Kenny Anthony. Ancient Philosophy: A New History of Western Philosophy Volume 1
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Contrasted with universal propositions there are particular propositions
(en merei) such as ‘Some Greeks are bearded’ (a particular afWrmative) or
‘Some Greeks are not bearded’ (a particular negative). In propositions of all
these kinds, Aristotle says, something is predicated of something else: e.g.
mortal is predicated of human in one case, and horse of Greek in another.
The presence or absence of a negative sign determine whether these
predications are afWrmations or negations respectively (1. 1. 24b17).
The items that enter into predications in propositions are called by
Aristotle terms (horoi). It is a feature of terms, as conceived by Aristotle,
that they can e ither Wgure as predicates themselve s or have other terms
predicated of them. Thus, in our Wrst example, human is predicated of
something in the Wrst sentence and has something predicated of it in the
second.
Aristotle assigns the terms occurring in a syllogism three distinct roles.
The term that is the predicate of the conclusion is the major term; the term
of which the major is predicated in the conclusion is the minor term; and the
term that appears in each of the premisses is the middle term (1. 4. 26a21–3).1
Thus, in the example given ‘mortal’ is the major term, ‘Greek’ the minor
term, and ‘human’ the middle term.
In addition to inventing these technical terms, Aristotle introduced the
practice of using schematic letters to bring out patterns of argument: a
device that is essential for the systematic study of inference and which is
ubiquitous in modern mathematical logic. Thus, the pattern of argument
we illustrated above is set out by Aristotle not by giving an example, but by
the following schematic sentence:
If A belongs to every B, and B belongs to every C, A belongs to
every C.2
If Aristotle wishes to produce an actual example, he commonly does it not
by spelling out a syllogistic argument, but by giving a schematic sentence
and then listing possible substitutions for A, B, and C (e.g. 1. 5. 27b30–2).
1 Aristotle’s use of these terms in the Prior Analytics is not consistent: the account given here,
from which he departs in considering the second and third Wgures of syllogism, has been
accepted as canonical since antiquity (see W. C. Kneale and M. Kneale, The Development of Logic
(Oxford: Clarendon Press, 1962), 69–71).
2 Note that beside being cast in schematic form, Aristotle’s exposition of syllogisms follows
the pattern ‘If p and q, then necessarily r’ rather than ‘p, q therefore r’.
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All syllogisms will contain three terms and three propositions; but given
that there are the four diVerent kinds of proposition Aristotle has distin-
guished, and that there are diVerent orders in which the terms can appear
in the premisses, there will be many diVerent syllogistic inference patterns.
Unlike our initial example, which contained only afWrmative universal
propositions, there will be triads containing negative and particular
propositions. Again, unlike our example in which the middle term
appeared in the Wrst premiss as a predicate and in the second as a subject,
there will be cases where the middle is subject in each premiss and cases
where it is predicate in each premiss. (By Aristotle’s preferred deWnition,
the conclusion will always have the minor term as its subject and the
major as its predicate.)
Aristotle grouped the triads into three Wgures (schemata) on the basis of
the position occupied in the premisses by the middle term. The Wrst Wgure,
illustrated by our initial example, has the middle once as predicate and
once as subject (the order in which the premisses are stated is immaterial).
In the second Wgure the middle term appears twice as subject, and in the
third Wgure it appears twice as predicate. Thus, using S for the minor, M for
the middle, and P for the major term, we have these Wgures:
(1) (2) (3)
S–M M–S S–M
M–P M–P P–M
Therefore, S–P S–P S–P
Aristotle was mainly interested in syllogisms of the Wrst Wgure, which he
regarded as alone being ‘perfect’, by which he probably meant that they had
an intuitive validity that was lacking to syllogisms in other Wgures (1. 4. 25b35).
Predication occurs in all propositions, but it comes in diVerent forms in the
four diVerent kinds of proposition: universal afWrmative, universal negative,
particular afWrmative, particular negative. Thus the predication S–P can be
either ‘All S is P’, ‘No S is P’, ‘Some S is P’, or ‘Some S is not P’. Within each
Wgure, therefore, we have many possible patterns of inference. In the Wrst
Wgure, for instance, we have, among many possibilities, the two following.
Every Greek is human. Some a nimals are dogs.
No human is immortal. Some dogs are white.
No Greek is immortal. Every animal is white.
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Triads of these diVerent kinds were, in later ages, called ‘moods’ of the
syllogism. Both of the given triads exemplify the pattern of a syllogism of
the Wrst Wgure, but there is obviously a great diVerence between them: the
Wrst is a valid argument, the second is invalid, having true premisses and a
false conclusion.3
Aristotle sets himself the task of determining which of the possible
moods produces a valid inference. He addresses it by trying out the various
possible pairs of premisses and asking whether any conclusion can be
drawn from them. If no conclusion can be validly drawn from a pair of
premisses, he says that there is no syllogism. For instance, he says that if B
belongs to no C, and A belongs to some B, there cannot be a syllogism; and
he gives the terms ‘white’, ‘horse’, ‘swan’ as the test instance (1. 3. 25a38).
What he is doing is inviting us to consider the pair of premisses ‘No swan is
a horse’ and ‘Some horses are white’ and to observe that from these
premisses no conclusion can be drawn about the whiteness or otherwise
of swans.
His procedure appears, at Wrst sight, to be both haphazard and intuitive;
but in the course of his discussion he is able to produce a number of general
rules which, between them, are adequate to determine which moods yield
a conclusion and which do not. There are three rules which apply to
syllogisms in all Wgures:
(1) At least one premiss must be universal.
(2) At least one premiss must be afWrmative.
(3) If either premiss is negative, the conclusion must be negative.
These rules are of universal application, but they take more speciWc
form in relation to particular Wgures. The rules peculiar to the Wrst
Wgure are
(4) The major premiss (the one containing the major term) must be
universal.
(5) The minor premiss (the one containing the minor term) must be
afWrmative.
3 No valid argument has true premisses and a false conclusion, but of course there can be
valid arguments from false premisses to false conclusions, and invalid arguments for true
conclusions.
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If we apply these rules we Wnd that there are four, and only four, valid
moods of syllogism in the Wrst Wgure.
Every S is M Every S is M Some S is M Some S is M
Every M is P No M is P Every M is P Every M is not P
Every S is P No S is P Some S is P Some S is not P
Aristotle also oVers rules to determine the validity of moods in the second
and third Wgures, but we do not need to go into these since he is able
to show that all second- and third- Wgure syllogisms are equivalent to
Wrst-Wgure syllogisms. In general, syllogisms in these Wgures can be
transformed into Wrst-Wgure syllogisms by a process he calls ‘conversion’
(antistrophe).
Conversion depends on a set of relations between propositions of
diVerent forms that Aristotle sets out early in the treatise. When we have
particular afWrmative and universal negative propositions, the order of the
terms can be reversed without alteration of sense: Some S is P if and only if
some P is S, and no S is P if and only if no P is S (1. 2. 25a5–10). (By contrast,
‘Every S is P’ may be true without ‘Every P is S’ being true.)
Consider the following syllogism in the third Wgure: ‘No Greek is a bird;
but all ravens are birds; therefore no Greek is a raven’. If we convert the
minor premiss into its equivalent ‘No bird is a Greek’ we have a Wrst-Wgure
syllogism in the second of the moods tabulated above. Aristotle shows in
the course of his treatise that almost all second- and third-Wgure syllogisms
can be reduced to Wrst-W gure ones by conversion in this manner. In the
rare cases where this is not possible he transforms the second- and third-
Wgure syllogisms by a process of reductio ad absurdum, showing that if one
premiss of the syllogism is taken in conjunction with the negation of its
conclusion as a second premiss, it will yield (by a deduction in the Wrst
Wgure) the negation of the original second premiss as a conclusion (1. 23.
41a21 V.).
Aristotle’s syllogistic was a remarkable achievement: it is a systematic
formulation of an impo rtant part of logic. Some of his followers in later
times—though not in antiquity or the Middle Ages—thought that syllo-
gistic was the whole of logic. Immanuel Kant, for instance, in the preface to
the second edition of his Critique of Pure Reason, said that since Aristotle logic
had neither advanced a single step nor been requi red to retrace a single
step.
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In fact, however, syllogistic is only a fragment of log ic. It deals only with
inferences that depend on words like ‘all’ or ‘some’, which classify the
premisses and conclusions of syllogisms, not with inferences that depend
on words like ‘if’ and ‘then’, which, instead of attaching to nouns, link
whole sentences. As we shall see, inferences such as ‘If it is not day, it is
A head of Aristo tle attributed to Lys ippus (fourth century bc)
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night; but it is not day; therefore it is night’ were formalized later in
antiquity. Another gap in Aristotle’s syllogistic took longer to Wll. Though
it was concerned above all with words like ‘all’, ‘every’, and ‘some’
(quantiWers, as they were later to be called), it could not cope with
inferences in which such words occurred not in subject place but some-
where in the grammatical predicate. Aristotle’s rules would not provide for
assessing the validity of inferences containing premisses such as ‘Every boy
loves some girl’ or ‘Nobody can avoid every mistake.’ It took more than
twenty centuries before such inferences were satisfactorily formalized.
Aristotle may perhaps, for a moment, have thought that his syllogistic
was sufWcient to deal with every possible valid inference. But his own
logical writings show that he realized that there was much more to logic
than was dreamt of in his syllogistic.
The de Interpretatione and the Categories
The de Interpretatione is principally interested, like the Prior Analytics, in general
propositions beginning with ‘every’, ‘no’, or ‘some’. But its main concern is
not to link them to each other in syllogisms, but to explore the relations of
compatibility and incompatib ility between them. ‘Every man is white’ and
‘No man is white’ can clearl y not both be true together: Aristotle calls such
propositions contraries (enantiai) (7. 17b4–15). They can, however, both be false,
if, as is the case, some men are white and some men are not. ‘Every man is
white’ and ‘Some man is not white’, like the earlier pair, cannot be true
together; but—on the assumption that there are such things as men—
they cannot be false together. If one of them is true, the other is false; if one
of them is false, the other is true. Aristotle calls such a pair contradictory
(antikeimenai) (7. 17b16–18).
Just as a universal afWrmative is contradictory to the corresponding
particular negative, so too a universal negative contradicts, and is contra-
dicted by, a particular afWrmative: thus ‘No man is white’ and ‘Some man is
white’. Two corresponding particular afWrmatives are neither contrary nor
contradictory to each other: ‘Some man is white’ and ‘Some man is not white’
can be, and in fact are, both true together. Given that there are men, the
propositions cannot, however, both be false together. This relationship was
not given a name: later followers called it the relationship of subcontrariety.
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Contra
dictory
Contra dictory
Contrary
Universal affirmative Universal negative
Every man is white No man is white
Particular affirmative Particular negative
Some man is white Some man is not whiteSubcontrary
The relationships set out in the de Interpretatione can be set out, and have
been set out for centuries by Aristotle’s followers, in a diagram known as a
square of opposition.
The propositions that enter into syllogisms and into the square of
opposition are all general propositions, whether they are universal or
particular. That is to say, none of them are propositions about individuals,
containing proper names, such as ‘Socrates is wise’. Of course, Aristotle was
familiar with singular propositions, and one such, ‘Pittacus is generous’,
turns up in an example in the Wnal chapter of the Prior Analytics (2. 27. 70a25).
But its appearance is incongruous in a treatise whose standard assumption
is that all premisses and conclusions are quantiWed general propositions. In
the de Interpretatione singular propositions are mentioned from time to time,
principally to point a contrast with general propositions. It is a simple
matter, for instance, to form the contradictory of ‘Socrates is white’: it is
‘Socrates is not white’ (7. 17b30). But to Wnd a systematic treatment of
singular propositions we must turn to the Categories.
Whereas the Analytics operates with a distinction between propositions
and terms, the Categories starts by dividing ‘things that are said’ into
complex (kata symploken) and simple (aneu symplokes) (2. 1a16). An example of
a complex saying is ‘A man is running’; simple sayings are the nouns and
verbs that enter into such complexes: ‘man’, ‘ox’, ‘run’, ‘win’, and so on.
Only complex sayings can be statements, true or false; simple sayings are
neither true nor false. A similar distinction appears in the de Interpretatione,
where we learn that a sentence (logos) has parts that signify on their own,
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while on the other hand there are signs that have no signiWcant parts.
These simple signs come in two diVerent kinds, names (Int.2.16a20–b5) and
verbs (Int.3.16b6–25): the two are distinguished from each other, we learn,
because a ver b, unlike a noun, ‘signiWes time in addition’, i.e. has a tense.
But in the Categories there is a much richer classiWcation of simple sayings. In
the fourth chapter of the treatise Aristotle has this to say:
Each one signiWes either substance (ousia), or how big, or what sort, or in relation to
something, or where, or when, or posture, or wearing, or doing, or being acted on.
To give a rough idea substance is e.g. human, horse; how big is e.g. four-feet, six-
feet; what sort is e.g. white, literate; in relation to something is e.g. double, half,
bigger than; where is e.g. in the Lyceum, in the forum; when is e.g. yesterday,
tomorrow, last year; posture is e.g. is lying, is sitting; wearing is e.g. is shod, is
armed; doing is e.g. cutting, burning; being acted on is e.g. being cut, being burnt.
(4. 1b25–2a4)
This compressed and cryptic passage has received repeated commentary
and has exercised enormous inXuence over the centuries. These ten things
signiWed by simple sayings are the categories that give the treatise its name.
Aristotle in this passage indicates the categories by a heterogene ous set of
expressions: nouns (e.g. ‘substance’), verbs (e.g. ‘wearing’), and interroga-
tives (e.g. ‘where?’ or ‘how big?’). It became customary to refer to every
category by a more or less abstract noun: substance, quantity, quality,
relation, place, time, posture, vesture, activity, passivity.
What are c ategories and what is Aristotle’s purpose in listing them? One
thing, at least, that he is doing is listing ten diVerent kinds of expression
that m ight appear in the predicate of a sentence about an individual
subject. We might say of Socrates, for example, that he was a man, that
he was Wve feet tall, that he was wise, that he was older than Plato, and that
he lived in Athens in the Wfth century bc. On a particular occasion his
friends might have said of him that he was sitting, wearing a cloak, cutting
a piece of cloth, and being warmed by the sun. Obviously, the teaching of
the Categories makes room for a variety of statements much richer than the
regimented propositions of the Prior Analytics.
The text makes clear, however, that Aristotle is not only classifying
expressions, pieces of language. He saw himself as making a classiWcation
of extra-linguistic entities, things signiWed as opposed to the signs that
signify them. In Chapter 6 we shall explore the metaphysical implications
of the doctrine of the categories. But one question must be addressed
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immediately. If we follow Aristotle’s lead, we shall easily be able to categor-
ize the predicates in sentences such as ‘Socrates was pot-bellied’, ‘Socrates
was wiser than Meletus’. But what are we to say about the ‘Socrates’ in such
sentences? Aristotle’s list seems to be a list of predicates not of subjects.
The answer to this is given in the succeeding chapter of the Categories.
Substance—strictly so called, primarily and par excellence—is that which is neither
said of a subject nor is in a subject, e.g. such-and-such a man, such-and-such a
horse.
Second substances are the species and genera to which the primary substances
belong. Thus, such-and-such a man belongs in the species human, and the genus
of this species is animal; so both human and animal are called second substances.
(5. 2a11–19)
When Aristotle speaks of a subject in this passage, it is clear that he is
talking not about a linguistic expression, but about what the expression
stands for. It is the man Socrates, not the word ‘Socrates’, that is the Wrst
substance. The substance that appeared Wrst in the list of categories, it now
emerges, was second sub stance: so the sentence ‘Socrates was human’
predicated a second substance (a species) of a Wrst substance (an individual).
When Aristotle in this passage c ontrasts a Wrst substance with things that
are in a subject, what he has in mind as being in a subject are the items
signiWed by predicates in the other categories. Thus, if ‘Socrates is wise’ is
true, then Socrates’ wisdom is one of the things that are in Socrates (cf. 2.
1a25).
Aristotle goes through the categories, discussing them in turn. Some,
such as substance, quantity, and quality, are treated at length; others, such
as activity and passivity, are brieXy touched on; yet others, such as posture
and vesture, pass into oblivion. Detailed logical points are made in order to
mark the distinctions between diVerent categories. For example, qualities
often admit of degrees, while particular quantities do not: one thing can be
darker than another, but cannot be more four-foot-long than another
(7. 6a19; 8. 10b26). Within individual categories, further subclasses are
identiWed. There are, for instance, two types of quantity (discrete and
continuous) and four types of quality, which Aristotle illustrates with
the following examples: virtue, healthiness, darkne ss, shape. The criteria
by which he distinguishes these types are not altogether clear, and the
reader is left in doubt whether a particular item can occur in more than
one of these classes, or indeed in more than one category. Aristotle’s
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commentators through the ages have laboured to Wll his gaps and reconcile
his inconsistencies.
The Categories contains more than the theory of categories: it deals also
with a mixed bag of other logical topics. It is clear that the treatise we have
was not written as a single whole by Aristotle, though there is no need to
question, as some scholars have done, that it is his authentic work.4
One cluster of topics discussed is that of homony my and synonymy.
These words are transliterations of the Greek words Aristotle uses; but
whereas the English words signify properties of bits of language, the Greek
words as he uses them signify properties of things in the world. Aristotle’s
account can be paraphrased thus: if A and B are called by the same name
with the same meaning, then A is synonymous with B; if A and B are called
by the same name with a diVerent meaning, then A is homonymous with
B. Because of peculiarities of Greek idiom, we have to tweak Aristotle’s
examples in English, but it is clear enough what he has in mind. A Persian
and a tabby are synonymous with each other because they are both called
cats; but they are only homonymous with the nine-tailed whip that is also
called a cat. The diVerence between homonymous and synonymous
things, Aristotle says, is that homonymous things have only the name in
common, whereas synonymous things have both the name and its deWni-
tion in common.
Aristotle’s distinction between homonymous and synonymous things is
an important one which is easily adapted—and was indeed later adapted by
himself—into a distinction between homonymous and synonymous bits of
language, that is to say between expressions that have only the symbol in
common and those that have also the meaning in common.
The study of homonymy was important for the treatment of fallacies in
arguments due to the ambiguity of terms used. It is undertaken for these
purposes in the Topics, and Aristotle gives rules for detecting it. ‘Sharp’, for
instance, has one meaning as applied to knives, and another as applied to
musical notes: the homonymy is made obvious because in the case of
knives the opposite of ‘sharp’ is ‘blunt’, whereas in the case of notes the
opposite is ‘Xat’ (Top. 1. 15. 106a13–14). In the course of his studies Aristotle
came to draw a distinction between mere chance homonymy (as in the
English word ‘bank’, which is used both for the side of a river and for a
4 With the exception of 8. 11 a10–18, an editorial insertion to link together two of the disparate
elements and to explain gaps in the treatment of the later categories.
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