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ARISTOTLE ON TRUTH




Aristotleā€™s theory of truth, which has been the most inļ¬‚uential account
of the concept of truth from Antiquity onwards, spans several areas
of philosophy: philosophy of language, logic, ontology, and episte-
mology. In this book, the ļ¬rst dedicated to this topic, Paolo Crivelli
discusses all the main aspects of Aristotleā€™s views on truth and false-
hood. He analyses in detail the main relevant passages, addresses some
well-known problems of Aristotelian semantics, and assesses Aristotleā€™s
theory from the point of view of modern analytic philosophy. In the
process he discusses most of the literature on Aristotleā€™s semantic
theory to have appeared in the last two centuries. His book vindi-
cates and clariļ¬es the often repeated claim that Aristotleā€™s is a corre-
spondence theory of truth. It will be of interest to a wide range of
readers working in both ancient philosophy and modern philosophy
of language.

paolo c ri vell i is Fellow and Tutor in Classical Philosophy at
New College, Oxford. He has published articles on Platoā€™s logic and
epistemology, Aristotleā€™s philosophical logic, and Stoic logic.
A R I S TOT L E O N T RU T H

PA O L O C R I V E L L I
University of Oxford
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, SĆ£o Paulo

Cambridge University Press
The Edinburgh Building, Cambridge cb2 2ru, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521823289

Ā© Paolo Crivelli 2004


This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.

First published in print format 2004

isbn-13 978-0-511-23002-8 eBook (EBL)
isbn-10 0-511-23002-8 eBook (EBL)

isbn-13 978-0-521-82328-9 hardback
isbn-10 0-521-82328-5 hardback




Cambridge University Press has no responsibility for the persistence or accuracy of urls
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
To the memory of my father
Renzo Crivelli
and to my mother
Katherine Lester Crivelli
Contents




Acknowledgements page ix
Notes on the text x
List of abbreviations of titles of Aristotleā€™s works xi

Introduction 1
1 An overview of Aristotleā€™s theory of truth 1
2 Methodology 39


pa rt i be a rers of tru th or fa ls e h o od
1 States of affairs, thoughts, and sentences 45
1 States of affairs 46
2 Thoughts 62
3 Sentences 72

2 Truth conditions for predicative assertions 77
1 Universals 78
2 Truth and falsehood in de Interpretatione 1 82
3 Afļ¬rmative and negative predicative assertions 86
4 Assertions about individuals vs assertions about universals 89
5 Truth and the categories 95

3 Truth conditions for existential assertions 99
1 Existential assertions concerning simple items 100
2 Non-composite substances 116
3 Singular existential assertions concerning material substances 121


pa rt ii ā€˜e mp t y ā€™ terms
4 Truth as correspondence 129
1 A correspondence theory of truth? 129
2 The Liar 139

vii
viii Contents
5 ā€˜Vacuousā€™ terms and ā€˜emptyā€™ terms 152
1 ā€˜Vacuousā€™ subjects or predicates 153
2 ā€˜Emptyā€™ subjects or predicates 158
3 One assertion vs many assertions 163


part iii t ru th a nd ti me
6 Truth and change 183
1 Different truth-values at different times 183
2 Truth and relatives 189
3 How far is truth from change? 194

7 Truth and Determinism in de Interpretatione 9 198
1 The modal attributes and theses involved in Int. 9 199
2 Close textual analysis of Int. 9 200
3 Alternative interpretations 226


10, 1051b 1: the text
Appendix 1 Metaph. 234
10, 1051b 2ā€“3: the text
Appendix 2 Metaph. 238
Int. 7, 17b 16ā€“18: the text
Appendix 3 239
Appendix 4 The two-place relations in Aristotleā€™s
deļ¬nition of truth 254
Appendix 5 Aristotleā€™s theory of truth for predicative
assertions: formal presentation 258
Appendix 6 The failure of Bivalence for future-tense
assertions: formal presentation 266

References 284
Index of names 313
Index of subjects 319
Index of passages 321
Acknowledgements




Many friends and colleagues helped me to shape my views on many of the
issues addressed by this study, and alerted me to points where improvement
was desirable. Early drafts of parts of the book were presented in Cambridge,
Clark, Edinburgh, Florence, Liverpool, Oxford, and Pisa. Among the indi-
viduals who in various ways helped me to bring this project to completion,
I should like to mention Francesco Ademollo, Francesco Adorno, Fab-
rizio Amerini, Sylvia Berryman, Susanne Bobzien, Ettore Casari, Walter
Cavini, David Charles, Francesco Del Punta, Paolo Fait, Michael Frede,
Gabriele Galluzzo, Richard Gaskin, Katerina Ierodiakonou, Fred Miller,
Peter Milne, Ben Morison, Massimo Mugnai, David Robinson, Gonzalo
Rodriguez-Pereyra, Theodore Scaltsas, Annamaria Schiaparelli, David Sed-
ley, Bob Sharples, Robin Smith, Christopher Strachan, John Thorp, Tim
Williamson, and an anonymous referee for Cambridge University Press.
The responsibility for the remaining shortcomings is of course mine alone.




ix
Notes on the text




ā€˜LSJā€™ abbreviates the Liddell, Scott, Jones Greekā€“English lexicon.
I refer to Aristotelian passages by the line numbers as they are printed in
Bekkerā€™s original edition: these in some cases differ from the ā€˜Bekker linesā€™
of widespread editions (e.g., 101b 38 of Rossā€™s edition of the Topics is 101b 39
of Bekkerā€™s original edition). Similarly, I follow Bekkerā€™s numbering of the
chapters within each book of the Nicomachean Ethics.
For Greek authors I use LSJā€™s standard abbreviations. For authors other
than Aristotle, I normally use the critical editions on which LSJ relies. For
Latin authors, I employ abbreviations which are easy to decode and I use
standard critical editions.
ā€˜Cf.ā€™ at the beginning of a footnote indicates that the passages subse-
quently referred to express views close to those formulated in the portion
of the main text to which the footnote pertains. If I disagree with an author,
I say so explicitly (I never use ā€˜cf.ā€™ to refer to one or more passages that for-
mulate views with which I disagree).
I use quotation marks for three purposes: (i) to mention linguistic expres-
sions, e.g. the word ā€˜dogā€™ is a noun; (ii) to indicate that a certain linguistic
expression is being used in some special or unusual sense, e.g. Homer is a
ā€˜philosopherā€™; (iii) to quote a portion of text from some author, e.g. Aristo-
tle says that ā€˜sentences are true in the same way as the objectsā€™ (Int. 9, 19a 33).
I use double quotation marks (ā€œandā€) only when what would otherwise be
occurrences of single quotation marks would be embedded within single
quotation marks.




x
Abbreviations of titles of Aristotleā€™s works




APo. Posterior Analytics
APr. Prior Analytics
Cael. de Caelo
Cat. Categories
de An. de Anima
Div. Somn. de Divinatione per Somnia
EE Eudemian Ethics
EN Nicomachean Ethics
GA de Generatione Animalium
GC de Generatione et Corruptione
HA Historia Animalium
Insomn. de Insomniis
Int. de Interpretatione
Long. de Longaevitate
MM Magna Moralia
Mem. de Memoria
Metaph. Metaphysics
PA de Partibus Animalium
Ph. Physics
Po. Poetics
Pol. Politics
Pr. Problems
Rh. Rhetoric
SE Sophistici Elenchi
Sens. de Sensu
Somn. Vig. de Somno et Vigilia
Top. Topics
Xen. de Xenophane



xi
Introduction




The study of truth is a central part of the philosophical tradition we have
inherited from classical Greece. Aristotle played an important role in devel-
oping and sharpening the debate in this area and on many issues that are
connected with it. I have two primary goals: to offer a precise reconstruction
of all of Aristotleā€™s most signiļ¬cant views on truth and falsehood and to gain
a philosophical understanding of them. In this introduction I ļ¬rst offer an
overview of Aristotleā€™s theory of truth and then discuss the methodology I
adopt in pursuing my primary goals.

1 a n overview of a ristot le ā€™s th eory of t ru th
Why an overview? Aristotle speaks about truth and falsehood in passages
from several works, mainly the Categories (chapters 4, 5, 10, and 12), de Inter-
pretatione (chapters 1ā€“9), Sophistici Elenchi (chapter 25), de Anima (chapter
3.6), and the Metaphysics (chapters 7, 7, 29, E 4, and 10). Truth
and falsehood are not the main topic of these works: their discussions of
truth and falsehood are asides. Reconstructing an Aristotelian theory of
truth and falsehood on the basis of such asides poses complicated problems
of various sorts. To help readers to keep their orientation through the many
bifurcations of the arguments addressing these problems, I decided to offer
a concise but precise map of the territory ā€“ an overview of Aristotleā€™s theory
of truth. References to the passages from Aristotleā€™s works that substantiate
the attribution of a certain view to him, and an examination of the rel-
evant secondary literature, will be found in the chapters that follow this
introduction.

Universals. To expound Aristotleā€™s theory of truth, I need to present some
of his views on universals and signiļ¬cation. I begin with universals.
Luckily, it is not necessary to embark on the daunting task of a com-
plete exposition of Aristotleā€™s views on universals. Aristotle is to this extent
1
2 Introduction
a realist about universals: in his view, universals are objects whose nature
is neither mental nor linguistic (they are neither concepts nor linguis-
tic expressions). He believes that every universal exists when and only
when1 it holds of some individual or other that at some time or other
exists.2
Let me spend a few words explaining why the phrase ā€˜at some time or
otherā€™ is needed. According to Aristotle, some universals sometimes hold
of individuals that do not exist then, but exist at other times. For example,
Aristotle seems to think that at any time the universal poet3 holds of all
and only those individual human beings (including those who at that time
do not exist) who by that time have authored some poem. In particular,
Aristotle would probably grant that although Homer does not exist now,
the universal poet holds now of Homer. It is because of universals of this
sort that the phrase ā€˜at some time or otherā€™ is needed.
Aristotle is likely to believe that every universal is everlasting, i.e. exists
always. Hence he is likely to be committed to the view that every universal
at all times holds of some individual or other that at some time or other
exists ā€“ in short, that all universals are always instantiated. This of course
leaves the possibility open that every individual that at some time or other
exists and of which a certain universal holds at one time could be other than
every individual that at some time or other exists and of which the same
universal holds at a certain other time ā€“ in short, the possibility remains that
some universal could be instantiated by different individuals at different
times.

Signiļ¬cation. I now move on to expound some of Aristotleā€™s views on signi-
ļ¬cation. Aristotle thinks that some utterances of certain noun-phrases and
certain adjectival phrases signify a single universal: e.g. he would grant that
some utterances of ā€˜manā€™ signify the universal man and that some utterances
of ā€˜whiteā€™ signify the universal white. He also thinks that some utterances
of certain noun-phrases signify a single individual: e.g. he would grant that
some utterances of ā€˜Socratesā€™ signify Socrates, the Athenian philosopher
executed in 399 bc. However, he believes that some utterances of certain

1 I use ā€˜when and only whenā€™ in a strictly temporal sense, i.e. as equivalent to ā€˜at all and only the times
at whichā€™.
2 I use ā€˜to hold of ā€™ to express the relation of a universal to its instances. Following Aristotleā€™s lead, I
sometimes use ā€˜to be predicated of ā€™ to express this same relation.
3 I normally refer to a universal by simply using a linguistic expression that signiļ¬es it (if this linguistic
expression is a phrase, I hyphenate it); I avoid referring to a universal by italicising, or enclosing in
quotation marks, a linguistic expression that signiļ¬es it. For example, I normally refer to universals
by means of expressions like ā€˜the universal poetā€™ or ā€˜the universal man-who-authored-a-poemā€™; I avoid
referring to universals by means of expressions like ā€˜the universal poetā€™ or ā€˜the universal ā€œpoetā€ā€™.
Introduction 3
noun-phrases and some of certain adjectival phrases signify neither a single
universal nor a single individual: e.g. he would concede that some utter-
ances of ā€˜walking white manā€™ or ā€˜walking, white, and tallā€™ signify neither
a single universal nor a single individual (he would claim that each of
these utterances signiļ¬es many universals which do not coalesce in a single
universal).

What can be true or false? Having presented Aristotleā€™s views on universals
and signiļ¬cation that are necessary to understand his theory of truth, I am
in a position to begin addressing the main themes of the latter. Let me start
with Aristotleā€™s conception of the bearers of truth or falsehood.
According to Aristotle, items that are true or false are of three main
kinds: sentences, thoughts, and certain objects whose nature is neither
mental nor linguistic. The sentences that are true or false are sentence-
tokens, utterances, events of speech that occur over relatively short portions
of time. Similarly, the thoughts that are true or false are thought-tokens,
either mental events that occur over relatively short portions of time or
thinker-individuated mental states.
For Aristotle, events of perceiving and imagining also are true or false.
Events of perceiving and imagining fall under none of the three kinds I just
mentioned: they are neither thoughts, nor sentences, nor objects whose
nature is neither mental nor linguistic. Since Aristotleā€™s views on the truth
and falsehood of events of perceiving and imagining are somewhat isolated
from the rest of his reļ¬‚ection on truth and falsehood, in this introduction
I shall say nothing more about them.

A puzzling view. A particularly puzzling part of Aristotleā€™s theory of truth is
his view that among items that are true or false there are objects (I sometimes
use ā€˜objectā€™ to mean ā€˜object whose nature is neither mental nor linguisticā€™:
I trust that the context will make it clear whether a given occurrence of
ā€˜objectā€™ is to be understood in this narrow sense). On this point Aristotleā€™s
theory of truth is radically different from some modern ones: modern
philosophers are ready to acknowledge that certain thoughts or sentences
are true or false, but some of them would jib at the suggestion that some
objects are true or false.
These objects that are true or false occupy a central position in Aristotleā€™s
theory of truth. What are they? What roles do they play in Aristotleā€™s theory
of truth?

What are the objects that are true or false? Aristotle distinguishes two kinds
of objects that are true or false: composite objects and simple objects.
4 Introduction
Some composite objects that are true or false are states of affairs.4 A state
of affairs, which is an object, is composed of two further objects: one of the
objects of which it is composed is a universal, the other is either a universal or
an individual. A state of affairs is true when and only when the objects of
which it is composed are reciprocally combined in the relevant way; it is
false when and only when the objects of which it is composed are recip-
rocally divided in the relevant way.5 For example, the state of affairs that
Socrates is seated is composed of the universal seated and of the individual
Socrates; it is true when and only when the universal seated is combined in
the relevant way with Socrates, i.e. when and only when Socrates is seated;
it is false when and only when the universal seated is divided in the relevant
way from Socrates, i.e. when and only when Socrates is not seated. Again,
the state of affairs that every diagonal is commensurable is composed of
the universal commensurable and of the universal diagonal; it is true when
and only when the universal commensurable is combined in the relevant
way with the universal diagonal, i.e. when and only when every diagonal is
commensurable; it is false when and only when the universal commensu-
rable is divided in the relevant way from the universal diagonal, i.e. when
and only when some diagonal is not commensurable. Since no diagonal
ever is commensurable, the state of affairs that the diagonal is commensu-
rable is never true but always false. Aristotle allows only ā€˜afļ¬rmativeā€™ states
of affairs: among states of affairs there are the state of affairs that Socrates
is seated and the state of affairs that every diagonal is commensurable, but
there is not a state of affairs that Socrates is not seated nor is there one that
not every diagonal is commensurable. In principle, a state of affairs can
exist at a time when it is false, i.e. at a time when the objects of which it
is composed are reciprocally divided in the relevant way. For example, the
state of affairs that Socrates is seated exists at certain times when it is false;
again, the state of affairs that every diagonal is commensurable always exists
and is always false. The combination that makes a state of affairs true is not
to be confused with the composition whereby the state of affairs is com-
posed of further objects. By the same token, the division that makes a state
of affairs false does not destroy the composition whereby the state of affairs
is composed of further objects (otherwise the state of affairs could not, even
in principle, exist at any time when it is false). For example, the state of

4 ā€˜State of affairsā€™ can be used in several senses. I use it to denote objects of a ā€˜propositionalā€™ nature of
which it is sensible to say both that they obtain and that they do not obtain at a time.
5 ā€˜To be combinedā€™ and ā€˜to be dividedā€™ are technical expressions. I hope that the examples in this
paragraphā€™s sequel will provide an intuitive grasp of their meaning. They will be discussed in greater
detail later in this introduction.
Introduction 5
affairs that Socrates is seated remains composed of the universal seated and
of the individual Socrates even when the universal seated is divided from
the individual Socrates in such a way as to make the state of affairs in ques-
tion false. It remains unclear whether in Aristotleā€™s view all states of affairs
are everlasting: does Aristotle believe that the state of affairs that Socrates
is seated exists both before and after Socrates exists? A state of affairs, as it
is conceived of by Aristotle, is best understood as an object corresponding
to a complete present-tense afļ¬rmative predicative assertion, and as being
composed of the objects signiļ¬ed by the assertionā€™s predicate and subject.
For example, the state of affairs that Socrates is seated corresponds to the
whole present-tense afļ¬rmative predicative assertion that is an utterance
of ā€˜Socrates is seatedā€™, and is composed of the universal seated, which is
signiļ¬ed by the assertionā€™s predicate (an utterance of ā€˜seatedā€™), and of the
individual Socrates, who is signiļ¬ed by the assertionā€™s subject (an utterance
of ā€˜Socratesā€™).
As I said, some composite objects that are true or false are states of
affairs. According to Aristotle, material substances (e.g. Socrates and the
horse Bucephalus) are composite objects in that they consist of form and
matter. Material substances are not states of affairs, but they resemble states
of affairs in interesting respects: as for a state of affairs to be true is to
be combined, so for a material substance to exist is to be combined, i.e.
it is for its form to be combined with its matter; as for a state of affairs
to be false is to be divided, so for a material substance not to exist is to
be divided, i.e. it is for its form to be divided from its matter. Aristotle
perhaps thinks that material substances rank among the composite objects
that are true or false, that for a material substance to be true is to exist,
and that for a material substance to be false is not to exist. I can use only
the cautious expression ā€˜Aristotle perhaps thinks . . .ā€™ because the evidence
for attributing the position in question to Aristotle is far less than clear cut.
However, independently of whether Aristotle does endorse the position
in question, at least two differences between states of affairs and material
substances are worth noting. First, while some state of affairs exists at times
when it is false, no material substance exists at times when it is false (because,
according to the position in question, for a material substance to be false
is not to exist). Second, although some material substances (i.e. celestial
bodies) are everlasting, most are not; on the other hand, Aristotle does not
state how long states of affairs exist, but his position might well be that all
states of affairs are everlasting.
Since a simple object has no components between which combination
or division could obtain, for a simple object to be true cannot be to be
6 Introduction
combined, nor can for it to be false be to be divided. Rather, for a simple
object to be true is simply to exist, and for it to be false is simply not
to exist. Aristotle distinguishes two kinds of simple objects: essences and
incorporeal substances. Essences are natural kinds (e.g. the kind horse).6
The remaining simple objects, incorporeal substances, are God and (per-
haps) the intellects that move the heavenly spheres.7 The application of
ā€˜trueā€™ to incorporeal substances should not arouse wonder: ā€˜trueā€™ is one of
the epithets traditionally used to speak of God. Both essences and incor-
poreal substances are everlasting, i.e. exist always. Hence, all simple objects
exist always.
The sense of ā€˜trueā€™ and ā€˜falseā€™ whereby they apply to objects is probably
Aristotleā€™s own creation: it is an extension of the ordinary sense of these
expressions which Aristotle introduces in order to construct a better theory
of truth. It is not, however, completely unconnected with ordinary usage:
ā€˜trueā€™ can be used (both in Greek and in English) to mean ā€˜realā€™ (as in ā€˜true
coinā€™), and ā€˜realā€™ is connected with ā€˜existentā€™ (although ā€˜realā€™ and ā€˜existentā€™
are used differently, one can employ the phrase ā€˜the contrast between dreams
and what is realā€™ to describe the discrepancy between what exists and what
someone would like to exist).
Aristotleā€™s views on the nature of the bearers of truth or falsehood can
now be conveniently summarised by the following schema:

bearers of truth or falsehood



sentences thoughts objects whose nature is
neither mental nor linguistic


composite simple


states of material essences incorporeal
affairs substances (?) substances

6 Aristotleā€™s remarks on essence are difļ¬cult to understand and are variously interpreted. The view I am
attributing to Aristotle here, i.e. that essences are natural kinds, is ā€˜minimalā€™ in that it is compatible
with, and perhaps implied by, several of these interpretations.
7 By ā€˜materialā€™ and ā€˜immaterialā€™ I mean ā€˜containing matterā€™ and (respectively) ā€˜not containing matterā€™.
By ā€˜corporealā€™ and ā€˜incorporealā€™ I mean ā€˜either containing or mixed with matterā€™ and (respectively)
ā€˜neither containing nor mixed with matterā€™. Thus: Socrates is a material and corporeal substance;
Socratesā€™ essence is an immaterial but corporeal substance; God is an immaterial and incorporeal
substance.
Introduction 7
What roles do the objects that are true or false play in Aristotleā€™s theory of truth?
Objects that are true or false play three roles in Aristotleā€™s theory of truth:
ļ¬rst, they contribute to explaining what it is to be true or false for items
of other kinds which can be such, i.e. for thoughts and sentences; second,
they are bearers of modal attributes; third, they are targets of propositional
attitudes. In the following subsections I shall examine these three roles in
turn.

The ļ¬rst role of objects that are true or false: contributing to explaining what
it is to be true or false for thoughts and sentences. As I just said, the ļ¬rst
role played in Aristotleā€™s theory of truth by objects that are true or false is
to contribute to explaining what it is to be true or false for thoughts and
sentences. This role recalls a strategy which is often adopted in modern
philosophy of logic, from Frege onwards: that of explaining the truth and
falsehood of certain mental states and certain sentences by appealing to the
truth and falsehood of propositions (abstract entities whose nature is neither
mental nor linguistic). Although there are important differences between
Aristotleā€™s conception and the modern strategy, at this stage I would like to
call attention to the resemblance.
To expound how objects that are true or false contribute to explaining
what it is to be true or false for thoughts and sentences, I must say some-
thing about Aristotleā€™s views on thoughts and sentences that are true or
false.

Truth-evaluable sentences. Not every sentence is either true or false: some
are neither (e.g. prayers). Every sentence that is true or false is an assertoric
sentence, or (as Aristotle often calls it) an assertion. But the converse fails:
some assertions are neither true nor false (read on to ļ¬nd out which).
Assertions coincide with truth-evaluable sentences, i.e. with the sentences
with regard to which the question ā€˜Is it true or false?ā€™ can be reasonably
asked. Note that this question cannot be reasonably asked with regard to
certain sentences (e.g. prayers). In the case of some sentences with regard to
which the question ā€˜Is it true or false?ā€™ can be reasonably asked, the correct
answer is ā€˜Neitherā€™. An analogy helps to clarify. Physical objects coincide
with colour-evaluable objects, i.e. with the objects with regard to which
the question ā€˜What colour is it?ā€™ can be reasonably asked. Note that this
question cannot be reasonably asked with regard to certain objects (e.g.
numbers). In the case of some objects with regard to which the question
ā€˜What colour is it?ā€™ can be reasonably asked, the correct answer is ā€˜Noneā€™
(e.g. some transparent objects like crystal balls or diamonds).
8 Introduction
Assertions are utterances, i.e. expression-tokens (not expression-types),
events of speech that occur over relatively short portions of time.

Truth-evaluable thoughts. Aristotle does not explicitly isolate a class of truth-
evaluable thoughts that constitute the mental counterparts of assertions.
However, since he regards the spheres of thought and speech as closely
analogous, indeed, almost as isomorphic, he is likely to believe that there
is such a class of truth-evaluable thoughts corresponding to the class of
truth-evaluable sentences, i.e. to the class of assertions.
Some of Aristotleā€™s remarks indicate that he would agree that every belief
is a truth-evaluable thought, i.e. a thought with regard to which the ques-
tion ā€˜Is it true or false?ā€™ can be reasonably asked. However, I doubt that
Aristotle would claim that every truth-evaluable thought is a belief. Hence,
for Aristotle beliefs probably constitute a proper subclass of truth-evaluable
thoughts. I guess Aristotle would grant that not every belief is either true
or false.

Simple and composite assertions. Aristotle distinguishes two kinds of
assertions: simple assertions and composite assertions. An assertion is sim-
ple just in case it concerns exactly one object; it is composite just in case it
concerns more than one object. Every simple assertion is either afļ¬rmative
or negative. Composite assertions are equivalent to utterances constructed
from several assertions linked by connective particles.
Aristotle concentrates on simple assertions, i.e. assertions that concern
exactly one object. He has little to say about composite assertions: he
acknowledges their existence, but they remain at the margins of his reļ¬‚ec-
tion. He never states that some sentences that are true or false have no
assertoric force (like the utterance of ā€˜Socrates is seatedā€™ which is a part of
an utterance of ā€˜Either Socrates is seated or Socrates is not seatedā€™). Nor
does he discuss utterances of ā€˜Either Socrates is seated or Socrates is seatedā€™:
are they simple (because they concern exactly one object, i.e. the state of
affairs that Socrates is seated) or composite (because they are disjunctive)?

Simple beliefs. Aristotle does not explicitly isolate a class of simple beliefs
that are the mental counterparts of simple assertions. However, since (as
I said) he regards the spheres of thought and speech as closely analogous,
he is likely to take such a class for granted: he probably thinks that simple
beliefs are those beliefs that concern exactly one object, and that every
simple belief is either afļ¬rmative or negative.
Introduction 9
A general deļ¬nition of truth and falsehood for simple beliefs and assertions.
Having expounded Aristotleā€™s views on thoughts and sentences that are
true or false, I am now in a position to address his conception of how
objects that are true or false contribute to explaining what it is to be true or
false for thoughts and sentences. Objects play this role, in particular, with
regard to simple beliefs and simple assertions.
Aristotleā€™s theory of truth and falsehood for simple beliefs and assertions
is governed by a general deļ¬nition of truth and falsehood (henceforth
ā€˜DTFā€™):

DTF Every simple belief, or assertion, concerns exactly one object and
is either afļ¬rmative or negative. Every afļ¬rmative simple belief, or
assertion, posits that the object it concerns is true. Accordingly, an
afļ¬rmative simple belief, or assertion, is true when and only when the
object it concerns is true; an afļ¬rmative simple belief, or assertion,
is false when and only when the object it concerns is false. Every
negative simple belief, or assertion, posits that the object it concerns
is false. Accordingly, a negative simple belief, or assertion, is true
when and only when the object it concerns is false; a negative simple
belief, or assertion, is false when and only when the object it concerns
is true.

DTF is a deļ¬nition of truth (at least for simple beliefs and assertions).
Aristotle does not address the issue of the criterion of truth (roughly, the
issue of establishing what, if any, reliable ways humans have of discovering
truths). Aristotleā€™s silence on the issue of the criterion of truth is remarkable
in view of the fact that shortly after his death, with the advent of the
Hellenistic philosophical schools of the third and second centuries bc, this
issue becomes a hot topic of philosophical debate.
DTF covers at one blow all simple beliefs and assertions, those concerning
composite objects as well as those concerning simple ones. It is worthwhile
working out the details of Aristotleā€™s account for each case. So, let us examine
the forms taken on by DTF with simple beliefs and assertions concerning
composite objects and with simple beliefs and assertions concerning simple
objects. However, there are two kinds of composite objects: states of affairs
and material substances. Let us then study the forms of DTF with regard
to simple beliefs and assertions concerning (i) those composite objects that
are states of affairs, (ii) those composite objects that are material substances,
and (iii) simple objects.
10 Introduction
Predicative assertions and beliefs. The simple assertions which concern those
composite objects that are states of affairs are predicative assertions; simi-
larly, the simple beliefs that concern those composite objects that are states
of affairs are predicative beliefs. Let me ļ¬rst spend a few paragraphs explain-
ing Aristotleā€™s views on predicative assertions and predicative beliefs.
Predicative assertions display a subjectā€“predicate structure (this can be
clearly seen in examples of predicative assertions like utterances of the
sentence-type ā€˜Socrates is seatedā€™ or of the sentence-type ā€˜Socrates is not
seatedā€™). Every predicative assertion has at least three parts: the predicate,
the subject, and the copula. In every predicative assertion, the predicate
signiļ¬es a universal, the subject signiļ¬es either a universal or an individual,
and the copula combines with the predicate to form a predicative expres-
sion. Consider a predicative assertion that is an utterance of ā€˜Socrates is
seatedā€™: the predicate is the part of the assertion that is an utterance of the
adjective ā€˜seatedā€™ and signiļ¬es the universal seated; the subject is the part
of the assertion that is an utterance of the name ā€˜Socratesā€™ and signiļ¬es the
individual Socrates; and the copula is the part of the assertion that is an
utterance of ā€˜isā€™ and combines with the predicate to form the predicative
expression that is an utterance of ā€˜is seatedā€™. Every predicative assertion is
either afļ¬rmative (e.g. an utterance of ā€˜Socrates is seatedā€™) or negative (e.g.
an utterance of ā€˜Socrates is not seatedā€™). Many predicative assertions have
further parts over and above the predicate, the subject, and the copula: they
contain utterances either of a negative particle (an utterance of ā€˜notā€™, as in
an utterance of ā€˜Socrates is not seatedā€™) or of a quantifying expression (an
utterance of ā€˜everyā€™, ā€˜noā€™, ā€˜someā€™, or ā€˜not everyā€™, as in an utterance of ā€˜No
horse is whiteā€™). Many assertions that contain no copula are regarded by
Aristotle as equivalent to assertions that do contain one: e.g. for Aristotle
an utterance of ā€˜Socrates walksā€™ is equivalent to one of ā€˜Socrates is walkingā€™.
Note that in English ā€˜Socrates is walkingā€™ is not equivalent to ā€˜Socrates
walksā€™. Aristotleā€™s view, however, is correct with respect to Greek usage: the
Greek sentence-type rendered by ā€˜Socrates is walkingā€™ is in fact equivalent
to that rendered by ā€˜Socrates walksā€™.
A predicative belief is a belief whose literal linguistic expression would
be a predicative assertion. For example, Platoā€™s belief that Socrates is seated
is a predicative belief because its literal linguistic expression would be
a predicative assertion that is an utterance of ā€˜Socrates is seatedā€™. Every
predicative belief has a part that constitutes its predicate (it is about, or
concerns, or ā€“ as I shall often say ā€“ grasps a universal) and one that
constitutes its subject (it grasps either a universal or an individual). For
example, in Platoā€™s belief that Socrates is seated, the predicate is the part
Introduction 11
of the belief that grasps the universal seated, the subject is the part that
grasps the individual Socrates. Every predicative belief is either afļ¬rmative
(e.g. Platoā€™s belief that Socrates is seated) or negative (e.g. Simmiasā€™ belief
that Socrates is not seated). Note that the predicate and the subject of
a predicative assertion are utterances, and they signify objects; the pred-
icate and the subject of a predicative belief are thoughts, and they grasp
objects.

Aristotleā€™s classiļ¬cation of predicative beliefs and assertions. Aristotle has a
richly articulated classiļ¬cation of predicative beliefs and assertions. Pred-
icative beliefs and assertions divide into two main groups: singular and
general predicative beliefs and assertions. A predicative belief, or assertion,
is singular just in case its subject grasps, or signiļ¬es, an individual; it is
general just in case its subject grasps, or signiļ¬es, a universal. Examples
of singular predicative assertions are utterances of ā€˜Socrates is seatedā€™ and
ā€˜Socrates is not seatedā€™. As for general predicative beliefs and assertions, they
divide into two subordinate groups: indeterminate and quantiļ¬ed predica-
tive beliefs and assertions. Examples of indeterminate predicative assertions
are utterances of ā€˜A horse is whiteā€™ and ā€˜A horse is not whiteā€™. As for quan-
tiļ¬ed predicative beliefs and assertions, they divide into two subordinate
groups: particular and universal predicative beliefs and assertions. Exam-
ples of particular predicative assertions are utterances of ā€˜Some horse is
whiteā€™ and ā€˜Not every horse is whiteā€™; examples of universal predicative
assertions are utterances of ā€˜Every horse is whiteā€™ and ā€˜No horse is whiteā€™.
Aristotleā€™s classiļ¬cation of predicative beliefs and assertions is conveniently
summarised by the following schema:

predicative beliefs and assertions



singular general


indeterminate quantified



particular universal

The distinction between afļ¬rmative and negative predicative beliefs and
assertions cuts across the above classiļ¬cation: every group within this
12 Introduction
classiļ¬cation is divided into an afļ¬rmative and a negative subordinate
group. That is, universal predicative beliefs and assertions divide into uni-
versal afļ¬rmative and universal negative predicative beliefs and assertions;
particular predicative beliefs and assertions divide into particular afļ¬rma-
tive and particular negative predicative beliefs and assertions; similarly with
indeterminate and singular predicative beliefs and assertions.
Aristotle has little to say about indeterminate predicative beliefs and
assertions. Following his lead, I shall concentrate on universal, particular,
and singular predicative beliefs and assertions.

The relationship of predicative beliefs and assertions to states of affairs. Having
explained Aristotleā€™s conception of predicative beliefs and assertions, I am
now in a position to report his views on how predicative beliefs and asser-
tions are related to states of affairs. Every predicative belief, or assertion,
concerns exactly one state of affairs whose two components are, ļ¬rst, the
universal grasped, or signiļ¬ed, by the predicate of the predicative belief, or
assertion, and, second, the object (a universal or an individual) grasped, or
signiļ¬ed, by the subject of the predicative belief, or assertion.
For example, a predicative assertion that is an utterance of ā€˜Socrates is
seatedā€™ concerns the state of affairs that Socrates is seated, which is composed
of the universal seated (signiļ¬ed by the assertionā€™s predicate, an utterance of
ā€˜seatedā€™) and the individual Socrates (signiļ¬ed by the assertionā€™s subject, an
utterance of ā€˜Socratesā€™). Note that a predicative assertion that is an utter-
ance of ā€˜Socrates is not seatedā€™ concerns the same state of affairs: the state
of affairs that Socrates is seated. Again, a predicative assertion that is an
utterance of ā€˜Every diagonal is commensurableā€™ concerns the state of affairs
that every diagonal is commensurable, which is composed of the univer-
sal commensurable (signiļ¬ed by the assertionā€™s predicate, an utterance of
ā€˜commensurableā€™) and the universal diagonal (signiļ¬ed by the assertionā€™s
subject, an utterance of ā€˜diagonalā€™). Note that a predicative assertion that is
an utterance of ā€˜Not every diagonal is commensurableā€™ concerns the same
state of affairs: the state of affairs that every diagonal is commensurable.

DTF and predications. In the case of predicative beliefs and assertions, DTF
takes on the following form: an afļ¬rmative predicative belief, or assertion, is
true when and only when the state of affairs it concerns is true, i.e. when and
only when the components of this state of affairs are reciprocally combined
in the relevant way, i.e. when and only when the universal grasped, or
signiļ¬ed, by the predicate is combined in the relevant way with the object
Introduction 13
(a universal or an individual) grasped, or signiļ¬ed, by the subject. An
afļ¬rmative predicative belief, or assertion, is false when and only when the
state of affairs it concerns is false, i.e. when and only when the components
of this state of affairs are reciprocally divided in the relevant way, i.e. when
and only when the universal grasped, or signiļ¬ed, by the predicate is divided
in the relevant way from the object grasped, or signiļ¬ed, by the subject.
A negative predicative belief, or assertion, is true when and only when the
state of affairs it concerns is false, i.e. when and only when the components
of this state of affairs are reciprocally divided in the relevant way, i.e. when
and only when the universal grasped, or signiļ¬ed, by the predicate is divided
in the relevant way from the object grasped, or signiļ¬ed, by the subject. A
negative predicative belief, or assertion, is false when and only when the state
of affairs it concerns is true, i.e. when and only when the components of this
state of affairs are reciprocally combined in the relevant way, i.e. when and
only when the universal grasped, or signiļ¬ed, by the predicate is combined
in the relevant way with the object grasped, or signiļ¬ed, by the subject.

Truth conditions for predications that differ in ā€˜quantityā€™. Different relations
of combination and division are associated with predicative beliefs and
assertions that differ in ā€˜quantityā€™ (i.e. by being universal, particular, or
singular). I shall ļ¬rst offer an abstract exposition of how different relations
of combination and division are called for in an account of true and false
predicative beliefs and assertions that differ in ā€˜quantityā€™; afterwards I shall
offer some examples. Here is the abstract exposition:
[a] Every universal afļ¬rmative predicative belief, or assertion, posits that
the universal grasped, or signiļ¬ed, by its predicate is combined with the
universal grasped, or signiļ¬ed, by its subject in such a way as universally
to hold of it. Accordingly, a universal afļ¬rmative predicative belief,
or assertion, is true when and only when the universal grasped, or
signiļ¬ed, by its predicate is combined with the universal grasped, or
signiļ¬ed, by its subject in such a way as universally to hold of it. A
universal afļ¬rmative predicative belief, or assertion, is false when and
only when the universal grasped, or signiļ¬ed, by its predicate is divided
from the universal grasped, or signiļ¬ed, by its subject in such a way as
not universally to hold of it.
[b] Every universal negative predicative belief, or assertion, posits that the
universal grasped, or signiļ¬ed, by its predicate is divided from the uni-
versal grasped, or signiļ¬ed, by its subject in such a way as universally to
14 Introduction
fail to hold of it. Accordingly, a universal negative predicative belief, or
assertion, is true when and only when the universal grasped, or signi-
ļ¬ed, by its predicate is divided from the universal grasped, or signiļ¬ed,
by its subject in such a way as universally to fail to hold of it. A universal
negative predicative belief, or assertion, is false when and only when
the universal grasped, or signiļ¬ed, by its predicate is combined with
the universal grasped, or signiļ¬ed, by its subject in such a way as not
universally to fail to hold of it.
[c] Every particular afļ¬rmative predicative belief, or assertion, posits that
the universal grasped, or signiļ¬ed, by its predicate is combined with
the universal grasped, or signiļ¬ed, by its subject in such a way as not
universally to fail to hold of it. Accordingly, a particular afļ¬rmative
predicative belief, or assertion, is true when and only when the universal
grasped, or signiļ¬ed, by its predicate is combined with the universal
grasped, or signiļ¬ed, by its subject in such a way as not universally to
fail to hold of it. A particular afļ¬rmative predicative belief, or assertion,
is false when and only when the universal grasped, or signiļ¬ed, by
its predicate is divided from the universal grasped, or signiļ¬ed, by its
subject in such a way as universally to fail to hold of it.
[d] Every particular negative predicative belief, or assertion, posits that
the universal grasped, or signiļ¬ed, by its predicate is divided from the
universal grasped, or signiļ¬ed, by its subject in such a way as not univer-
sally to hold of it. Accordingly, a particular negative predicative belief,
or assertion, is true when and only when the universal grasped, or signi-
ļ¬ed, by its predicate is divided from the universal grasped, or signiļ¬ed,
by its subject in such a way as not universally to hold of it. A particular
negative predicative belief, or assertion, is false when and only when
the universal grasped, or signiļ¬ed, by its predicate is combined with the
universal grasped, or signiļ¬ed, by its subject in such a way as universally
to hold of it.
[e] Every singular afļ¬rmative predicative belief, or assertion, posits that the
universal grasped, or signiļ¬ed, by its predicate is combined with the
individual grasped, or signiļ¬ed, by its subject in such a way as to hold
of it. Accordingly, a singular afļ¬rmative predicative belief, or assertion,
is true when and only when the universal grasped, or signiļ¬ed, by its
predicate is combined with the individual grasped, or signiļ¬ed, by its
subject in such a way as to hold of it. A singular afļ¬rmative predicative
belief, or assertion, is false when and only when the universal grasped,
Introduction 15
or signiļ¬ed, by its predicate is divided from the individual grasped, or
signiļ¬ed, by its subject in such a way as to hold outside it.
[f ] Every singular negative predicative belief, or assertion, posits that the
universal grasped, or signiļ¬ed, by its predicate is divided from the
individual grasped, or signiļ¬ed, by its subject in such a way as to hold
outside it. Accordingly, a singular negative predicative belief, or asser-
tion, is true when and only when the universal grasped, or signiļ¬ed, by
its predicate is divided from the individual grasped, or signiļ¬ed, by its
subject in such a way as to hold outside it. A singular negative pred-
icative belief, or assertion, is false when and only when the universal
grasped, or signiļ¬ed, by its predicate is combined with the individual
grasped, or signiļ¬ed, by its subject in such a way as to hold of it.
To pin down the above, a deļ¬nition of the relevant relations of combination
and division is called for. A universal u is combined with a universal v in
such a way as universally to hold of it when and only when u holds of every
individual of which v holds. A universal u is divided from a universal v in
such a way as universally to fail to hold of it when and only when every
individual of which v holds is other than every individual of which u holds.
A universal u is combined with a universal v in such a way as not universally
to fail to hold of it when and only when u holds of at least one individual of
which v holds. A universal u is divided from a universal v in such a way as
not universally to hold of it when and only when at least one individual of
which v holds is other than every individual of which u holds. A universal
u is combined with an individual i in such a way as to hold of it when and
only when u holds of i. A universal u is divided from an individual i in
such a way as to hold outside it when and only when i is other than every
individual of which u holds.

Some examples will clarify the abstract exposition of the previous subsection.
A universal afļ¬rmative predicative assertion that is an utterance of ā€˜Every
horse is whiteā€™ posits that the universal white, signiļ¬ed by the predicate (an
utterance of ā€˜whiteā€™), is combined with the universal horse, signiļ¬ed by the
subject (an utterance of ā€˜horseā€™), in such a way as universally to hold of it.
Accordingly, this utterance is true when and only when the universal white
is combined with the universal horse in such a way as universally to hold
of it, i.e. when and only when the universal white holds of every individual
of which the universal horse holds; the same utterance is false when and
only when the universal white is divided from the universal horse in such
a way as not universally to hold of it, i.e. when and only when at least one
16 Introduction
individual of which the universal horse holds is other than every individual
of which the universal white holds. Hence, now the utterance of ā€˜Every
horse is whiteā€™ is not true (for it is not the case that the universal white now
holds of every individual of which the universal horse now holds), but false
(for at least one individual of which the universal horse now holds is other
than every individual of which the universal white now holds).
Again, a universal negative predicative assertion that is an utterance of
ā€˜No horse is whiteā€™ posits that the universal white, signiļ¬ed by the predicate
(an utterance of ā€˜whiteā€™), is divided from the universal horse, signiļ¬ed by
the subject (an utterance of ā€˜horseā€™), in such a way as universally to fail
to hold of it. Accordingly, this utterance is true when and only when
the universal white is divided from the universal horse in such a way as
universally to fail to hold of it, i.e. when and only when every individual of
which the universal horse holds is other than every individual of which the
universal white holds; the same utterance is false when and only when the
universal white is combined with the universal horse in such a way as not
universally to fail to hold of it, i.e. when and only when the universal white
holds of at least one individual of which the universal horse holds. Hence,
now the utterance of ā€˜No horse is whiteā€™ is not true (for it is not the case
that every individual of which the universal horse now holds is other than
every individual of which the universal white now holds), but false (for the
universal white now holds of at least one individual of which the universal
horse now holds).


Predications that differ in category. Different relations of combination and
division are associated (not only with predicative beliefs and assertions that
differ in ā€˜quantityā€™, but also) with predicative beliefs and assertions that
differ in ā€˜categoryā€™. There are several versions (or, perhaps, aspects) of Aris-
totleā€™s theory of the categories. In one of these versions, the categories are
predicative relations linking objects. Different categories correspond to dif-
ferent fundamental questions: the category of substance is the predicative
relation linking a kind to its subordinate kinds and to its members, and
corresponds to the question ā€˜What is it?ā€™; the category of quality is the pred-
icative relation linking a quality to the items it holds of, and corresponds to
the question ā€˜What is it like?ā€™; etc.8 Moreover, there are predicative relations

8 The question ā€˜What is it?ā€™ can be used in a wide range of ways. Within this range we can pick out
a sharp question which is truly and appropriately answered by mentioning the kind under which
the object referred to by ā€˜itā€™ falls. If someone pointing to Socrates (who, as it happens, is pale) asks
ā€˜What is it?ā€™, ā€˜It is a manā€™ and ā€˜It is an animalā€™ are true and appropriate answers (they mention the
Introduction 17
that are the negative counterparts of those predicative relations that are the
categories. Now:
[g] Every afļ¬rmative predicative belief, or assertion, corresponding to the
question ā€˜What is it?ā€™ posits that the predicative relation of combina-
tion which is the category of substance links the universal grasped, or
signiļ¬ed, by the predicate to the object grasped, or signiļ¬ed, by the
subject. Accordingly, an afļ¬rmative predicative belief, or assertion, cor-
responding to the question ā€˜What is it?ā€™ is true when and only when
the predicative relation of combination that is the category of substance
links the universal grasped, or signiļ¬ed, by the predicate to the object
grasped, or signiļ¬ed, by the subject. Accordingly, an afļ¬rmative pred-
icative belief, or assertion, corresponding to the question ā€˜What is it?ā€™
is false when and only when the predicative relation of division that is
the negative counterpart of the category of substance links the universal
grasped, or signiļ¬ed, by the predicate to the object grasped, or signiļ¬ed,
by the subject.
[h] Every afļ¬rmative predicative belief, or assertion, corresponding to the
question ā€˜What is it like?ā€™ posits that the predicative relation of com-
bination that is the category of quality links the universal grasped, or
signiļ¬ed, by the predicate to the object grasped, or signiļ¬ed, by the
subject. Accordingly, an afļ¬rmative predicative belief, or assertion, cor-
responding to the question ā€˜What is it like?ā€™ is true when and only when
the predicative relation of combination that is the category of quality
links the universal grasped, or signiļ¬ed, by the predicate to the object
grasped, or signiļ¬ed, by the subject. An afļ¬rmative predicative belief, or
assertion, corresponding to the question ā€˜What is it like?ā€™ is false when
and only when the predicative relation of division that is the negative
counterpart of the category of quality links the universal grasped, or
signiļ¬ed, by the predicate to the object grasped, or signiļ¬ed, by the
subject.
I forgo spelling out the similar descriptions of the truth and falsehood of
predicative beliefs and assertions that correspond to other categories.
Here are some examples to clarify the foregoing abstract exposition. An
utterance of ā€˜Socrates is a manā€™ is true when and only when the predicative
relation of combination that is the category of substance links the universal
universals animal and man), ā€˜It is paleā€™ is true but in most cases inappropriate (in Greek, which is of
course the language at issue here, the answer corresponding to the English ā€˜It is paleā€™ would probably
be inappropriate in all cases). If, on the other hand, someone pointing to pale Socrates asks ā€˜What is
it like?ā€™, ā€˜It is paleā€™ is a true and appropriate answer, while ā€˜It is a manā€™ and ā€˜It is an animalā€™ are both
true but inappropriate.
18 Introduction
man, signiļ¬ed by the predicate (an utterance of ā€˜a manā€™), to the individual
Socrates, signiļ¬ed by the subject (an utterance of ā€˜Socratesā€™). Again, an
utterance of ā€˜Socrates is paleā€™ is true when and only when the predicative
relation of combination that is the category of quality links the universal
pale, signiļ¬ed by the predicate (an utterance of ā€˜paleā€™) to the individual
Socrates, signiļ¬ed by the subject (an utterance of ā€˜Socratesā€™).
In this account, truth and falsehood are parasitical upon the categories
because they are deļ¬ned by mentioning the categories. In Aristotleā€™s view,
such parasitism is a reason for leaving truth and falsehood at the mar-
gins of metaphysical inquiry, which should concentrate on ontologically
fundamental items, i.e. on the categories and their inhabitants.

DTF and existentials concerning material substances. In the case of those
composite objects that are material substances, DTF is speciļ¬ed as follows:
an afļ¬rmative simple belief, or assertion, concerning a material substance
is true when and only when this material substance is true, i.e. when and
only when this material substance exists, i.e. when and only when its form
is combined with its matter. An afļ¬rmative simple belief, or assertion,
concerning a material substance is false when and only when this material
substance is false, i.e. when and only when this material substance does
not exist, i.e. when and only when its form is divided from its matter.
A negative simple belief, or assertion, concerning a material substance is
true when and only when this material substance is false, i.e. when and
only when this material substance does not exist, i.e. when and only when
its form is divided from its matter. A negative simple belief, or assertion,
concerning a material substance is false when and only when this material
substance is true, i.e. when and only when this material substance exists,
i.e. when and only when its form is combined with its matter.
The above truth conditions make it natural to assume that simple beliefs
and assertions concerning material substances should be singular existential
beliefs and assertions. Let me spend a few words explaining what I mean by
ā€˜existential belief ā€™ and ā€˜existential assertionā€™. An existential assertion is an
assertion that consists of an utterance of a name followed by an utterance of a
form of ā€˜to existā€™ or of its negative counterpart ā€˜not to existā€™ (e.g. an utterance
of ā€˜Socrates existsā€™). Every existential assertion is either afļ¬rmative (e.g. an
utterance of ā€˜Socrates existsā€™) or negative (e.g. an utterance of ā€˜Socrates does
not existā€™). An existential belief is a belief whose literal linguistic expression
would be an existential assertion (e.g. Platoā€™s belief that Socrates exists).
Every existential belief is either afļ¬rmative (e.g. Platoā€™s belief that Socrates
exists) or negative (e.g. Simmiasā€™ belief that Homer does not exist).
Introduction 19
The conditions of truth and falsehood for singular existential beliefs and
assertions concerning material substances are clearly analogous to those for
predicative beliefs and assertions. For example, an utterance of ā€˜Socrates
does not existā€™, which is a singular negative existential assertion concerning
the material substance Socrates, is true when and only when Socratesā€™ form
is divided from his matter; analogously, an utterance of ā€˜Socrates is not
seatedā€™, which is a singular negative predicative assertion concerning the
state of affairs that Socrates is seated, is true when and only when the
universal seated is divided from Socrates in such a way as to hold outside
him.
When a material substance does not exist, i.e. when its form is divided
from its matter, a singular afļ¬rmative existential belief, or assertion, con-
cerning it will be false, and a singular negative existential belief, or assertion,
concerning it will be true. The reference to a form and to a portion of mat-
ter is secured by passing through a material substance that at some time or
other does exist. There is no account of the truth and falsehood of singular
existential beliefs or assertions concerning what never exists as a material
substance (e.g. my belief that Pegasus does not exist remains unexplained).

DTF and existentials concerning simple objects. In the case of simple objects,
DTF takes on the following form: an afļ¬rmative simple belief, or assertion,
concerning a simple object is true when and only when this simple object
is true, i.e. when and only when it exists. An afļ¬rmative simple belief,
or assertion, concerning a simple object is false when and only when this
simple object is false, i.e. when and only when it does not exist. A negative
simple belief, or assertion, concerning a simple object is true when and only
when this simple object is false, i.e. when and only when it does not exist.
A negative simple belief, or assertion, concerning a simple object is false
when and only when this simple object is true, i.e. when and only when it
exists. Thus, simple beliefs and simple assertions concerning simple objects
also are existential beliefs and assertions. For example, an utterance of ā€˜Man
existsā€™, which is an afļ¬rmative simple existential assertion concerning the
natural kind man (an essence, and therefore a simple object), is true when
and only when man exists.
Since all simple objects exist always, every afļ¬rmative existential belief,
or assertion, concerning a simple object is always true, and every negative
existential belief, or assertion, concerning a simple object is always false.
For example, an utterance of ā€˜Man existsā€™ is always true because the simple
object it concerns, the natural kind man, exists always. Aristotle describes
thoughts concerning simple objects as unerring: what he means is that
20 Introduction
all afļ¬rmative existential beliefs concerning them are always true. He fails
to mention the negative counterpart of this claim, i.e. that all negative
existential beliefs concerning simple objects are always false. Note that no
corresponding result holds with regard to material substances: since some
material substances are not everlasting, some singular afļ¬rmative existential
beliefs and assertions concerning material substances are sometimes false
and some singular negative existential beliefs and assertions concerning
material substances are sometimes true.
As I just said, if one has an afļ¬rmative existential belief concerning a sim-
ple object, and expresses it by an afļ¬rmative existential assertion, then oneā€™s
belief and the assertion expressing it are always true. However, it does not
follow that one will be able to understand or deļ¬ne the simple object one is
thinking or speaking about. In fact, it does not even follow that one will be
able to tell whether one is thinking or speaking about a simple rather than
a composite object. However, an everlastingly true afļ¬rmative existential
belief, or assertion, concerning a simple object can be the starting-point of
an inquiry that will eventually lead to understanding or deļ¬ning that simple
object: as this inquiry progresses, one passes from a belief or an assertion
ā€˜that it isā€™ to a belief or an assertion about ā€˜what it isā€™. Beliefs and assertions
of these two sorts (i.e. existential beliefs and assertions concerning essences,
on the one hand, and beliefs and assertions deļ¬ning these essences, on the
other) are among the indemonstrable premisses (principles) of scientiļ¬c
demonstrations. What I just said applies also to those simple objects that
are incorporeal substances (God and, perhaps, the heavenly intellects): even
if one has everlastingly true afļ¬rmative existential beliefs concerning them,
and expresses these beliefs in everlastingly true afļ¬rmative existential asser-
tions, it does not follow that one can understand or deļ¬ne them (one can
of course begin an inquiry which, if successful, will lead to oneā€™s under-
standing and deļ¬ning them). Thus, Aristotleā€™s remarks about afļ¬rmative
existential beliefs and assertions concerning incorporeal substances do not
commit him to any form of ā€˜religious intuitionismā€™.

The second role of true and false objects: bearing modal attributes. As I said,
objects that are true or false play three roles in Aristotleā€™s theory of truth.
In the preceding subsections I focused on their ļ¬rst role: contributing to
explaining what it is to be true or false for thoughts and sentences. Let me
now touch upon their second role: bearing modal attributes, i.e. necessity,
impossibility, possibility, and contingency. These modal attributes are on a
par with truth and falsehood in that they hold of the same items of which
truth and falsehood hold: objects, thoughts, and sentences.
Introduction 21
Aristotle offers ā€˜statisticalā€™ deļ¬nitions of modal attributes in so far as
they hold of objects: an object is necessary just in case it is always true,
it is impossible just in case it is always false, etc. (these deļ¬nitions are
called ā€˜statisticalā€™ because they turn on how often something is the case).
These modal attributes are then transferred from objects to certain beliefs
and assertions: e.g. an afļ¬rmative (negative) simple belief, or assertion,
concerning a necessary object is necessary (impossible). The analysis covers
at one blow objects, simple beliefs, and simple assertions of all sorts.
In some passages Aristotle seems to apply his statistical approach to modal
attributes of a different sort: to ā€˜diachronicā€™ modalities, i.e. modal attributes
with two ā€˜slots for datesā€™, characteristics such as its being at a certain time
necessary that something or other should be the case at a different time. For
example, he seems committed to claiming that it is now necessary that the
state of affairs of there being a sea-battle should be true in 24 hours just in
case in the inļ¬nite course of time up to 24 hours ago, every time when the
total state of the world resembled in relevant respects the total state of the
world now was followed 24 hours later by a time when the state of affairs of
there being a sea-battle was true. I hope that this example will enable one to
understand the following general characterisation of diachronic necessity to
which Aristotle seems committed: at t it is necessary that o should be true
i later just in case in the inļ¬nite course of time up to i before t, every
time when the total state of the world resembled in relevant respects the
total state of the world at t was followed i later by a time when o was true
(where t is a time, i a non-zero interval, and o an object). As we shall soon
see, diachronic modalities play a central role in Aristotleā€™s discussion of
Determinism.
Aristotleā€™s statistical approach to modalities in terms of time is surprising
to modern ears: modern philosophers usually analyse modal attributes dif-
ferently (e.g. in terms of possible worlds). The surprise slightly eases when
one recalls that for Aristotle time is inļ¬nite towards the past as well as the
future: given that time is thus inļ¬nite, it is not unreasonable to postulate
that what is possible should be what is true at some time or other.

The third role of true and false objects: serving as targets of propositional atti-
tudes. The third and ļ¬nal role played in Aristotleā€™s theory of truth by objects
that are true or false is to serve as targets of propositional attitudes: they are
what is believed or disbelieved, desired or shunned, etc. Aristotle is some-
what economical in his assumptions concerning these objects: in the case
of states of affairs, which are the most important ingredients in his account
of propositional attitudes, he allows only ā€˜afļ¬rmativeā€™ states of affairs. This
22 Introduction
metaphysical economy creates some difļ¬culty for the role of states of affairs
as targets of propositional attitudes. For it is clear how this theory can
analyse ā€˜afļ¬rmative propositional attitudesā€™, like an ā€˜afļ¬rmative beliefā€™ or
an ā€˜afļ¬rmative desireā€™: e.g. my ā€˜afļ¬rmative beliefā€™ that this is a sheet of paper
can be analysed as my bearing the relationship of believing to the state of
affairs that this is a sheet of paper. But it is not immediately clear how this
theory can analyse ā€˜negative propositional attitudesā€™, like a ā€˜negative beliefā€™
or a ā€˜negative desireā€™: e.g. my ā€˜negative beliefā€™ that this is not a wax-tablet
cannot be analysed as my bearing the relationship of believing to the state
of affairs that this is not a wax-tablet, simply because there is no such state
of affairs (for there are no ā€˜negativeā€™ states of affairs). Aristotleā€™s solution is
to introduce negative counterparts of the ordinary propositional attitudes:
thus, alongside belief there is its negative counterpart, disbelief, and along-
side desire there is its negative counterpart, shunning. Now my ā€˜negative
beliefā€™ that this is not a wax-tablet can be straightforwardly analysed as my
bearing the relationship of disbelieving to the state of affairs that this is a
wax-tablet.
One major problem with this theory is how it can deal with proposi-
tional attitudes bearing on complex propositional contents. For example,
to analyse my belief that if it is day it is light, the theory should introduce
a two-pronged propositional attitude to the states of affairs of its being day
and of its being light, while to explain my belief that if it is day it is not night
the theory should introduce a different two-pronged propositional attitude
to the states of affairs of its being day and of its being night. In general, to
account for beliefs expressed by conditionals whose antecedents and conse-
quents are either ā€˜atomicā€™ sentences or negations thereof, the theory should
introduce four two-pronged propositional attitudes. For beliefs expressed
by conditionals with more complex antecedents or consequents, the theory
will need more numerous and complicated multi-pronged propositional
attitudes (speciļ¬cally, the number of n-pronged propositional attitudes
must be 2n ). It should be clear that these are pretty cumbersome compli-
cations ā€“ complications Aristotle never looked into. Aristotleā€™s theorising
in this area did not go beyond a vague recognition of some issues, and was
driven mainly by the metaphysical concern of keeping down the number
of the entities postulated.

Correspondence, time, and Bivalence. In the preceding subsections I
expounded Aristotleā€™s ideas on the bearers of truth or falsehood. I focused
on his views about certain objects which are neither thoughts nor linguistic
expressions, but are, none the less, true or false. In the course of showing
Introduction 23
how, according to Aristotle, these objects that are true or false contribute to
explaining what it is to be true and what it is to be false for beliefs and asser-
tions, I reconstructed Aristotleā€™s views on the truth conditions of beliefs and
assertions of various types. In the remainder of this introductionā€™s overview
I intend to address three other important issues: ļ¬rst, whether Aristo-
tle can be said to propound a correspondence theory of truth; second,
Aristotleā€™s conception of the relation of truth to time; third, his views on
Bivalence.

Correspondence-as-isomorphism. Aristotle is often said to propound a cor-
respondence theory of truth. What claim does Aristotleā€™s theory of truth
have to being a correspondence theory of truth?
There are various conceptions of what it is to be a correspondence theory
of truth. Each different conception introduces different necessary and suf-
ļ¬cient conditions for a given theory of truth to be a correspondence theory
of truth. According to one of these conceptions ā€“ ā€˜the correspondence-as-
isomorphism conceptionā€™, as I shall call it ā€“ a theory of truth is a correspon-
dence theory of truth just in case it takes the truth of a belief, or assertion,
to consist in its being isomorphic to reality. Speciļ¬cally, according to the
correspondence-as-isomorphism conception, a theory of truth is a corre-
spondence theory of truth for beliefs (assertions) just in case it enjoys the
following threefold condition: ļ¬rst, it provides a classiļ¬cation of beliefs
(assertions); second, it maps one-to-one the classes of beliefs (assertions)
onto characteristics that can hold of the item or items a belief (assertion) is
about; third, it states that a belief (assertion) is true when and only when
the characteristic on which the class it belongs to is mapped holds of the
item or items it is about.
Aristotleā€™s theory of truth surely counts as a correspondence theory of
truth according to the correspondence-as-isomorphism conception. In fact,
the condition introduced by the correspondence-as-isomorphism concep-
tion is met at two levels by Aristotleā€™s theory of truth. First it is met at the
theoryā€™s most general level, i.e. in DTF, the deļ¬nition of truth and falsehood
for simple beliefs and assertions. DTF relies on a very simple classiļ¬cation
of beliefs and assertions: afļ¬rmations and denials are the only two classes.
These classes are mapped one-to-one onto characteristics that can hold of
the objects with which beliefs, or assertions, are concerned: afļ¬rmations are
mapped on truth, denials on falsehood. An afļ¬rmation is true when and
only when truth holds of the object with which it is concerned; a denial
is true when and only when falsehood holds of the object with which it is
concerned.
24 Introduction
The condition introduced by the correspondence-as-isomorphism con-
ception is met a second time by Aristotleā€™s theory of truth, at a more speciļ¬c
level: in the deļ¬nition of truth and falsehood for beliefs and assertions that
concern composite objects. Each belief, or assertion, concerning a com-
posite object is then regarded as being about two objects: those of which
the composite object it concerns is composed. For the sake of simplicity,
I concentrate on predicative beliefs and assertions. One of the two objects
a predicative belief, or assertion, is about is a universal (it is grasped, or
signiļ¬ed, by the predicate), the other is either a universal or an individual
(it is grasped, or signiļ¬ed, by the subject). The deļ¬nition of truth relies on a
classiļ¬cation that introduces six classes of predicative beliefs, or assertions:
universal afļ¬rmative, universal negative, particular afļ¬rmative, particular
negative, singular afļ¬rmative, and singular negative predicative beliefs, or
assertions (again for simplicityā€™s sake, I ignore the more ļ¬ne-grained dis-
tinctions induced by the categories). These classes are mapped one-to-one
onto characteristics (binary relations) that can hold of the objects (univer-
sals or individuals) that are grasped, or signiļ¬ed, by predicates and subjects
of predicative beliefs, or assertions: universal afļ¬rmative predicative beliefs
and assertions are mapped on the combination of holding universally;
universal negative predicative beliefs and assertions on the division of uni-
versally failing to hold; etc. A universal afļ¬rmative predicative belief, or
assertion, is true when and only when the universal grasped, or signiļ¬ed,
by its predicate is combined with the universal grasped, or signiļ¬ed, by its
subject in such a way as universally to hold of it; a universal negative predi-
cative belief, or assertion, is true when and only when the universal grasped,
or signiļ¬ed, by its predicate is divided from the universal grasped, or sig-
niļ¬ed, by its subject in such a way as universally to fail to hold of it; etc.

Correspondence-as-mirroring. As I said, there are various conceptions of what
it is to be a correspondence theory of truth, and each different conception
introduces different necessary and sufļ¬cient conditions for a given theory
of truth to be a correspondence theory of truth. We have just seen that Aris-
totleā€™s theory of truth is a correspondence theory of truth according to one
of these conceptions, i.e. according to the correspondence-as-isomorphism
conception. However, Aristotleā€™s theory of truth is a correspondence theory
of truth also according to a different, stricter conception. This is because
Aristotleā€™s theory of truth describes each class of beliefs, or assertions, in such
a way that each belief, or assertion, ā€˜mirrorsā€™ the characteristic on which the
class to which it belongs is mapped. Let me explain what I mean by ā€˜mirror-
ingā€™ here. Consider the two classes of beliefs, or assertions, introduced by
Introduction 25
Aristotleā€™s theory of truth at its most general level: afļ¬rmations and denials.
Afļ¬rmations are described as positing that the objects they concern are
true, denials as positing that the objects they concern are false. But now, by
positing that the object it concerns is true, an afļ¬rmation ā€˜mirrorsā€™ truth,
the characteristic of objects on which afļ¬rmations are mapped; and, by
positing that the object it concerns is false, a denial ā€˜mirrorsā€™ falsehood, the
characteristic of objects on which denials are mapped. In general, each class
of beliefs, or assertions, in Aristotleā€™s theory of truth is so described that
each member of that class posits that the characteristic the class is mapped
on obtains. By virtue of this ā€˜mirroringā€™ it assumes with regard to assertions
and beliefs, Aristotleā€™s theory of truth counts as a correspondence theory of
truth in that a belief, or assertion, is regarded as true when and only when
it ā€˜posits its object to be as it isā€™.

Subjects and predicates are ā€˜non-emptyā€™. I pointed out that Aristotleā€™s theory
of truth is a correspondence theory of truth at least in the sense that it
takes the truth of a belief, or assertion, to consist in its being isomorphic to
reality. I also described the particular form assumed by the idea that truth
consists in being isomorphic to reality in the case of predicative beliefs and
assertions: a predicative belief, or assertion, is true when and only when a
certain relation of combination or division obtains between the objects (uni-
versals or individuals) that are grasped, or signiļ¬ed, by its predicate and its
subject. This requires that there should be objects of the appropriate kinds
that are grasped, or signiļ¬ed, by the predicate and the subject: otherwise
the theory would lose one of its toeholds. Since for Aristotle all objects
are existent objects, the requirement imposed by his correspondence-as-
isomorphism theory of truth entails that in every predicative belief, or
assertion, the predicate and the subject grasp, or signify, existent objects
(universals or individuals), i.e. that both the predicate and the subject are
ā€˜non-emptyā€™.

Apparent cases of ā€˜emptyā€™ subjects or predicates. But how are those beliefs, or
utterances, that seem to be predicative beliefs, or assertions, whose predicate
or subject is ā€˜emptyā€™, to be treated with regard to truth and falsehood? For
example, how are utterances of ā€˜A goat is a goatstagā€™ and ā€˜A goatstag is
whiteā€™ to be treated?
Aristotleā€™s solution is that a thought, or utterance, that seems to be a
predicative belief, or assertion, whose predicate or subject is ā€˜emptyā€™, really
is not a predicative belief, or assertion: it is not even a simple belief, or
assertion, but a composite belief, or assertion, in disguise, i.e. a belief, or
26 Introduction
assertion, which could be accurately formulated as an utterance constructed
from several assertions linked by connective particles. Aristotle does not
develop this solution in detail: had he done this, he would have realised
that it faces serious difļ¬culties.

The laws of the Square of Opposition are valid. The laws of the Square of
Opposition are the basic principles which in Aristotleā€™s view govern the
logical relations between quantiļ¬ed predicative assertions (i.e. universal or
particular predicative assertions). These laws concern quartets consisting of
ā€˜coincidentā€™ universal afļ¬rmative, universal negative, particular afļ¬rmative,
and particular negative predicative assertions.9 For example, one of the
quartets concerned is that consisting of an utterance of ā€˜Every horse is
whiteā€™, one of ā€˜No horse is whiteā€™, one of ā€˜Some horse is whiteā€™, and one of
ā€˜Not every horse is whiteā€™.
One law of the Square of Opposition is the Law of Contraries: it states
that a universal afļ¬rmative and a ā€˜coincidentā€™ universal negative predicative
assertion are never both true (e.g. an utterance of ā€˜Every horse is whiteā€™
and one of ā€˜No horse is whiteā€™ are never both true). Another law of the
Square of Opposition is the Law of Contradictories: it states that a universal
afļ¬rmative (negative) predicative assertion is true when and only when any
ā€˜coincidentā€™ particular negative (afļ¬rmative) predicative assertion is not true
(e.g. an utterance of ā€˜Every horse is whiteā€™ is true when and only when any
utterance of ā€˜Not every horse is whiteā€™ is not true, and an utterance of ā€˜No
horse is whiteā€™ is true when and only when any utterance of ā€˜Some horse is
whiteā€™ is not true).
One plausible assumption concerning quantiļ¬ed predicative assertions
is that every particular predicative assertion is true only when its subject
denotes at least one individual that at some time or other exists (e.g. if at
noon on 1 January 1997 no horse exists, then at noon on 1 January 1997 no
utterance of ā€˜Some horse is whiteā€™ or of ā€˜Not every horse is whiteā€™ is true).
It should be noted that the plausible assumption I just mentioned is not
among the laws of the Square of Opposition: it is a further principle which
has a lot of intuitive plausibility.
The laws of the Square of Opposition, combined with the plausible
assumption I just mentioned, encounter difļ¬culties if at some time or other
the subject of some quantiļ¬ed predicative assertion denotes no individual
that at some time or other exists. For suppose that at a time t the subject of
9 The adjective ā€˜coincidentā€™ here indicates that the subjects of the predicative assertions involved are
tokens (utterances) of the same type, and, similarly, the predicates of the predicative assertions involved
are tokens (utterances) of the same type.
Introduction 27
some quantiļ¬ed predicative assertion denotes no individual that at some
time or other exists. Consider a quartet of ā€˜coincidentā€™ quantiļ¬ed predica-
tive assertions. By the assumption that every particular predicative assertion
is true only when its subject denotes at least one individual that at some
time or other exists, both the particular afļ¬rmative and the particular neg-
ative predicative assertion from this quartet are not true at t. Then, by
the Law of Contradictories, both the universal negative and the universal
afļ¬rmative assertion from the same quartet are true at t. This consequence
conļ¬‚icts with the Law of Contraries.
As I said in a preceding subsection, Aristotle is committed to the view
that in every predicative assertion both the predicate and the subject are
ā€˜non-emptyā€™. An important consequence of the ā€˜non-emptinessā€™ of subjects
and predicates of predicative assertions is that the Square of Oppositionā€™s
difļ¬culties evaporate. Assume that in every quantiļ¬ed predicative assertion
the subject is ā€˜non-emptyā€™, i.e. signiļ¬es an existent universal. As I said in the
subsection concerning Aristotleā€™s views on universals, Aristotle is probably
committed to the view that every universal at all times holds of some
individual or other that at some time or other exists. Hence he is probably
committed to the view that in every quantiļ¬ed predicative assertion the
subject at all times denotes some individual or other that at some time or
other exists. But the laws of the Square of Opposition face no difļ¬culty if in
every quantiļ¬ed predicative assertion the subject at all times denotes some
individual or other that at some time or other exists. The laws of the Square
of Opposition only concern genuine quantiļ¬ed predicative assertions: those
utterances that seem counter-examples to them, i.e. utterances that seem
quantiļ¬ed predicative assertions with ā€˜emptyā€™ subjects, are not real counter-
examples. They really are composite assertions, and therefore fall outside
the realm ruled by the laws of the Square of Opposition.

Singular predications, existence, and time. As we saw, in every singular pred-
icative belief, or assertion, the subject must be ā€˜non-emptyā€™, and therefore
must grasp, or signify, an existent individual. This requirement is to be
understood loosely, as postulating that the subject of the belief or assertion
should grasp, or signify, an individual that exists at some time or other : the
time of the individualā€™s existence can be very distant from that when the
belief is held, or the assertion uttered (e.g. although Homer no longer exists
you can now have a singular predicative belief that Homer is sick, and you
can now have one that Homer is a poet).
The times when the individual grasped, or signiļ¬ed, by the subject exists
need not coincide with the times when the whole singular predicative
28 Introduction
belief, or assertion, is true or false. There is no general law governing the
behaviour of all singular predicative beliefs, or assertions, with respect to
truth, existence, and time. In particular, it is not required that every singular
predicative assertion should be true only when the individual signiļ¬ed by
its subject exists, nor is it required that every singular afļ¬rmative predicative
assertion should be true only when the individual signiļ¬ed by its subject
exists. Different cases behave differently. What determines the behaviour
is the predicate, or, more precisely, the universal signiļ¬ed by the predicate.
For example, it is because of the nature of the universal sick that a singular
afļ¬rmative predicative assertion that is an utterance of ā€˜Homer is sickā€™ is
true only when Homer exists (for at any time, the universal sick holds only
of individuals that exist then). Speciļ¬cally, since Homer does not exist now,
the assertion in question is now false because the universal sick (signiļ¬ed
by its predicate) is now divided from Homer (the individual signiļ¬ed by
its subject) in such a way as to hold outside him. For the same reason, a
singular negative predicative assertion that is an utterance of ā€˜Homer is not
sickā€™ is now true. Again, it is because of the nature of the universal poet that
a singular afļ¬rmative predicative assertion that is an utterance of ā€˜Homer
is a poetā€™ is true also at times when Homer does not exist (for the universal
poet sometimes holds of individuals that do not exist then). Speciļ¬cally,
although Homer does not exist now, the assertion in question is now true
because the universal poet (signiļ¬ed by its predicate) now holds of Homer
(the individual signiļ¬ed by its subject).10 For the same reason, a singular
negative predicative assertion that is an utterance of ā€˜Homer is not a poetā€™
is now false. (This distribution of truth-values will never change because
the universal poet will always hold of Homer ā€“ for it will always be the case
that Homer has authored some poem.)

Utterances true at one time and false at another. Aristotle takes the bearers
of truth or falsehood, i.e. beliefs, assertions, and objects, to be true or false
at times: some of them are always true, others always false, yet others true
at one time and false at another. This Aristotelian view that the bearers of
truth or falsehood are true or false at times was widespread in Antiquity ā€“
in fact, it remained unchallenged.
Assertions, the only sentences that for Aristotle are true or false, are
utterances, i.e. expression-tokens, events of speech that occur over relatively
short portions of time. Aristotle is therefore committed to claiming that
some utterances are true or false at times, and that some of them are even true
at one time and false at another. The time when an utterance is produced

10 Cf. the paragraph to which n. 3 above is appended.
Introduction 29
must not be confused with the time or times when it is true or false: an
utterance is true or false even at times that are very distant from that when
it is produced.

Truth and time in Aristotle and in modern philosophy. From a purely onto-
logical point of view there is nothing unusual in Aristotleā€™s position about
utterances, truth, and time: an event can have, lack, acquire, and lose prop-
erties at times very distant from when it happens (e.g. the big bang has
been unknown for many centuries but is well known now). None the less,
modern philosophers disagree with Aristotle about utterances, truth, and
time. Modern philosophers claim that no utterance is true or false at a
time: rather, they say, some truth-evaluable utterances are true and others
are false ā€“ time does not come into the picture at all.
It is worthwhile examining the motivation behind the modern con-
ception. This is most easily done by considering present-tense predicative
assertions, i.e. assertions that are utterances of present-tense predicative
sentence-types. Modern philosophers take a present-tense predicative asser-
tion to assert that a certain state of affairs obtains (or fails to obtain) at the
time when the assertion itself is produced. Since ā€“ modern philosophers

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