expected under the traditional

account, (a) is less contradictory than either (b) or (c),

k2

but again we see a difference within a category. Example (b)
is less contradictory than (c), even though both are in the
traditional "internal" classification. Thus, there is
reason to believe that neither internal nor external
negation are discrete categories, and that negation, like
presupposition, is nondiscrete.

To extend Karttunen's plumbing analogy, negation seems
to function like a valve rather than as a plug or a hole.
Of course, in plumbing, the limits of a valve are the hole
and the plug (except in the case of drippy faucets when the
plug limit is never reached), but there is plenty of room in
between.

Another example will suffice to make the point. in
Shenaut (197k), misleading evasion was discussed. Without
going into detail about the content of that discussion, we
observe that there are different degrees both of misleading
and of evasion which are possible. This results in a
nondiscrete category of speech act (one of the
circumlocutionary acts) which is called "misleading
evasion." it works like this. In order to make an evasion,
the speaker must have been asked a question (or otherwise
been requested to tell something). The speaker must say
something (or do something) instead of responding to the
request for information. if the speaker actually lies or
issues (or attempts to issue) a misleading utterance, then
he has not evaded the question, but has only answered it

insincerely. However, since there are degrees of

143

misleading, it is possible for the speaker to both evade the
question, sort of, and mislead the bearer, sort of, but do
neither to a full degree. If either is done to a full
degree (or not at all), then the act does not qualify as a
misleading evasion. However, there is a range of degrees of
misleading and evasion which do qualify. The following

story should make this more clear:

(20) Bill and Mary are talking. Bill believes that Tom is
not married, and never has been. Mary, on the other
hand, thinks that the girl Tom lives with is his
wife. Bill knows that Mary would be offended if she
knew that Tom and his convivant were "living in sin."
Mary thinks that Bill is trying to move on Tom's
wife, and this is upsetting her. She wishes to find
out for once and for all what Bill's intentions are.
Bill, of course, wants to evade the question and at
the same time indicate that he has no interest in the
girl. There are several ways he could reply:

(Mary): You're interested in Tom's wife, aren't you?

a. Tom isn't married. (truthful, evasive)

b. i have no interest in Tom's wife. (misleading,
not evasive)

c. No, its not the case that i'm interested in
Tom's wife. (less misleading, more evasive)

d. No, it's not true that I'm interested in Tom's
wife. (still less misleading, more evasive)

e. No, it wouldn't be true for you to say that...
(even less misleading, more evasive).

Notice that as one goes down the list from (b) to (c), the
degree of misleading decreases, and the degree of evasion
increases. This can be taken to show that the
presuppositions of the possessesive are weakened to
different degrees by the different negators used in the

replies. In other words, as one reads down the list of

Ah

replies, the valve becomes more closed, approaching a
plug-like state. But even (e) is misleading to some extent,
so some of the presupposition that Tom has a wife is present

in all of them.

WILSON'S HYPOTHESIS

Wilson (1972) observed that in almost all cases of
negative sentences with material marked as presUpposeJ, it
is possible to get the so-called external reading,
cancelling the presuppositions of the sentence. This would
imply that all negations are potentially external as far as
presuppositions are concerned, and that therefore, the
notion of presupposition as a relation maintained after
negation is not correct. An example is the syllogism, which

seems to force the external reading, at least for Wilson:

(21) If it was John who robbed the bank, then someone
robbed the bank.
No one robbed the bank.

llit wasn't John who robbed the bank.

Wilson uses the relative acceptability of such
syllogisms as evidence to support the hypothesis that there
is no difference between what we have called semi-entailment
and presupposition, since the only difference has to do with

the maintenance of the relation under negation. If the

BS

"external" reading is possible in every case, then clearly
the distinction is not viable. Wilson suggests that certain
forms mildly indicate that the speaker tends toward belief
of the semi-entailed material even under negation, but the
indication is not the same as the commitment or "necessary"
belief as in semi-entailment.

The present account suggests another explanation of
Wilson' facts.

If there is Indeed a continuum of negation in terms of
presuppositionai cancellation, and if contradiction is
nondiscrete, then one might expect to find differences in
the amount of contradiction in the syllogisms, just as in

the contradiction test. in fact, this seems to be the case:

(22) If it was John who robbed the bank, then
someone robbed the bank.
No one robbed the bank.
1
a. it wasn't John who robbed the bank.
b. it isn't the case that John robbed the bank.
c. The sentence "It was John who robbed the

bank" is false.

There is an increase in acceptability as one proceeds down
the list. This indicates that the speaker of cleft
sentences commits himself to the truth of the complement

even under negation, although to different degrees depending

AB

on the type of negation used. This does not hold for all

semi-entailment:

(23) If John is a bachelor, then he is not married.
John is married.
1
a. John is not a bachelor.
b. it is n0t the case that JOhn is a bachelor.

c. The sentence "John is a bachelor" is false.

There is no difference in acceptability among the syllogisms
of (23).

Under Wilson's account, there is no way to account for
(a) differences in acceptability of syllogisms which depend
upon the surface form of negation used, and (b) differences
in degree of contradiction resulting from type of negation
and type of presupposer. The present account handles both
of these differences. This suggests that it is still
meaningful to include the notion "presupposition" In
linguistic analyses, but that it is merely a nondiscrete
relation, as is negation. It is this nondiscreteness that
results in the facts reported by Wilson.

In Chapter Two, it was pointed out that presupposition
is a transitive relation, that is, presuppositions may be
presupposed by presuppositions, resulting in complex
presuppositionai structure. The next section gives evidence

that there are differences in the strength of

A7

presuppositions due to their level in presuppositionai

structure.

DIFFERENCES DUE TO DEPTH OF PRESUPPOSITION

G. Lakoff (1970) claims that secondary presuppositions
are impossible to qualify (i.e., suspend or cancel by means
of an if- phrase), where a secondary presupposition is a
sentence presupposed by a presupposition of the matrix

sentence:

(2A) a. Few men have beaten their wives, if any men have
beaten them at all.
b. Few men have stopped beating their wives, if any

have ever beaten them at all.

In (a), use of the quantifier "few" presupposes "some men
have beaten their wives." This presupposition is qualified
by the if- clause, which is sort of a hedge on the
presupposition of the first clause. in (b), on the other
hand, use of the verb "stopped" presupposes "a few men have
beaten their wives," which in turn presupposes "some men
have beaten their wives." This secondary presupposition is
qualified by the if- clause, but only at the cost of a loss
of grammaticality for the sentence. Lakoff concludes from
this and other facts that only primary presuppositions nay

be qualified.

AB

There is, however, another possibility, not considered
by Lakoff, namely that there is a hierarchy such that
secondary presuppositions are harder to qualify than primary
ones, and tertiary presuppositions are harder to qualify
than secondary ones, and so on. it is possible to use the
contradiction test to determine whether this is true.

That is, it might be the case that the reason why the
decrease in grammaticality occurs is that embedded
presuppositions have more strigent requirements on truth for
satisfaction. Therefore, use of a qualifier with a
proposition marked as very true might not be able to
diminish the truth requirements of the presupposition enough
to avoid contradiction.

Consider the following examples:

(25) John didn't know that it was Bill who married
Fred's sister, because
a. it was Jack who married her.
b. no one married her.

c. Fred doesn't have a sister.

b9

(26) It isn't John who knows that Bill married Fred's
sister, because
a. no one knows it (yet).
b. Tom married her.

c. Fred doesn't have a sister.

In both cases, there is an increase in contradiction as one
descends the list of alternatives. The presuppositionai

structures of the sentences are

(25') (NOT) FACTIVE>>CLEFT>>POSSESSIVS
(26') (NOT) CLEFT>)FACTIVE>>POSSESSIVE ,
where ">>" is to be interpreted "presupposes." There is a

very obvious increase in the degree of contradiction when
lower-level presuppositions are denied. This is in support
of the hierarchy proposed above. For further support of

this hypothesis, consider

(27) Few feminists know that some men have stopped beating
their wives, if
a. any feminists know it at all.
b. any men have stopped beating their wives at all.

c. any men have ever beaten them at all.

This example, which seems very similar to that of Lakoff

SO

(cited above), shows that the same increase in
ungrammaticality obtains for qualification of n-ary
presuppositions as for contradiction of them.

To sum up, in this chapter, we present evidence that
(a) presupposers are of different strengths in terms of the
degree of contradiction resulting from their direct denial,
(b) negators act like valves in that they diminish the
presuppositions of a lower sentence to different degrees,
depending upon the surface form used, and (c)
presuppositions appear to increase in strength as a result

2 We have

of being presupposed by a higher presupposition.
used this evidence to suggest changes in the hypotheses of
Wilson (1972) and Lakoff (1970). in the next chapter, we
shall discuss the definitions of Chapter Two in the light of

the facts in the present chapter.

NOTES TO CHAPTER THREE

1. Karttunen (1970) divides factive predicates into
two sub-classes:

a. Semi-factives predicates are those for which the
following relation obtains:

p is a semi-factive if and only if for all
propositions A, p(A) semi-entails A and the
internal negation of p(A) semi-entails A.

b. True factives are defined as:

p is a true factive if and only if for all
pr0positions A, "p(A) is possible" semi-entails
A, and "the internal negation of p(A) is
possible" semi-entails A.

Karttunen also suggests that something like the definition
(b) is the proper definition for all presupposition, and
that therefore semi-factives are not presupposers. Since
all predicates meeting (b) also meet (a), and since (a)
corresponds to the usual definition for presupposition, I do
not see anything to be gained by this proposal.

2. As was noted in the introduction, there is good
reason to doubt linguists’lntuitions when they are given as
the sole support for an analysis. To this end, several
attempts were made to gather support for the intuitions
reported here. Some of this evidence is reported in Shenaut
(1975) and Shenaut and Warren (1973). in general, it would
be fair to say that all of the intuitions included here were
supported by this experimental data.

Chapter Four
FUZZY RELATIONS BETWEEN SENTENCES

in the previous chapter, evidence supporting the
hypothesis that the relations "negation" and
"presupposition" are nondiscrete is presented. If this
hypothesis is correct, then the definitions given in the
first chapter must be altered in such a way as to maintain
their original correspondence with intuitions, but at the
same time account for the new data reported here. It is only
necessay to amend the original definitions slightly to
accomplish this. in the case of negation, it is possible to
actually replace a concept (internal negation) with another
one (valve). Some of the changes are not explanatory, in
that they allow a range of variation, but make no attempt to
account for this variation. This is not true in the case of
complex presuppositions, however, since it is possible to
give a relatively straightforward explanation of the facts
there. The order of presentation follows roughly that of

Chapter Two.

52

53

SEMI-ENTAILMENT

Semi-entailment may be redefined as follows:

(1) Sentence A semi-entails sentence 8 (to degree d0 =
d1 - d2) if and only if for all speakers S who believe
A is true to degree d2, S must believe B is true to

degree d2, and B is synthetic.

In other words, for a sentence to semi-entail another, the
latter must be believed to be as true or more true than the
former. The degree of semi-entailment is the extent that
the minimum degree of truth of the latter sentence must

exceed that of the former. Here are some examples:

(2) a. John knows Bill is tall.
Bill is tall.
b. Bill just found out that Nixon is popular.

Nixon is popular.

5h

c. Some
Quite a few Arkkites are mothers.
Most
All
Some Arkkites are female.
some
d. No Arkkites are female, but quite a few
most
all

Arkkites are mothers.

In (a), (b), and (c), the first sentence(s) semi-entall(s)
the second. In (c), however, the strength of this
semi-entailment varies as seen by the increase in
contradiction resulting from the different surface markers
of semi-entailment as one goes down the list in (d).

At this point, it is useful to note that, while for
the relation "semi-entail" to obtain between two sentences,
the degree of truth d2 of the semi-entailed sentence must be
greater than or equal to the degree of truth of the
semi-entailing sentence, it is logically possible for
another relation, which might be dubbed "sort-of entailment"

to hold between two sentences:

55

(3) Sentence A sort-of entails sentence B if and only if
for all speakers 8 who believe that A is true to some
degree d1 greater than 0, S must believe that B is

true to degree d2 greater than 0, and B is synthetic.

That is, if A Is believed to be even partially true, B must
be believed at least partially true, but it is not necessary
that d2 be greater than or equal to dl. Extent of sort-of
entailment is equal to d2. Clearly, sort-of entailment
Implies (in the logical sense) semi-entailment. Sort-of
entailment might be what obtains between sentences which
have had their presuppositions valved down by negation. For
present purposes, we will not go into this distinction any

further, but merely point it out as a possibility.

NEGATION

As was observed in Chapter Three, negation is a valve.

At this point, we make that notion more explicit:

(5) For all sentences T of the form p(q) where q
semi-entails r to degree d greater than or equal to
0, and p is some abstract predicate with surface
realizations p',D",..., and for all S who believe
T to be true to degree t1 8 must believe r to be

true to degree t2;

56

a. if t2=0, then p is a plug.
b. if t2;0, then p is a hole.
c. if for some T and for all p, t2=0, and for some
T and for all p, t2)0, then p is a filter.
d. if t2 Is located at several different points on
either side of t1 for different realizations of
p, then p is a valve.
Since it is desirable to have the value of the valve
vary in the same range as the other fuzzy variables, i.e.,
from 0 to 1, this value can be conceptualized as the

difference between t2 and t1, or

(6) min(t2-t1, O) .

In other words, the value of the valve is the extent to
which the semi-entailment is reduced. When the value is
equal to 1, then the predicate is a hole; when the value is
equal to 0, then the predicate is a plug. Intermediate
values are expressed by location along the interval.

As an example, consider

57

(7) it wasn't John

it's not true that it was John who robbed the bank.

(etc.)

which has the following presuppositionai structure:

(8) T: p q r
(NOT)(it was John who robbed the bank>>someone
did)

When NOT is a plug, T may be true to any degree regardless
of the truth of r. When NOT is a hole, r must be at least
as true as T. And when NOT is in between, r must be at
least partially true, but needn't be as true as when NOT is
a hole.

Since on the initial definitions for Internal and
external negation, external negation implies (in the logical
sense) internal negation, it is possible to define all
negation by applying the definition for external negation.
Once the set of all pairs of sentences (A, B) such that A is
a negation of B has been so defined, the value of the
negator for some subset of the pairs in terms of
presupposition cancelling is determined by testing, as was
carried out for several negators in the previous chapter.
Since internal negation under this system reduces to a

theoretical endpoint to the hypothetical valve continuum, it

seems that there is no use to continue to maintain the
distinction between it and external negation in the natural

logic.

PRESUPPOSITION AND FULL ENTAILMENT

Since internal negation was used in our definitions of
both presupposition and full entailment, and we have
discarded internal negation from the natural logic, it now
becomes necessary to redefine these definitions to include
the changes. in the case of full entailment, this may be

accomplished straightforwardly:

(9) Sentence A fully entails sentence B if and only if A
semi-entails B, and for all pairs (A', B') such that
A' is a negation of A, B' is a negation of B, and
value of the negators of A' and B' are equal (in terms
of cancellation of presupposition), B' semi-entails

A'.

Since it is probably impossible to determine the actual
value of some surface negator, much less decide whether two
such negators have the same value, in practice, the only
cases which can be decided with any real confidence are
those in which the surface negators are identical. Thus the
test for semi-entailment involves comparison of sentences

with the same surface form:

59

(10) a. A: Mary's sister has two apples.
B: Mary's sister has at least one apple.
b. B': Mary's sister doesn't have at least one apple.
A': Mary's sister doesn't have two apples.
c. 8': It's not the case that Mary has at least one
apple.

A': It's not the case that Mary has two apples.

The problem is somewhat more complicated for
presupposition. There seem to be two alternatives. We
could simply alter the old definition to read "negation with
a value of 1" instead of "internal negation." This would
preserve the old distinction exactly. The problem with this
alternative is that it might be the case that some (or
perhaps all) speakers are linguistic counterparts to leaky
faucets; that is, their valves never open or close all the
way. Thus, for these speakers, there might not exist
negations with the value 1. Yet it would be stupid (in the
sense of Ross 1972) to infer from this that for these
speakers, presupposition does not ever obtain.

The second alternative involves quantifying over

negations, as in

60

(37) Sentence A presupposes sentence B if and only if A
semi-entails B to some degree d1 greater than 0, and
there exists some A' such that A' is a negation of A
and A' semi-entails B to some degree d2 greater

than 0.

This seems to correspond more closely to the facts.

A measure of the strength of a presupposition is the
degree of semi-entailment which remains under some negation.
Figure (1) sums up some relations between presupposers and
negators in terms of this measure.

in Figure (1), the ordinate axis represents the values
of the negators considered, running in order from 0 (plug)
to 1 (hole). The relative position on this scale for
various surface negators is in the key. The abcissa
n

ESCLTI“(HILL]IIIILIIL rm;sL:ItiI;r' fzcn: ti»-

Ll

represents strength 0
LCLCCCC sentence. Plotted ch :Ie coordinates are srvcrrl
surface presupposers. It should be remarked at this point
that not all of these combinations have been tested, and
that the relation might be more complex than suggested here.
Also, the relation might not be linear. However, Figure (1)
represents my intuitions about the interaction of five
surface negators and five surface presupposers.

So far, we have modified the definitions of

semi-entailment and presupposition to allow for

nondiscreteness, and have done away with the concept

61

STRONG I
I e e
I v v
I i i
I t t
I c c
S I a a
E I f f
M I i
i I m t
E I e f
N I s t e
T I f l
A I e c
i I l o e
L I c d v
M l u i
E I e s
N I s s
T I p e
I s
I s
I o
I p
i
I
WEAK I
l
VALVE: closed a b c d e open
(plug) (hole)

Figure (1):

D resupposer

negation.

Key:

a
b
c
d
e

Chart summarizing the relation of negator and
in terms of strength of semi-entailment under

The sentence X is false

The sentence X is not true

it's not true that X

internal negation (matrix verb)
it's not the case that X.

62

"internal negation," replacing it with the more general
"valve." This allows us the flexibility to represent certain
empirical observations which were impossible (or difficult)
to deal with under the old system.

One problem remains. As we have observed,
presuppositions increase in strength as a result of being
embedded in the presuppositionai structure of a sentence.
We have seen how surface negators and presupposers interact
to give rise to different degrees of semi-entailment. The
account we have given of this interaction suggests a natural
explanation of the facts for complex presuppositions.

If we compute the increment of truth associated with
the primary presupposer, use it to compute the minimum truth
for its presuppositions, then compute the increment of truth
for the secondary presupposer, use it to compute the minimum
truth of its presuppositions, and so on, then the proper
result Is automatic. This follows because whenever the
minimum truth of the presupposing sentence is higher, the
minimum value of its presuppositions is higher, since the
latter are lower bounded by the truth of the presupposer.
Thus a simple recursive algorithm such as Figure (2) is
capable of representing the observed facts.

In Figure (2), the matrix sentence is denoted P(0),
the primary presupposition as P(l), and so on. The process
represented in the flow diagram is: (1) determine the
immediate presupposition; (2) using the truth of the

presupposer as the lower bound, with regard to the strength

63

 

 

 

P(O) = T

(I

i t 1

 

 

 

 

 

 

 

’ i a i+1

 

 

 

 

 

 

 

find P(i)
v
t(P(i)) . s(i)(1 t(P(i - 1))) + t(P(i - ))

 

 

 

 

 

 

 

no P(i) yes

0 g divide- g
V

Figure (2): Hypothetical routine for computing the minimum

truth for satisfaction of the presuppositions of a sentence
T. "t(x)" means "minimum truth of x"; "s(i) means "degree

of semi-entailment at level i."

 

'i

 

6B

of the presupposer, compute the minimum truth of the
.immediate presupposition by adding a pr0portion of the
difference between the minimum truth of the presupposer and
1 to the minimum truth of the presupposer; and (3) if the
presupposition has presuppositions, go on to the the next
level, otherwise exit.

In this chapter we have examined certain fuzzy
relations between sentences. Motivated by evidence from
Chapter Three, we changed the definition of semi-entailment,
presupposition, and full entailment from the initial forms
in Chapter One. We explicitly define the notion "valve,"
introduced In Chapter Three, and used this concept to
motivate the abandonment of "internal negation" as a useful
natural logic concept. Finally, we suggest a means of
accounting for an increase in strength of semi-entailment
for higher order presuppositions using a simple recursive

process 0

65

NOTES TO CHAPTER FOUR

1. This is based upon G. Lakoff's (1972) treatment of
material implication in a fuzzy system:
"P-->Q" will hold in all cases where there is a real

logical implication relation between P and O, that is,
where it is necessarily the case that [the truth of E)

g [the truth of Q] .

2. See Haviland and Clark (197k) for some remarks on
real-time processing of simple presuppositions.

Chapter Five

SUMMARY AND DISCUSSION

The aim of this thesis has been to demonstrate that
nondiscrete variation occurs in the interaction of the
semantic relations "presupposition" and "negation." To do
this, first the terms were defined in a manner roughly
reflecting their current usage, but in a way which was
internally consistent, allowing a careful examination of the
interaction between them, and the theoretical implications
of this interaction. Part of this defining involved making
explicit the distinctions internal/external negation, full
and semi- entailment, and pragmatic and logical
presupposition.

Next, it was shown that contradiction can be indirect;
that Is, it can result from the conjunction of some
proposition and the negation of some semi-entailment of the
proposition. Also, it was shown that contradiction is not
categorical; that is, it is possible for there to be
different degrees of contradiction. Finally a test, called
the causal contradiction test, was defined. This test
involves conjoining a negated proposition and a negation of
one of its presuppositions, using a "causal" conjunction
(so, since, because). The resulting degree of Indirect
contradiction was used to examine the status of negation and

presupposition as discrete phenomena.

65

67

The first result was the finding that there are
differences between different surface presupposers (e.g.
cleft, pseudocleft, factives, semi-factives, and
possessives) in tenns of the degree of contradiction
resulting from the causal contradiction test. This result
was interpreted as showing that there are differences in the
strength of presuppositions resulting from different
presupposers.

The next result was the similar finding that there are
differences in degree of contradiction resulting from the
test due to surface negator. That is, some negations seem to
diminish the presuppositions of a sentence to a greater
degree than do others. Following the plumbing analogy of
Karttunen (1970), who referred to internal negation as a
"hole" (presuppositions of the complement pass freely into
the matrix sentence), and to external negation as a "plug"
(presuppositions of the complement are blocked), the data
were interpreted as indicating that negation seems to be
more like a valve. This means that some negators are
relatively open (to lower presuppositions) and some are
relatively closed, but there are many degrees in between
these two endpoints.

The final result was the finding that when a
presupposition is presupposed by presuppositions, its
strength ls increased. This was accounted for formally by
means of a top-to-bottom recursive process which determines

the minimum degree of truth for each presupposition of a

68

sentence (Figure 2).

There might be disagreement with some of the facts
presented in support of the analysis, but it is only
necessary to find a single instance of nondiscrete variation
concerning one of the variables to prove that such variation
exists. It is believed that more than ample evidence has
been presented to support this thesis.

What is Interesting, especially in the light of a
burgeoning trend toward functional explanation in
linguistics, is to speculate about the role that this
nondiscreteness might play in the actual use of language for
communication.

One implication of the process in Figure 2 for
assigning degrees of truth to the presuppositions of the
sentence is that perhaps the truth value of presuppositions
(and, one might add, especially of deeper presuppositions)
is usually unimportant to the understanding of the sentence.
That Is, it might be the case that the normal function of
presupposition is to identify the location of some mental
storage so that the stored information might be accessed,
allowing the new information (or, in the case of speech acts
with other than declarative force, speaker propositional
attitude), to be added to (or conflated with) the store.
There is experimental evidence for this position (at least
for simple presuppositions). For example, Haviland and
Clark (197k) report that it takes less time to understand a

sentence if the presuppositions are known than if they are

69

not. That is, if Tom happens to know that Sue has a
brother, it would take him less time to understand the
sentence (said by Sue) "My brother has red hair" than if he
did not have this information. Haviland and Clark dub this
(and other related phenomena) the "given-new contract."
This implies that in normal conversation, the speaker
follows a convention (or "contract") to mark as presupposed
(by clefting, pseudoclefting, use of anaphora, etc.) only
material which he believes is shared by both himself and
the bearer. This contract allows the hearer to disregard
the content of the presupposed portion of the utterance,
except as an indication of reference and topic, speeding
comprehension of the sentence. Given this analysis, the
present results lead to several predictions.

First, it seems that the results with embedded
presuppositions show that deeper presuppositions may be
processed (for truth value) only after all less embedded
presuppositions (and the nonpresupposed material). That is,
when presuppositions are more deeply embedded in the
presuppositionai structure of the sentence, they are marked
(in the above sense) as being believed more "given" (in some
sense) by the speaker. Since the bearer is following the
given-new strategy, he will tend to "take the speaker's word
for it" unless there is some indication to the contrary.
This prediction can be tested by application of the
Haviland-Clark methodology, which involves measuring

comprehension time tachistoscoplcally.

70

Second, there needs to be some way for the speaker to
indicate to the bearer that he is not following the
contract. That is, even though there is some presupposer in
the sentence, it is not the speaker's intention to imply
that he believes its presuppositions. This might be the
function of what Karttunen (1970) calls "plugs." The
present results on negation suggest that the function of the
differences in presupposition-cancelling by the various
negators might be to indicate the level of belief in the
presuppositions of a sentence held by the speaker. For
example, a relatively plug-like negator (like "it is not the
case that...") would indicate that the speaker is saying the
sentence, but does not necessarily go along with its
presuppositions. The prediction in this case is that it
would take longer to understand such sentences than
sentences with relatively hole-like negators, and also for
the former that pre-knowledge of the "presupposed" material
would not speed comprehension time. This predication also
seems amenable to testing using the Haviland-Clark paradigm.

Another area which seems relevant to the examination
of the function of presuppositionai nondiscreteness is
politeness. Attempts have been made to develop
semantic/pragmatic explanations of intuitions about level of
conventional politeness in requests (see R. Lakoff 1973 and
B. Mohan 197k). However, these attempts have not been
totally satisfactory (in our opinion) due to the essential

nondiscreteness of politeness judgments and the lack of a

71

fuzzy theoretical apparatus in semantics and pragmatics.

For example, consider the following indirect requests:

(1) a. Can you sweep the floor?
b. Can't you sweep the floor?

c. You can sweep the floor.

Clearly, the conventional politeness decreases from (1a) to
(1c). How is this fact to be accounted for?

Gordon and Lakoff (1971) state that one way to
conversationally convey a request is by questioning a
bearer-based sincerity condition (in our framework,
sincerity conditions are pragmatic presuppositions). One

such condition is

(2) The hearer is able to carry out the request.

That Is, a request cannot be sincere unless the speaker
believes the bearer is able to carry it out. Both (1a) and
(1b) question (2). Normally one does not ask questions
about that for which he already knows the answer (or at
least does not ask such questions sincerely). Thus since
the speaker indicates by the question that he does not know
the answer, and indicates by the fact that he is making a
request that he does know it, it seems that (1a&b) are
paradoxical. That is, they must be insincere If they are to

be sincere. This account, which seems to follow from the

72

consideration of sincerity conditions on questions and on
requests, is clearly flawed, since no one would judge (1a&b)
as either necessarily insincere or as paradoxical. The
explanation of this state of affairs comes from
consideration of the function of asking questions to convey
requests. Questions, as was pointed out above, normally
pragmatically presuppose that the speaker does not know the
answer. But it is possible for different types of questions
to indicate different levels of sureness about the answer.

This is shown by the different degrees of contradiction in

(3) I don't think you can do it, but
a. you can sweep my floor.
b. can't you sweep my floor?

c. can you sweep my floor?

That is, (3a), a nonquestion, is more contradictory than
(3b), and (3b) is more contradictory than (3c). Now, if (2)
is false, it is possible for the bearer to refuse the
request with no impoliteness at all. This suggests that the
function of question-requests of the type in (1) could be to
make the request less strongly, leaving the hearer a way (at
least nominally) out of doing the request without actually
refusing to c00perate. And further, the function of the
negative question seems to be to weaken the pragmatic
presuppositons of the requests, but not to the degree of

nonnegative questions.

73

The research reported here, then, seems to provide a
means to examine some of the traditional problems of
linguistic description from a broader base. Now it appears
possible to discuss questions and explanations which would
have been much harder to consider under previous accounts.
While this seems to represent genuine progress, it is not an
endpoint, but only a rung in the ladder which hopefully will

lead us to an adequate theory of grammar.

Appendix
ALTERNATE DEFINITIONS

As was pointed out in the preliminary remarks to
Chapter Two, there exists a certain amount of confusion
concerning terminology In the literature. What follows is a
list, by no means complete, of definitions given by various
writers for some of the concepts we have been discussing
here. The purpose of this Appendix is to allow the reader
to relate the findings of the thesis to other viewpoints
concerning semantic relations. Some of the definitions were
garnered from secondary sources, as noted.

SEMI-ENTAILMENT

Horn (1972) p. 11

Semantic entailment: P I- Q =df Q is true under every
assignment of truth values (i.e., In every possible world)
under which P is true.

Givon (1973) p. 99

An implicative verb is a verb implying the truth of its
complement . . . a negative implicative verb implies the
falsity of its complement.

Karttunen (1970) p. 58
P I) Q iff whenever it is true that P, it is true that Q.

_______ (1971b) p. 6
P implies Q iff whenever P is asserted, the speaker ought to
believe that Q.

(1973b) p. 177
A semantically entails 8 iff B is true . . . whenever A is
true.

Keenan (1971) p. 255

A sentence is a logical consequence of (logically implied
by) a sentence 8' just in case S is true under all the
conditions under which 5' is true.

FULL ENTAILMENT

Austin (1962) p. #7, #9

"All men blush" entails "some men blush" . . . if p entails
q then -q entails -p: if "the cat is on the mat" entails
"the mat is under the cat," then "the mat is not under the
cat" entails "the cat is not on the mat."

Horn (1969) p.98
If (S ---> S') and ("S' ---> ‘8) then S II- 8'.

7h

75

PRESUPPOSITION (LOGICAL)

Austin (1962) p. 50

Both "John's children are bald" and "John's children are not
bald" presuppose that John has children . . . the statement
that "John's children are bald," if made when John has no
children . . . (is usually said to be) not false because it
is devoid of reference . . . the utterance is void.

Chomsky (1972) p. 100 ff
The truth of the presuppositions is a prerequisite for the
utterance to have a truth value.

Givon (1973) p. 105
Neg-factive verbs . . . presuppose the falsity of their
complements.

Horn (1969) p. 98
If (S ---> S') and ("S ---> S') then S >) S'.

(1972) p. 12
P >> Q =df (P I- Q) A ("P I- Q). (see Horn's definition of
"I-" above)

Frege (1892) p.69(*)

if anything is asserted there is always an obvious
presupposition that the simple or compound proper names
(i.e., all singular referring expressions or definite
descriptions: Garner's note) used have a reference.

Karttunen (1970) p. 67 ff 8

A presupposes B iff M(A) I) B & M("A) I) B. (M is the modal
possibility operator. See Karttunen's definition for I>
above.)

Keenan (1971) p. 256

A sentence S is a logical presupposition of a sentence 8'
just in case S is a logical consequence of S' and also a
logical consequence of the logical denial of 8'. (See
Keenan's definition for "logical consequence" above. No
definition given for "logical denial.")

Van Fraasen (quoted in Karttunen 1973 p. 169)
Sentence A semantically presupposes another sentence 8 just
in case B is true whenever A is true or false.

Strawson (1952) p. 207-8 (*)
A statement S presupposes a statement 3' iff the truth of S'
is a precondition on the truth or falsity of S.

76

PRAGMATIC PRESUPPOSITION

Austin (1962) p. B8
My saying "the cat is on the mat" implies that I believe it
is.

Chomsky (1972) p.100

In many cases it seems that . . . the focus is a phrase
containing the the infonmation center, the presupposition is
an expression derived by replacing the focus with a
variable.

Fillmore (1971) p. 380
The presuppositions of a sentence . . . (are)

. . . those conditions which must be satisfied before the
sentence can be used . . . (for asking questions, giving
commands, making assertions, etc.)

Givon (1973) p. 105 .
A person using a factive verb presupposes the truth of its
complement.

Heringer (1971) p. 73

. . . A speaker performing a propositional act presupposes
. . . for a speaker to presuppose something is for him
necessarily to believe that another proposition is true.

Jackendoff (1972) p.73

. . . information in the sentence that is assumed by the
speaker to be shared by him and the bearer (is the
presupposition of the sentence).

Karttunen (1971b) p.3
P presupposes Q just in case that if P is asserted, denied
or questioned, then the speaker ought to believe that Q.

(1973a) p. 1
Sentence A pragmatically presupposes sentence B iff A can be
felicitously uttered only in contexts that entail B.

(1973b) D. 169-70

. . . "The sentence pragmatically presupposes B" can be
understood as an abbreviation for ". . . whenever A is
uttered sincerely, the speaker of A . . . assumes B and
believes that his audience assumes B as well."

 

Keenan (1971) p. A9
A utterance of a sentence pragmatically presupposes that its
context is appropriate.

G. Lakoff (1972) 9. 1h
SINCERE(x, STATE(x, y, P)) --> BELIEVE(x, P)

77

Sellars (195B) p. 207-8 (*)

An utterance of "the table over here is large" does indeed
presuppose that there is one and only one table "over here."
To say that the utterance presupposes this is to say that it
is correct to make the utterance . . . only if one believes
there is to be one and only one table "over here" and that
this belief is shared by the listener. Furthermore, to say
"that's false" when told that the table is large equally
presupposes that the uniqueness condition is satisfied:
where this in turn means that it is correct to say "that's
false" only if one believes the uniqueness condition to be
satisfied and that the original speaker shares this belief.
But even though the original utterance and the reply
presuppose that the uniqueness condition is satisfied, the
utterance is nevertheless false if the uniqueness condition
is not satisfied even though it is not correct to say it is
false unless one believes that the condition is satisfied.

*Note: the quotations from Frege, Strawson, and Sellars were
taken from Garner (1971).

REFERENCES

Austin, J. L. (1962) How to Do Things with Words. New York.
Oxford University Press.

Borkin Ann (1971) "Polarity items in Questions," Papers from
the 7th Regional meeting of the Chicago Linguistic
Society. pp. 53-62.

Carden, Guy (1970) "A Note on Conflicting ideolects,"
Linguistic inquiry, I, pp. 32-h0.

(1972) "Multiple Dialects in Multiple Negation,"
Papers from the 8th Regional Meeting of the Chicago
Linguistic Society, pp. 32-uo.

Chomsky, N. (1965) Aspects of the Theory of Syntax.
Cambridge, MIT Press.

 

(1972) "Deep Structure, Surface Structure, and
Semantic Interpretation," in (1972) Studies in
Semantics in Generative Grammar. The Hague, Mouton,
pp. 62-119.

 

Cedargren, Henrietta (1972) "On the Nature of Variable
Constraints" (n.s.)

, and David Sankoff (197k) "Variable Rules: Performance
as a Statistical Reflection of Competence," Language
50 (2) pp. 333-55.

 

Clark, H. H. (1973) "Comprehension and the Given-New
Contract," Paper prepared for the conference on "the
role of grammar in interdisciplinary language
research," U. Bielefield, Germany.

Fillmore, C. J. (1971) "Verbs of Judging," in _____J and D.
T. Langendoen, eds, Studies in Linguistic Semantics.
New York: Holt, Rinehart, and Winston, pp. 273-91

 

Frege, G. (1892) "Ueber Sinn und Bedeutung," translated in
Feigl, H. and W. Sellars, eds, Readings in
Philosophical Analysis. New York, pp. 85-102.

 

Garner, R. (1971) "'Presupposition' in Phii050phy and
Linguistics," in Fillmore, C.J., and D. T.
Langendoen, eds, Studies in Linguistic Semantics. New
York, Holt, Rinehart, and Winston, pp. 23-uu.

78

79

Givon, T. (1972) "Forward Implications, Backward
Presuppositions, and the Time Axis of Verbs," in
Kimball, J. (1972) Syntax and Semantics, Volume One.
New York, Seminar Press, pp. 29-50.

(1973) "Opacity and Reference in Language," in
Kimball, J. (1973) Syntax and Semantics, Volume Two.
New York, Seminar Press, pp. 95-122.

Gordon, D. and G. Lakoff (1971) "Conversational Postulates,"
Papers from the 7th Regional Meeting of the Chicago
Linguistic Society, Dp. 63-8h.

Haviland, S. E. and H. H. Clark (197A) "What's New?
Acquiring New 'lnformation as a Process in
Comprehension." (n.s.)

Heringer, J. T. (1971) Some Grammatical Correlates of
Felicity Conditions. Ohio State U. dissertation.

Horn, L. R. (1969) "A Presuppositional Analysis of 'only'
and 'even'," Papers from the 5th Regional Meeting of
the Chicago Linguistic Society, pp. 98-107.

(1970) "Ain't it hard (anymore)," Papers from the 6th
Regional Meeting of the Chicago Linguistic Society,
pp. 318-27.

 

(1972) On the Semantic Properties of Logical Operators
in English. UCLA dissertation.

Jackendoff, R. S. (1972) Semantic Interpretation in
Generative Grammar. Cambridge, MIT Press.

Karttunen, L. (1970) "Some Observations on Factivity," paper
read at the 1970 Winter LSA meeting.

(1971a) "Counterfactual Conditionals," Linguistic
inquiry ii (A) pp. 566-9.

(1971b) "The Logic of English Predicate Complement
Constructions," Indiana U. Linguistics Club mimeo.

(1973a) "Possible and Must," in Kimball, J (1973)
Syntax and Semantics, Volume Two. New York, Seminar
Press, pp. 1-20.

(1973b) "Presuppositions of Compound Sentences,"
Linguistic Inquiry IV (2) pp. 169-9u.

80

Katz, J. J. (1973) "On Defining 'Presupposition',"
Linguistic Inquiry iV (2) pp. 256-60.

Keenan, E. L. (1971) "Two Kinds of Presupposition in Natural
Language,” in Fillmore, C.J., and D. T. Langendoen
(1971) Studies in Linguistic Semantics. New York,
Holt, Rinehart, and Winstion, pp. AS-Sh.

Kiparsky, P., and C. Kiparsky (1971) "Fact," in D. Steinberg
and L. Jakobovits, (1971) Semantics: An
Interdisciplinary Reader. pp. 3h5-69.

Laberge, S. (1972) Changement dans l'Usage des Pronoms
lndefinis chez les Montrealais. U. Montreal
dissertation.

Labov, W. (1972a) Sociolinguistic Patterns. Philadelphia, U.
Pennsylvania Press.

(1972b) "For an End to the Uncontrolled Use of
Linguistic intuitions," paper read at the Winter LSA
meeting in Atlanta.

Lakoff, G. (1970) "Linguistic and Natural Logic," Synthese
22, pp. 151-271.

(1972) "Hedges: A Study in Meaning Criteria and the
Logic of Fuzzy Concepts," Papers from the 8th
Regional Meeting of the Chicago Linguistic Society,
pp. 183-2280

 

(1973a) "Fuzzy Grammar and the Performance/Competence
Terminology Game," Papers from the 9th Regional
Meeting of the Chicago Linguistic Society, pp.
271-91.

 

(1973b) "Pragmatics in Natural Logic," paper delivered
at the Texas Conference on Performatives,
lmplicatures, and Presuppositions, Austin.

 

Lakoff, R. (1969) "Some Reasons Why There Can't Be Any
some-any Rule," Language AS (3), pp. 608-15.

(1970a) "Questionable Answers and Answerable
Questions," to appear in Papers in Linguistics in
Honor of Henry and Renee Kahane, ed. by B. Kachru, R.
B. Lees, Y. Malkiel, and S, Saporta.

(1970b) "Tense and its Relation to Participants,"
Language AB (A), pp. 838-h9.

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(1971) "If's, And's, and But's about Conjunction," in
Fillmore, C. J., and D. T. Langendoen, Studies in
Linguistic Semantics. New York, Holt, Rinehart, and
Winston, pp. 115-50.

 

(1972a) "Language in Context" (n. s.)

(1972b) "The Pragmatics of Modality," Papers from the
8th Regional Meeting of the Chicago Linguistic
Society, pp. 229-h6.

 

(1973) "The Logic of Politeness; or, Minding Your P's
and Q's," Papers from the 9th Regional meeting of the
Chicago Linguistic Society, pp. 292-305.

Mohan 8. (197B) "Principles, Postulates, Politeness," Papers
from the 10th Regional Meeting of the Chicago
Linguistic Society, 00. hh6-h59

Quine, W. (1960) Word and Object. Cambridge, MIT Press.

Ross, J. R. (1972) "Doubl-ing," Linguistic Inquiry iII (1)
pp. 61-86.

(1973) "A Fake NP Squish," NWAVE I, pp. 96-1h0.

Searle, J. R. (1971a) ed, The Philosophy of Language.
London, Oxford U. Press. T

 

(1971b) "What is a Speech Act," in Searle op cit, pp.
3q-530

Sellars, W. (195h) "Presupposing," Philosophical Review 63,
pp. 197-215.

Shenaut, Greg, and Judy Warren (1973) "Presuppositional
Downs," paper read at the MLS meeting in Kalamazoo.
Forthcoming in the papers from that meeting.

Shenaut, Greg (197A) "Circumlocutionary Acts," paper read at
the Summer LSA meeting, Amherst.

(1975) "Valves: Plumbing the Presuppositional Depths
(or, What's a Plug Like You Doing in a Hole Like
This?)," paper read at the 11th Regional Meeting of
the Chicago Linguistic Society. Forthcoming in the
papers from the meeting.

 

Spencer, N. J. (1972) "Differences between Linguists and
Non-Linguists in Intuitions of Grammaticality-
Acceptability," Paper read at the Winter LSA meeting
in Atlanta.

82

Stokes, W. (197k) "All of the Work on Quantifier-Negation
isn't Convincing," Papers from the 10th Regional

Meeting of the Chicago Linguistic Society, pp.
692-700.

Strawson, P. (1952) Introduction to Logical Theory. London.

Wilson, D. (1972) "Presuppositions on Factives," Linguistic
Inquiry Ill (3), pp. ABS-10.

(1973) Public dissertation defense, MIT.

 

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