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120 Predicates and Subjects

could each appeal to textual evidence. Here, then, is his brief answer to the

objection:

—If the work is about signiﬁcant utterances, how does it come about that the whole

of the later discussion is about objects?

—Because expressions, like announcers, announce the objects, and they take their

differences from the objects which they announce.

(in Cat 58.21–24)⁴⁵

Since expressions take their pertinent differences from, or are classiﬁed

according to, the sorts of object which they signify, you may easily talk about

predicates as though they were not the expressions which signify objects

but the objects which are signiﬁed by expressions. So although Aristotle

does often talk of predicates as if they were objects, that is no objection to

Porphyry’s thesis that predicates are expressions; for objects are, or can be

called, predicates just insofar as their names are predicates. Is white—the

colour white—predicated of a well-laundered shirt? No, of course not; for

predicates are expressions and the colour white is not an expression. And yet

also Yes, if you like—you may say that the colour is predicated of the shirt

inasmuch as the expression ‘white’ is predicated of the shirt (or of ‘the shirt’)

and the expression ‘white’ signiﬁes the colour white.

Well, it will be said, there argues a commentator desperate to defend his

own interpretation against a deﬁnitive textual objection. True. But there

are deﬁnitive textual objections to any interpretation. After all, Porphyry

has—and produces—impeccable evidence in favour of his own interpretation

and therefore against any rival account. He points out, for example, that

if Aristotle had been talking about objects, he would not have said ‘Either they signify

substances …’: objects do not signify—they are signiﬁed.

(in Cat 57.10–12)⁴⁶

Porphyry is right—and he can cite half a dozen other passages in the same

direction.

The textual situation looks like this. Most of the numerous passages in

which Aristotle discusses or alludes to subjects and predicates offer no clear

⁴⁵ —ἀλλὰ πῶς, εἰ περὶ φωνῶν σημαντικῶν ἐστιν ἡ πραγματεία, ἐν τοῖς ἑξῆς περὶ τῶν

πραγμάτων ὁ πᾶς αὐτῷ γεγένηται λόγος;—ὅτι αἱ φωναὶ ἀγγέλῳ ἐοικυῖαι τὰ πράγματα

ἀγγέλλουσιν, ἀπὸ δὲ τῶν πραγμάτων ὧν ἀγγέλλουσι τὰς διαφορὰς λαμβάνουσιν.

⁴⁶ εἰ γὰρ περὶ πραγμάτων ἦν αὐτῷ ὁ λόγος, οὐκ ἂν εἶπεν τὸ ἤτοι οὐσίαν σημαίνει· οὐ γὰρ

σημαίνουσι τὰ πράγματα ἀλλὰ σημαίνεται.

Porphyrean Predicates 121

answer one way or another to the question ‘What sort of item is a predicate?’.

(You wouldn’t expect the texts to do so.) Several texts quite plainly indicate

that Aristotle took objects, and not signiﬁcant expressions, to be predicates

and subjects. Several texts quite plainly indicate that Aristotle took signiﬁcant

expressions, and not objects, to be subjects and predicates. That is to say,

Aristotle was muddled or inconsistent when he thought about the status of

predicates and subjects; or rather (what comes in the end to the same thing),

Aristotle probably never thought very long about the status of the things.

Anyone who determines to think about the matter on Aristotle’s behalf

will be confronted by a number of pertinent considerations of very different

sorts. One such consideration starts from Dexippus’ example,

Animal is predicated of man.

There the ﬁrst word represents the predicate and the last the subject. The

particular example is taken from the Categories; but it occurs again and again

in the Analytics; and in general, when the Analytics offers illustrative terms

they are usually conveyed by words like ‘animal’, ‘man’, ‘white’, … Roughly

speaking, they are conveyed by words which will make a verbal phrase when

they are preﬁxed by ‘is (a)’.

Dexippus’ illustrative sentence, and sentences like it, are so much part of

the jargon of traditional logic that we are inclined to think that we understand

them. But what on earth does

Animal is predicated of man

mean? The sentence—or at least, its English version—looks ungrammatical,

or babu. Perhaps it is comparable to

Animal is eaten by man

—which might just be construed as an off-colour way of saying that some

or all animals are used as human fodder. The Greek, in fact, admits that

construal less unwillingly than the English; for in the Greek the word ‘animal’

is preceded by the deﬁnite article (‘τὸ ζῷον’), and in Greek as in English the

deﬁnite article may indicate universality (‘The triangle has an angle-sum of

180

◦

’). In that case, Dexippus’ sentence means that every animal is predicated

of man.

But that interpretation cannot be correct. You can do all sorts of things to

animals, legal and illegal; but one thing you can’t do is predicate them. It is

terms which are predicated, and animals are not terms. And if that objection

is deemed unsatisfactory, then recall that

Animal is predicated of man

is supposed to convey a truth. Now

122 Predicates and Subjects

All animals are predicated of man

presumably entails that

Zebras are predicated of man.

And that—whatever it may mean—is surely not true.

Rather, if the Dexippan sentence is to be understood, then its ﬁrst

word must be taken as a singular term. Perhaps, then, ‘animal’ stands for

‘animality’, or for ‘being an animal’, or for ‘to be an animal’, or for some

other such abstract expression? After all, it was philippism—or being a

partisan of Philip—which was so scandalously imputed to or predicated of

Demosthenes. That construal ﬁts well with some of the Aristotelian texts,

anditisinmanywaysattractive.WhenIsaythatJeoffryisgrey,Isay

something of him, namely that he is grey; that is to say, I predicate being

grey of him—or I predicate greyness of him. Such things trip neatly off the

tongue.

But the construal has its drawbacks. First, and most obviously, it is difﬁcult

to see why Aristotle should have written ‘animal’ and ‘white’ and the like if

he really meant ‘animality’ and ‘being white’ and the like.

Secondly, the requirement of homogeneity will not be met unless subjects

as well as predicates are taken as abstract objects. So the sentence

Animal is predicated of man

will come out as, say,

Animality is predicated of humanity.

But what could that mean? Like the Platonic sentence

Man participates in animality,

the Aristotelian sentence

Animal is predicated of man

is intended somehow to reveal the truth, or an aspect of the truth, which is

conveyed by the ordinary sentence

Men are animals.

But, like the genuine Platonic sentence, the pseudo-Aristotelian sentence

Animality is predicated of humanity

is at best an inﬂated and an obscure way of saying that men are animals.

The Porphyrean account of predication takes the ﬁrst word of the Dexippan

sentence as a singular term—it is a name of an expression. In

Animal is predicated of man

the word ‘animal’ occurs autonomously; and that is, of course, a perfectly

normal piece of English (and of Greek). Homogeneity then requires the same

treatment for ‘man’; but, again, that does not unduly force the Greek.

Problems for Porphyry 123

I do not claim (and neither did Porphyry) that the Porphyrean account

represents what Aristotle said; I do not claim (though Porphyry did) that it

represents what Aristotle really meant to say or what he ought to have said.

Rather, I make a doubly conditional claim, thus: if, ﬁrst, the homogeneity

requirement is to be met and subjects and predicates are to be items of the same

sort, and if, secondly, the general notion of predication is to be understood

in the same way in the Categories and in the Analytics (and throughout the

Organon), then the Porphyrean account of predication is at least as good as

any other account. The two conditions are not independent of one another.

If the second condition is met and predication is uniform across the Organon,

then the ﬁrst condition must also be met; for the syllogistic of the Analytics

demands homogeneity. The second condition will be accepted—insisted

upon—by anyone who takes the Organon to constitute a uniﬁed treatment

of logic. And even for those of us who know that the Organon was a botch,

the second condition must be at least mildly enticing: after all, Aristotle never

indicates that he changed his mind about predication, or that he worked with

different conceptions of predication in different contexts.

PROBLEMS FOR PORPHYRY

Predication is a relation between a pair of terms in a proposition; and, on

the Porphyrean account of the matter, terms and propositions are linguistic

items, so that predication is a relation between a pair of expressions in a

sentence. In the sentence

Full fathom ﬁve thy father lies,

something is said of something, a term is predicated of a term, the expression

‘an item which lies ﬁve fathoms deep’ is predicated of the expression ‘thy

father’. So the sentence might be compared to what I shall call its Porphyrean

partner, namely

‘an item which lies ﬁve fathoms deep’ is predicated of ‘thy father’.

In general, any sentence in which something is said of something will have a

Porphyrean partner which says what item it says of what item.

What is the relation between a sentence and its Porphyrean partner?

Inasmuch as the partner purports to analyse the sentence, or to make explicit

what the sentence leaves implicit, you might be tempted to think that the

two things must be very close to one another; more particularly, you might

be tempted to think that a Porphyrean partner ought to have the same

124 Predicates and Subjects

structure as its mate, and that it ought to be logically equivalent to its mate.

But it looks as though a Porphyrean partner has a different structure from

its mate—it is explicitly relational whereas its mate is not. And it looks as

though a Porphyrean partner is not equivalent to its mate—it implies various

things about linguistic expressions whereas its mate does not. There are, it

seems, two problems for Porphyry: they indicate that Porphyrean partners are

too distant from their mates, and they thereby suggest that the Porphyrean

account of predication must be called into doubt.

As far as identity of structure goes, it has been pointed out that Porphyrean

partners, like their mates, have a subject–predicate structure or say something

of something. Thus the sentence

‘an item which lies ﬁve fathoms deep’ is predicated of ‘thy father’

predicates ‘an item predicated of ‘thy father’’ of ‘‘an item which lies ﬁve

fathoms deep’’. In general, any sentence of the form ‘x is predicated of y’ says

something of something: it predicates ‘an item predicated of y’ of ‘x’. But that

observation does not go very far—indeed it hardly leaves the starting-gates.

For the problem is not that the Porphyrean partner lacks a structure which

its mate possesses: rather, it is that the partner has a structure which its

mate lacks. The Porphyrean partner has a relational structure—insofar as

predication is a two-placed relation. The sentence

Full fathom ﬁve thy father lies

is not relational (or at any rate, it is not relational in the pertinent way). A

Platonist might demur, alleging that the real form of the sentence comes out

from a paraphrase such as

Thy father participates in being-at-a-depth-of-ﬁve-full-fathoms

But that way madness lies, and an inﬁnite regression.

In any case, there is a far better way of dealing with the matter. It is true

that the Porphyrean sentence

‘an item which lies ﬁve fathoms deep’ is predicated of ‘thy father’

has a relational structure. And from that indisputable fact we are invited to

infer that, if the partnership is genuine, then its mate

Full fathom ﬁve thy father lies,

must also have a relational structure. But why make the inference? Here is a

rough parallel. In the sentence

The weeping Pleiads wester and I lie down alone,

‘the weeping Pleiads wester’ is conjoined with ‘I lie down alone’. Now the

sentence

‘the weeping Pleaids wester’ is conjoined with ‘I lie down alone’

Problems for Porphyry 125

expresses a relation—and a relation between two linguistic items. Must we

infer that

The weeping Pleiads wester and I lie down alone

also expresses a relation between two linguistic items? Of course not: how

can we infer something evidently false from two palpable truths? The moral

is this: a sentence which explicates the structure of a given sentence need not

itself have the structure which it explicates. Why ever think that it ought to?

This point, or something fairly close to it, was acknowledged in antiquity.

According to Alexander,

the later thinkers, attending to expressions and not to meanings, deny that the same

thing comes about when terms are replaced by equipollent expressions. For although

‘If A, B’ means the same as ‘B follows A’,

they claim that those two sorts of expression have different logical characters

(in APr 373.29–32).⁴⁷ The claim made by the later thinkers will be addressed

in a later chapter. Here I cite the passage to show that Alexander took two

sentences with very different syntactical structures to have the same sense.

Alexander’s remark is echoed in Apollonius Dyscolus, who reports that

Trypho says that items which are replaced do not necessarily fall into the same

species—the verb ‘follows’ is replaced by the connector ‘if’:

Its being light follows its being day

—that is the same as

If it is day, it is light.

(conj 220.7–10)⁴⁸

Thepointisnotmadeverycleanly;butthegeneralmessageisplain.Noris

it an isolated remark. Elsewhere, where he is arguing against the suggestion

that articles are a form of pronoun, Apollonius has this to say:

It is feeble to say that articles are used in place of pronouns and for that reason form

a single part of sayings with them. For ﬁrst, it is not the case that if one item is

taken in place of another, then it is for that reason the same as it. … The conditional

connector ‘if’ has the same force as the verb ‘follows’:

⁴⁷ οἱ δὲ νεώτεροι ταῖς λέξεσιν ἐπακολουθοῦντες οὐκέτι δὲ τοῖς σημαινομένοις οὐ ταὐτόν

φασι γίνεσθαι ἐν ταῖς εἰς τὰς ἰσοδυναμούσας λέξεις μεταλήψεσι τῶν ὅρων. ταὐτὸν γὰρ

σημαίνοντος τοῦ εἰ τὸ Α, τὸ Β τῷ ἀκολουθεῖν τῷ Α τὸ Β, ...

⁴⁸ καί φησι Τρύφων ὡς οὐ πάντως τὰ μεταλαμβανόμενα εἰς τὸ αὐτὸ εἶδος ἐπάγεται. τὸ

ἀκολουθεῖ ῥῆμα μετάληψιν ἔχει τὴν εἰς τὸν εἴ σύνδεσμον· ἀκολουθεῖ τῷ ἡμέραν εἶναι τὸ φῶς

εἶναι· ἴσον γὰρ τῷ εἰ ἡμέρα ἐστί, φῶς ἐστίν.

126 Predicates and Subjects

Its being light follows its being day.

If it is day, it is light.

(pron 7.8–15)⁴⁹

A couple of sentences may have the same force or sense and yet display

different syntactical structures.

The conditional sentence

If it is day, it is light

says that ‘It is light’ follows from ‘It is day’, so that it has what I may call an

Apollonian partner, namely

‘It is light’ follows from ‘It is day’.

Every conditional sentence has its Apollonian partner. The partner has a

relational structure, being of the form ‘x follows from y’. The conditional

sentence itself does not have a relational structure. Apollonius rightly ﬁnds

nothing odd about that; and we should ﬁnd nothing odd about the fact that

Porphyrean partners are relational while their mates are not.

That is surely true; and it is perhaps quite uncontroversially true that

equivalent sentences need not have all their structures in common. But the

second problem for Porphyry remains; for surely a Porphyrean partner and

its mate are not logically equivalent to one another? (Nor, come to that, do

Apollonian partners and their mates form logically equivalent couples.) The

sentence

Full fathom ﬁve thy father lies

does not imply anything about any relations between signiﬁcant expressions,

whereas the Porphyrean partner,

‘an item which lies ﬁve fathoms deep’ is predicated of ‘thy father’

entails that at least one linguistic expression is predicated of another linguistic

expression. The Porphyrean sentence is true only if the expression ‘‘thy father’’

designates something—and designates a linguistic expression. Its mate is true

only if ‘thy father’ designates something (and designates a man); but the truth

of the mate does not require that ‘‘thy father’’ designate anything—indeed,

it does not require that there be such an expression as ‘‘thy father’’. Two

sentences which have different implications are not equivalent to one another.

So a Porphyrean partner is not equivalent to its mate. (Nor is an Apollonian

partner equivalent to its mate.)

⁴⁹ κἀκεῖνο δ᾿ εὔηθες τὸ λέγειν ἄρθρα ἀντὶ ἀντωνυμιῶν καὶ διὰ τοῦτο ἓν μέρος λόγου.

πρῶτον οὐκ εἴ τι ἀντί τινος παραλαμβάνεται, εὐθέως ταὐτὸν ἐκείνῳ ἐστίν. ... καὶ ὁ εἴ

συναπτικὸς ἰσοδυναμεῖ τῷ ἀκολουθεῖ ῥήματι·ἀκολουθεῖ τῷ ἡμέραν εἶναι καὶ φῶς εἶναι—εἰ

ἡμέρα ἐστί, φῶς ἐστί.

Problems for Porphyry 127

It is tempting to reply to that argument along the following lines.

Philosophers of a certain persuasion have long been fond of what they

call T-sentences. The ‘T’ stands for truth. The familiar example of a

T-sentence is

‘Snow is white’ is true if and only if snow is white.

The general form of a T-sentence is this:

SistrueifandonlyifP.

Such equivalences are the theorems of the only respectable theory of truth,

and they form the heart of the only serious theory of meaning.

Now the pertinent Shakespearean T-sentence guarantees that

Full fathom ﬁve thy father lies

is equivalent to

‘Full fathom ﬁve thy father lies’ is true.

But that is equivalent to

‘item which lies ﬁve fathoms deep’ is true of what ‘thy father’ is true of.

And that, in turn—to anticipate a later contention—is equivalent to

‘item which lies ﬁve fathoms deep’ is predicated of ‘thy father’.

So the Porphyrean partner is in fact demonstrably equivalent to its mate.

Of course, anyone who rejects the equivalence will hesitate at the very ﬁrst

step in the argument. After all,

‘Full fathom ﬁve thy father lies’ is true

entails that there exists at least one sentence, whereas the Shakespearean

line does not—so those two items are not equivalent. And quite generally,

T-sentences do not express logical equivalences; that familiar proposition,

‘Snow is white’ is true if and only if snow is white

is true; but it is not a truth of logic—still less, despite what tiros often incau-

tiously think, is it an empty tautology: it is a contingent truth, an empirical

truth, a truth which is underwritten by certain facts about English usage.

That is the indisputable truth about T-sentences. But it is something

which should hearten rather than depress the Porphyreans. They may, after

all, claim that the equivalence

‘an item which lies ﬁve fathoms deep’ is predicated of ‘thy father’ if and

only if full fathom ﬁve thy father lies

is not a logical but an empirical truth, which has the same status as the

T-sentence

‘Full fathom ﬁve thy father lies’ is true if and only if thy father lies full

fathom ﬁve.

128 Predicates and Subjects

There is no reason why the Porphyreans, or anyone else, should want more

than that.

COMPLEX PREDICATIONS

However all that may be, the ancient commentator on the Categories,will

state, with a bow to Porphyry, that predicates are signiﬁcant expressions. But

signiﬁcant expressions come in several varieties, and the commentator will

next ask what sort of expressions predicates are. To that question there was a

standard answer: Predicates are simple signiﬁcant expressions. In discussing

predicates of quantity and the difﬁculty of ﬁnding any genuine examples of

the things, Plotinus observed that

after all, three oxen are not a quantity—rather, their number is. For three oxen

are thereby two predications—and in the same way a line thus-and-so long is two

predications, and a surface thus-and-so large is two.

(enn vi i 4.[17–20])⁵⁰

When the poet, contemplating the infant’s grave, cries

’Tis three feet long and two feet wide

surely he has predicated something of something? And if predicates are

signiﬁcant expressions, then presumably he has predicated ‘three feet long

and two feet wide’ of something. According to Plotinus, that is not so; or at

any rate, it is not so strictly speaking. For although in uttering

’Tis three feet long and two feet wide

the poet has indeed done some predication, he has predicated several items

rather than one. Perhaps it is evident that he has predicated both ‘three feet

long’ and also ‘two feet wide’. But Plotinus will go further than that. At any

rate, if ‘three oxen are thereby two predicates’, then ‘three feet long’ must be

two (or three) predicates; so that in saying

’Tis three feet long

the poet predicates both ‘three feet’ and also ‘long’ of something—or perhaps

he predicates ‘three’ and ‘feet’ and ‘long’ of something.

That, for several reasons, is what we might call moderately satisfactory

only. And since Plotinus was absolutely right when he argued that predicates

⁵⁰ ἐπεὶ οὐδὲ τοὺς τρεῖς βοῦς ποσόν, ἀλλὰ τὸν ἐπ᾿ αὐτοῖς ἀριθμόν· βόες γὰρ τρεῖς δύο

κατηγορίαι ἤδη. οὕτως οὖν καὶ γραμμὴ τοσήδε δύο κατηγορίαι, καὶ ἐπιφάνεια τοσήδε δύο.

Complex Predications 129

in the Aristotelian class of quantity are puzzling items, let me turn to a

different poet and an easier sort of example:

The mouse is a creature of great personal valour.

There—Plotinus would have urged—are (at least) two predicates; for the

sentence, or its user, predicates (at least) two different things of ‘mouse’,

namely ‘creature’ and ‘of great personal valour’. Why so? Why not say that

the predicate is ‘creature of great personal valour’, or ‘brave beast’? The

answer lies in the Categories. There Aristotle distinguishes ten types or classes

of predicate. The division was taken to be exhaustive and exclusive: an item

is a predicate if and only if it is a member of exactly one of the ten classes.

(In truth, there were rumblings about exclusivity—but they do not concern

the present point.) But ‘brave beast’ belongs to none of the ten classes. True,

‘brave’ is a predicate in the class of quality, and ‘beast’ is a predicate in the class

of substance; but ‘brave beast’ is neither in quality nor in substance—nor

anywhere else. Hence it is not a predicate; that is to say, it is not one predicate

but several predicates.

Then what is to be done with such items? They cannot simply be

disregarded by the logician. After all, they may occur in seemingly decent

Aristotelian syllogisms:

The mouse is a creature of great personal valour, and brave beasts die

young—so there are no old mice.

So, as well as being two predicates, ‘brave beast’ is perhaps also, in a way,

a single predicate—a single complex predicate? Aristotle once or twice

mentions what he calls conjoined predicates. For example:

That this holds of that, and that this is true of that, should be taken in as many ways

as the predications have been divided—and those either with a certain qualiﬁcation

or simply, and again either simple or conjoined. Similarly for not holding. We must

look into that and distinguish it better.

(APr 49a6–10)⁵¹

Alexander comments as follows:

And again, they should be predicated either simply and without composition—i.e.

a single item which belongs to a single predication—or else conjoined and com-

bined. For

⁵¹ τὸ δ᾿ ὑπάρχειν τόδε τῷδε καὶ τὸ ἀληθεύεσθαι τόδε κατὰ τοῦδε τοσαυταχῶς ληπτέον

ὁσαχῶς αἱ κατηγορίαι διῄρηνται· καὶ ταύτας ἢ πῇ ἢ ἁπλῶς, ἔτι ἢ ἁπλᾶς ἢ συμπεπλεγμένας·

ὁμοίως δὲ καὶ τὸ μὴ ὑπάρχειν. ἐπισκεπτέον δὲ ταῦτα καὶ διοριστέον βέλτιον.