Barnes Jonathan. Truth, etc
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140 Predicates and Subjects
An expression holds of, or belongs to, something if and only if it is true of
it; and that suggests that predication is best explained in terms of truth—that
is to say, in terms of something’s being true of something. A first version of
the suggestion—which is neither eccentric nor exciting—amounts to this:
xispredicatedofyifandonlyifxistrueofwhatyistrueof.
‘An item which sang’ is predicated of ‘bugle’ inasmuch as ‘an item which
sang’ is true of what ‘bugle’ is true of—and hence inasmuch as bugles are
items which sang, or bugles sang. The sentence, or an utterer of the sentence,
Bugles sang
predicates ‘an item which sang’ of ‘bugle’ inasmuch as what it or he says is
true if and only if ‘an item which sang’ is in fact predicated of ‘bugle’.
But that explanation cannot capture the notion of predication which
governs the Analytics. For consider this sentence:
And no bird sings.
What is there predicated of what? The right answer to that question, within
the context of Aristotle’s logic, is this: ‘singing item’ is predicated of ‘bird’.
But although the sentence predicates ‘singing item’ of ‘bird’, it is not true if
and only if ‘singing item’ is true of what ‘bird’ is true of. Quite the contrary.
How, then, is ‘singing item’ predicated of ‘bird’? Well, it is predicated
of it in a certain style—and the style’s the thing. (The point still holds,
mutatis mutandis, if you reject the Porphyrean view which makes subjects
and predicates expressions. For then you will say that in
And no bird sings
singing is predicated of bird.)
Predication—despite what I have so far been pretending—is not in fact a
two-place relation which might hold between, say, ‘singing item’ and ‘bird’.
Certainly, predication is a matter of two-placed relations; but the formula
‘x is predicated of y’ does not itself express a two-placed relation. Rather,
the two-placed relations involved in predication are expressed by formulas
of the sort ‘x is predicated-in-style-S of y’. So if we ask, what, in general,
are the truth-conditions for sentences of the form ‘x is predicated of y’, then
we shall receive no general answer: we shall receive a disjunction of specific
answers. (To be sure, you may always define ‘x is predicated of y’ as ‘x is
predicated-in-some-style-or-other of y’.)
What are the styles of predication? They are numerous; but the ones
which concern me here are the ones which bear on Aristotle’s syllogistic.
If we leave aside modality, which complicates matters impertinently, then a
style is a combination of a quantity and a quality. Very roughly speaking,
Styles of Predication 141
a quality indicates in what manner a predicate attaches to a subject, and a
quantity indicates to how much of the subject the predicate attaches. There
are two qualities: positive and negative, or affirmative and privative. There
are infinitely many quantities; but Aristotle’s logic restricts itself in principle
to three of them and in practice to two. The three quantities are universal,
particular, and indeterminate. But the indeterminate quantity is scarcely
mentioned in the Analytics, Aristotle taking it to be equivalent to the particular
quantity; and so we may confine ourselves—as the later Aristotelians generally
did—to two quantities. Two qualities multiplied by two quantities give four
styles of predication—or four sorts of predicative proposition.
The tradition speaks of propositions of the types A, E, I and O; and we
might speak of four styles of predication A, E, I and O—universal and
affirmative, universal and negative, particular and affirmative, particular and
negative. An attempt to elucidate the Aristotelian notion of predication might
then start from the schema:
x is predicated in style S of y if and only if, in style S,xistrueofwhatyis
true of.
And it might proceed to define the four canonical styles, along familiar lines.
For example, the universal affirmative style, or style A, is explained thus:
In style A, x is true of what y is true of if and only if there is nothing of
which y is true and x is not true.
Or, in Aristotle’s words,
we say that something is predicated of every item when it is not possible to take any
of the items of which the other will not be said.
(APr 24b28–30)⁵⁸
That explication has its ennuis, to which I shall return in a later context. But
they need not derange us here.
The other three styles may be explained along the same lines. So let us
return to the withered sage. In the sentence
And no bird sings
‘singing item’ is indeed predicated of ‘bird’; for it is predicated of ‘bird’
universally and negatively, or in style E. In style E, x is true of what y is true
of if and only if there is nothing of which y is true and x is true. So
⁵⁸ λέγομεν δὲ τὸ κατὰ παντὸς κατηγορεῖσθαι ὅταν μηδὲν ᾖ λαβεῖν καθ ᾿ οὗ θάτερον οὐ
λεχθήσεται.
142 Predicates and Subjects
No bird sings
is true if and only if there is nothing of which ‘singing item’ is true and ‘bird’
is true—that is to say, if and only if no bird sings.
THE TRANSITIVITY OF PREDICATION
Earlier I wondered whether the relation of predication was reflexive, symmet-
rical, transitive, and the like; and I postponed the question. The reason for
the postponement should now be clear: there is no such thing as the relation
of predication of which such questions can be asked. Rather, there are—in
Aristotelian logic—four relations. With regard to each of the four styles of
predication it may be asked whether it is reflexive, symmetrical, transitive,
and so on. And, rather more excitingly, we can ask what logical links can be
established among the four styles of predication. Suppose, for example, that
x is A-predicated of y—does it follow that y is I-predicated of x? Or suppose
that x is A-predicated of y and E-predicated of z—does it follow that y is
predicated of z in some style or other?
Those questions were all asked by Aristotle and his successors—though
not, to be sure, in that form. Thus Aristotle’s argument in favour of what is
called the accidental conversion of A-style predication is an argument that
if x is A-predicated of y then y is I-predicated of x; and his proof of the
validity of the second figure mood known as Camestres is a proof that if x is
A-predicated of y and E-predicated of z, then y is E-predicated of z.
Or consider A-predication. It seems clear that this relation is reflexive; for
x is surely true of everything of which x is true. It seems equally plain that
it is neither symmetrical nor asymmetrical; for when x is true of everything
of which y is true, y may or may not be true of everything of which x is
true. (Let x be ‘a man’ and y first ‘an item capable of laughter’ and then ‘a
philosopher’.) Finally, it seems evident that the relation is transitive: if x is
true of everything of which y is true, and y is true of everything of which z is
true, then x is true of everything of which z is true.
The transitivity of A-style predication—of universal affirmative predica-
tion—corresponds to Barbara, the first mood of Aristotelian syllogistic; and
Aristotle explicitly notices the point:
Now when three terms are so related to one another that the last is in the middle as
in a whole and the middle is in the first as in a whole … , it is necessary for there to
The Transitivity of Predication 143
be a perfect syllogism of the extremes. … For if A of every B and B of every C, then
it is necessary for A to be predicated of every C.
(APr 25b32–39)⁵⁹
The last sentence—‘For if A of every B …’—is as clear an affirmation of the
transitivity of A-predication as you could hope to find. The sentence is there,
as its initial particle shows, in order to explain why from
A holds of every B
and
B holds of every C
there is a syllogism to
A holds of every C.
And arguments of that sort are syllogisms in Barbara.
Later in the Prior Analytics, where Aristotle is discussing the best way to
select terms which stand in logical relationships to one another, he remarks
that
you should not select for the universal the terms which a contained item follows—for
example, for animal you should not select the terms which man follows. For it is
necessary that, if animal follows man, then it also follows all those items—and those
items are more appropriate to the selection for man.
(APr 43b29–32)⁶⁰
Suppose that you are looking for items which ‘animal’ follows—that is to say,
of which ‘animal’ is A-predicated; and suppose that you hit upon ‘man’ and
add it to your list. You then come across ‘grammarian’: it is true that ‘animal’
is A-predicated of ‘grammarian’. Nonetheless, you should not add it to your
list; for ‘man’ too is A-predicated of ‘grammarian’, and you have already got
‘man’ on the list. ‘For it is necessary that, if animal follows man, then it also
follows all those items’; that is to say, generalized and schematically put:
If x is A-predicated of y, then for any z, if y is A-predicated of z, then x is
A-predicated of z.
⁵⁹ ὅταν οὖν ὅροι τρεῖς οὕτως ἔχωσι πρὸς ἀλλήλους ὥστε τὸν ἔσχατον ἐν ὅλῳ εἶναι τῷ
μέσῳ καὶ τὸν μέσον ἐν ὅλῳ τῷ πρώτῳ ..., ἀνάγκη τῶν ἄκρων εἶναι συλλογισμὸν τέλειον.
... εἰ γὰρ τὸ Α κατὰ παντὸς τοῦ Β καὶ τὸ Β κατὰ παντὸς τοῦ Γ, ἀνάγκη τὸ Α κατὰ παντὸς
τοῦ Γ κατηγορεῖσθαι.
⁶⁰ οὐδὲ δὴ τῷ καθόλου ἐκλεκτέον οἷς ἕπεται τὸ περιεχόμενον, οἷον ζῴῳ οἷς ἕπεται
ἄνθρωπος· ἀνάγκη γάρ, εἰ ἀνθρώπῳ ἀκολουθεῖ τὸ ζῷον, καὶ τούτοις ἅπασιν ἀκολουθεῖν·
οἰκειότερα δὲ ταῦτα τῆς τοῦ ἀνθρώπου ἐκλογῆς.
144 Predicates and Subjects
And that is one way of expressing the transitivity of universal affirmative
predication.
Of course it is transitive—why fuss over such a banality? Well, I fuss
because the banality was officially rejected by a large part of the ancient
tradition: according to that tradition, A-predication is not transitive.
To be sure, the tradition did not thereby reject Barbara—how could it have
done? But it accepted only a restricted form of Barbara. Here is Simplicius
on the subject:
Having said what being of a subject is not, he now says what it is—namely, that
being predicated synonymously and essentially is what being said of a subject is. And
that comes about when, presenting the definitory formula of the subject, we present
it through the predicate. For if someone presents what man is, he will say animal. So,
when something is predicated as of a subject (e.g. man of Socrates) and something
else is predicated of the predicate (and that too not accidentally but as of a subject
and synonymously—e.g. animal of man), then animal will also be predicated of
Socrates—for in this way we shall have the first mood of the first figure, the middle
being in the major extreme as in a whole and being said of all the minor.
(in Cat 51.30–52.10)⁶¹
According to this passage, the relation expressed by ‘x is universally and
affirmatively predicated essentially of y’ is transitive, and supports the first
mood of the first figure or Barbara. Thus the argument
Men are animals and animals are substances—and so men must be
substances
is valid; for its two premisses express essential A-predications.
But consider an argument which is apparently on all fours with it:
Frenchmen are heavily taxed and heavy taxes make for disgruntlement—so
it’s not surprising that the French are so disgruntled.
There the premisses are indeed A-predications; but they are not essential
A-predications—it is no part of the essence of being French that you are
⁶¹ εἰπών τί οὐκ ἔστιν καθ ᾿ ὑποκειμένου, νῦν τί ἐστιν λέγει, ὅτι τὸ συνωνύμως καὶ ἐν τῷ
τί ἐστιν κατηγορεῖσθαι, τοῦτό ἐστιν τὸ καθ ᾿ ὑποκειμένου λέγεσθαι· τοῦτο δέ ἐστιν ὅταν τὸν
λόγον τὸν ὁριστικὸν ἀποδιδόντες τοῦ ὑποκειμένου διὰ τοῦ κατηγορουμένου ἀποδιδῶμεν. ἐὰν
γὰρ ἀποδιδῷ τις τί ἐστιν ἄνθρωπος, ζῷον ἐρεῖ. ὅταν οὖν ὡς καθ᾿ ὑποκειμένου κατηγορῆται,
οἷον ὁ ἄνθρωπος τοῦ Σωκράτους, καὶ τοῦ κατηγορουμένου ἄλλο τι κατηγορῆται καὶ αὐτὸ
μὴ ὡς ἔτυχεν ἀλλ᾿ ὡς καθ ᾿ ὑποκειμένου καὶ συνωνύμως, οἷον τὸ ζῷον τοῦ ἀνθρώπου, καὶ
τοῦ Σωκράτους τὸ ζῷον κατηγορηθήσεται· ἔσται γὰρ ὁ πρῶτος τρόπος οὕτως τοῦ πρώτου
σχήματος, τοῦ μέσου ἐν ὅλῳ μέν ὄντος τῷ μείζονι ἄκρῳ, κατὰ παντὸς δὲ τοῦ ἐλάττονος
λεγομένου.
The Transitivity of Predication 145
rudely taxed. Since it is essential A-predications which are transitive and the
predications in the argument are not essential, the argument is not valid—or
at any rate, it is not a valid syllogism in Barbara.
True, Simplicius does not explicitly mention arguments the component
predications of which are not essential, nor does he explicitly say that
A-predication is not in general transitive. But he quite clearly commits himself
to such a view, and the view was orthodox among the later commentators on
Aristotle. It must sound a strange view—a perverse view. So why ever was
it promoted? It was promoted because Aristotle himself was taken to have
promoted it. In the Categories, he states that
whenever one item is predicated of another as of a subject, everything which is said
of the predicate will also be said of the subject. For example, man is predicated of
an individual man, and animal of man: so animal will be predicated also of the
individual man.
(Cat 1b10–15)⁶²
That is transitivity; but it is transitivity not for A-predication, but for the
relation ‘x is predicated of y as of a subject’. You might think that the phrase
‘as of a subject’ was an idle addition, a pleonasm—after all, how could
x be predicated of y but not of y as a subject? Surely what something is
predicated of simply is its subject? Perhaps—but the ancient commentators
were persuaded that ‘as of a subject’ was anything but pleonastic.
The clearest ancient account of the matter is found in Porphyry’s com-
mentary on the Categories. He sets out the gist of the Aristotelian passage I
have just quoted, and then he raises an objection to it:
—But how can that be true? After all, man is said of Socrates as of a subject, and
of man is predicated not only animal but also species (for man is a species). But
they won’t all be predicated of Socrates; rather, animal will be predicated of him but
species will not—for Socrates isn’t a species.
—But look: the absurdity depends on the fact that you have mistaken what ‘which
is said of the predicate’ means. He didn’t simply say ‘which is said of the predicate’;
rather, inasmuch as he has just said ‘whenever one item is predicated of another
as of a subject’, he gives us to understand ‘synonymously and essentially’ when he
says ‘everything which is said of the predicate will also be said of the subject’. For
⁶² ὅταν ἕτερον καθ ᾿ ἑτέρου κατηγορῆται ὡς καθ ᾿ ὑποκειμένου, ὅσα κατὰ τοῦ κατηγορ-
ουμένου λέγεται, πάντα καὶ κατὰ τοῦ ὑποκειμένου ῥηθήσεται· οἷον ἄνθρωπος κατὰ τοῦ
τινὸς ἀνθρώπου κατηγορεῖται, τὸ δὲ ζῷον κατὰ τοῦ ἀνθρώπου· οὐκοῦν καὶ κατὰ τοῦ τινὸς
ἀνθρώπου τὸ ζῷον κατηγορηθήσεται.
146 Predicates and Subjects
example, animal is predicated of man as of a subject; for both the name of animal
and its account fit man.
(in Cat 80.32–81.11)⁶³
Transitivity, according to Porphyry, cannot hold unrestrictedly; for in that
case we should have to accept as valid the following argument:
Socrates is a man.
Man is a species.
So Socrates is a species.
And Aristotle does not in fact propose an unrestricted transitivity: it is
predication-as-of-a-subject, not predication tout court, which he claims to
be transitive. And in the fallacious argument, the predication in the second
premiss is not predication-as-of-a-subject.
Predication-as-of-a-subject is taken by Porphyry to be the same as essential
predication, and essential predication is taken to be the same as what he calls
‘synonymous’ predication, or predication in which both the name and the
account (or the definition) of the predicate hold of the subject. That notion
of synonymous predication derives from a later paragraph in the Categories:
It is clear from what we have said that in the case of items said of a subject, both
the name and the account are predicated of the subject … But with items which are
in a subject, in most cases neither the name nor the account is predicated of the
subject, but in some cases nothing prevents the name from being predicated of the
subject, although it is impossible for the account to be predicated of it. For example,
white, which is in a subject, namely a body, is predicated of the subject—for a body
is called white. But the account of white will never be predicated of a body.
(Cat 2a19–34)⁶⁴
⁶³ —ἀλλὰ πῶς τοῦτο ἀληθές; ὁ μὲν γὰρ ἄνθρωπος κατὰ Σωκράτους λέγεται καθ ᾿
ὑποκειμένου· κατὰ δὲ τοῦ ἀνθρώπου κατηγορεῖται οὐ μόνον τὸ ζῷον ἀλλὰ καὶ τὸ εἶδος· εἶδος
γὰρ ὁ ἄνθρωπος. οὐ μὴν ἔτι κατὰ τοῦ Σωκράτους πάντα κατηγορηθήσεται, ἀλλὰ τὸ μὲν ζῷον
κατηγορηθήσεται, οὐκέτι δὲ καὶ τὸ εἶδος· οὐ γὰρ Σωκράτης εἶδος.—ἀλλ᾿ ὁρᾷς ὅτι ἡ ἀτοπία
γέγονε παρὰ τὸ μὴ ἐκδέξασθαι ὀρθῶς πῶς εἴρηται ὅσα κατὰ τοῦ κατηγορουμένου λέγεται·
οὐ γὰρ ἁπλῶς εἴρηκεν ὅσα κατὰ τοῦ κατηγορουμένου λέγεται, ἀλλ᾿ εἰπὼν ὅταν ἕτερον καθ ᾿
ἑτέρου κατηγορῆται ὡς καθ ᾿ ὑποκειμένου δέδωκεν ὑπολαβεῖν τὸ συνωνύμως καὶ ἐν τῷ τί ἐστι
τὸ τηνικαῦτα· ὅσα κατὰ τοῦ κατηγορουμένου λέγεται, τοσαῦτα καὶ κατὰ τοῦ ὑποκειμένου
ῥηθήσεται. οἷον τὸ ζῷον κατὰ τοῦ ἀνθρώπου ὡς καθ ᾿ ὑποκειμένου κατηγορεῖται· ἐφαρμόζει
γὰρ τῷ ἀνθρώπῳ καὶ τοὔνομα τοῦ ζῴου καὶ ὁ λόγος.
⁶⁴ φανερὸν δὲ ἐκ τῶν εἰρημένων ὅτι τῶν καθ ᾿ ὑποκειμένου λεγομένων ἀναγκαῖον καὶ
τοὔνομα καὶ τὸν λόγον κατηγορεῖσθαι τοῦ ὑποκειμένου· ... τῶν δ᾿ ἐν ὑποκειμένῳ ὄντων
ἐπὶ μὲν τῶν πλείστων οὔτε τοὔνομα οὔτε ὁ λόγος κατηγορεῖται τοῦ ὑποκειμένου· ἐπ᾿ ἐνίων
δὲ τοὔνομα μὲν οὐδέν κωλύει κατηγορεῖσθαι τοῦ ὑποκειμένου, τὸν δὲ λόγον ἀδύνατον· οἷον
τὸ λευκὸν ἐν ὑποκειμένῳ ὂν τῷ σώματι κατηγορεῖται τοῦ ὑποκειμένου (λευκὸν γὰρ σῶμα
λέγεται), ὁ δὲ λόγος τοῦ λευκοῦ οὐδέποτε κατὰ τοῦ σώματος κατηγορηθήσεται.
The Transitivity of Predication 147
Items which are ‘in a subject’ are—or so the tradition uniformly sup-
posed—accidents or accidental predicates of that subject. Predication is
transitive only if both the name and the definition of the predicate hold of
the subject. In accidental predication the name rarely holds of the subject
and the definition never.
Consider a case in which the name of an accident is predicated of the
subject and ask whether such predication is transitive. If it is, then the
following argument must be valid:
Socrates is white.
White is a colour.
So Socrates is a colour.
Of course, the argument is not valid, and so transitivity does not hold for
accidental predication. To be sure, Aristotle does not say that in so many
words. But—so Porphyry and others thought—he is plainly committed to
it; and after all—so they thought—it is true.
I will consider my Cat Jeoffry; for the English Cats are the best in
Europe. Now Jeoffry is quintessentially a cat; and so, according to Aris-
totle, both the name ‘cat’ and the definition of the name ‘cat’ are
predicated of him. Jeoffry is also tenacious of his point. But neither
the name ‘tenacity’ nor any definition of that name is predicated of
him—after all, Jeoffry is not tenacity itself. Finally, Jeoffry is of the
Tribe of Tiger—but here truth must be sacrificed to the demands of
the example, and I shall pretend that Jeoffry is grey. Here, according
to Aristotle, the name ‘grey’ is predicated of Jeoffry; but the defini-
tion of that name, which must be ‘colour of such-and-such a kind’,
is not.
That illustrates what Aristotle appears to say in the Categories;andit
illustrates what Porphyry, and other Aristotelian commentators, took to be
quite generally true. But whether or not it is Aristotelian, it is odd. In
particular, what Aristotle says about
Jeoffry is grey
cannot possibly be true—and cannot possibly be true by Aristotle’s own
lights. The passage from the Categories claims that sometimes a name, but not
the account or definition of the name, may be true of something. But it is a
trivial truth, and a truth known to Aristotle and his successors, that a definiens
must be true of all and only those items of which the definiendum is true,
that definiens and definiendum must be logically equivalent. So it cannot be
148 Predicates and Subjects
the case that sometimes a name, but not its definition, applies to something.
If the name ‘grey’ is predicated of Jeoffry, then so is the definition—or
an appropriate definition—of that name. That is not, or should not be, a
controversial claim: it is a childish truth.
How on earth did Aristotle come to deny it? He denied it on the basis of
an example—and his successors found further examples, and offered some
sort of classification of them. But Aristotle’s example is false.
Jeoffry is grey
is on all counts parallel to
Jeoffry is tenacious.
If the name ‘grey’ (or the expression ‘a grey item’, or the word ‘greyness’, …)
is predicated in the sentence of ‘Jeoffry’ (or of Jeoffry), then—and trivi-
ally—the definition of the name is predicated of Jeoffry. The definition of
‘grey’, as it appears in
Jeoffry is grey
is not ‘colour of such-and-such a sort’ but rather ‘of such-and-such a
colour’; and for Jeoffry, as for anything else, to be grey is precisely to be of
such-and-such a colour.
Aristotle’s example is specious. How did he come to be taken in by it? It is
difficult not to think that he was misled by a simple syntactical ambiguity. In
English, the word ‘grey’ may be either an adjective or a noun. In Greek, the
word ‘λευκός’ is an adjective; but in the neuter singular form ‘λευκόν’itfunc-
tions not only as an ordinary adjective but also as a noun. When Aristotle says
that ‘the account of white will never be predicated of a body’, then what he says
is true provided that the word ‘white’ is construed as a noun. But then the name
‘white’—when that is construed as a noun—is not predicated of body either.
It is as though Aristotle were to remark that the definition of the noun ‘grey’ is
not predicated of the grey Jeoffry. Of course it isn’t—nor is the noun ‘grey’.
Aristotle finds important differences among ‘cat’, ‘tenacious’ and ‘grey’. He
is wrong when he claims that ‘grey’ is interestingly different from ‘tenacious’.
He is also wrong when he claims that ‘tenacious’ is interestingly different
from ‘cat’. Or rather, he is wrong if that claim is interpreted as a claim about
predication. Jeoffry is tenacious, according to the Categories, inasmuch as
tenacity is in Jeoffry; it is not the case that he is a cat inasmuch as cat or catness
is in him. Perhaps those claims are intelligible, and perhaps they are true. But
here they interest me only insofar as they bear upon the theory of predication.
Their bearing on predication was supposed (I think) to be something like
this. In
The Transitivity of Predication 149
Jeoffry is a cat
there is an essential predication; and so both the word ‘cat’ and its definition
are predicated of ‘Jeoffry’. In
Jeoffry is tenacious
there is an accidental predication; and so neither the word ‘tenacity’ nor
its definition is predicated of Jeoffry. All that—with the exception of the
repeated ‘and so’—is indisputable. But it does not set up a difference
between being a cat and being tenacious, or between the predications in the
two pertinent sentences. Just as neither the word ‘tenacity’ nor its definition
is predicated of Jeoffry, inasmuch as Jeoffry is not tenacity, so neither the
word ‘cathood’ nor its definition is predicated of Jeoffry, inasmuch as Jeoffry
is not cathood. Just as both the word ‘cat’ and its definition are predicated
of Jeoffry, inasmuch as Jeoffry is a cat, so both the word ‘tenacious’ and its
definition are predicated of Jeoffry, inasmuch as Jeoffry is tenacious.
Aristotle’s infelicitous remarks about ‘white’ provided the later comment-
ators with one spurious counterexample to the transitivity of A-predication.
Porphyry—in the passage I cited earlier—invokes the sentence
Man is a species.
The difficulties raised by that are different from any which might be raised
by ‘Jeoffry is grey’. In particular, if the word ‘species’ is replaced by its
definition—say ‘item which is ordered under a genus’—then the resulting
sentence is no odder than ‘Man is a species’: it is perfectly plain that, however
we should parse ‘Man is a species’, it cannot be that the word ‘species’ is
predicated of ‘man’ and its definition not. Nonetheless, however we should
parse ‘Man is a species’, it raises no difficulty for transitivity.
The central point may be brought out as follows. Here are three arguments
which, in an obvious way, run parallel to one another:
(1) Jeoffry is a cat. A cat is an animal. So Jeoffry is an animal.
(2) Jeoffry is grey. Grey is a colour. So Jeoffry is a colour.
(3) Jeoffry is a cat. The cat is a species. So Jeoffry is a species.
The first argument is valid, the second and third are invalid. So although
they are superficially similar, there must be some underlying difference which
distinguishes (1) from (2) and (3). What is it? The ancient tradition answers
as follows: ‘In argument (1) both premisses are predications-as-of-a-subject;
and since predication-as-of-a-subject is transitive, argument (1) is valid. In
arguments (2) and (3) the two premisses are predications; but in each case
one of them is not a predication-as-of-a-subject. And since predication is not
in general transitive, the arguments are not valid.’