Barnes Jonathan. Truth, etc

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160 Predicates and Subjects

Aristotle has not in fact shown—or even said—anything of the sort in the de

Interpretatione. But Alexander is presumably thinking of the passage in which

it is stated that

‘every’ signiﬁes not the universal but that something is universally so.

(Int 17b11–12)⁷²

He reads too much into that phrase; but the thesis which he and Galen

uphold and which he ascribes to Aristotle is scarcely outlandish.

True, we may say things like ‘All the Campbells were massacred’, and

‘Every Napoleon meets his Waterloo’; but there ‘Campbell’ means ‘member

of the Campbell clan’ and ‘Napoleon’ does not designate the Corsican

adventurer. Such idioms apart, the juxtaposition of a quantiﬁer and a

proper name breeds nonsense. True, an e.e.cummings—whoops—might

have written

and some of i embraces every you,

though ‘I’ and ‘you’ are singular pronouns. But poetry does not count—and

in any case, the cummings’ style sculpts sense from nonsense. As for items

Every the horse I put my shirt on loses

Somethecatforonceisn’tdemandingtobefed,

they are merely deformed. To be sure, we can easily understand them. But

there is a lot of nonsense which we easily understand, and we do so precisely

insofar as we recognize it as a deformation of a piece of sense.

Now a sentence may contribute to an Aristotelian syllogism only insofar

as it makes a predication in one of the four Aristotelian styles. Galen, in the

passage I have just cited, requires that there be a quantiﬁer in every sentence

which forms part of an Aristotelian syllogism: ‘it must be determined in

the saying whether the predicate is predicated of all of it or of some’. He

does not state—and he should not be taken to mean—that (say) every

universal afﬁrmative sentence in an Aristotelian syllogism must contain the

word‘every’,stilllessthatitmustbeaninstanceoftheformula‘Every

so-and-so is such-and-such’. For he elsewhere notices explicitly that there are

several ways of determining a sentence as universal. For example, he holds

that in

The mouse is a creature of great personal valour,

⁷² τὸ γὰρ πᾶς οὐ τὸ καθόλου σημαίνει ἀλλ᾿ ὅτι καθόλου.

Singular Predication 161

the deﬁnite article functions as a universal quantiﬁer. So too does the

indeﬁnite article in

A garden is a lovesome thing, God wot.

In general, there are numerous idiomatic ways of determining a sentence as

universal or particular. But by one crook or another, Aristotelian sentences

must be determined as universal or particular.

Those two facts—that you can’t attach quantiﬁers to singular terms and

that propositions which appear in syllogisms must be quantiﬁed—do not

of course in themselves entail that singular propositions cannot appear in

syllogisms. I have just urged that some singular propositions may quite

decently sport quantiﬁers—for example,

Every snub-nosed Greek philosopher is Socrates.

Do not such things slip through a gap in the fence so that a little singularity

may sneak into the syllogistic? No; for such things are blocked by the require-

ment of homogeneity. If ‘Socrates’ may function as a predicate in a syllogistic

proposition, then it may function as a subject—that is homogeneity. If

‘Socrates’ may function as a subject in a syllogistic proposition, then it may

carry a quantiﬁer. But ‘Socrates’ cannot carry a quantiﬁer.

In sum, there seems to be good reason to hold, ﬁrst, that singular propos-

itions may and do appear as such as components of Aristotelian syllogisms;

secondly, that only quantiﬁed propositions may appear as components of

such syllogisms; and thirdly, that propositions with singular subjects may

not be quantiﬁed. But those three propositions are mutually inconsistent.

What—if anything—can be done?

It is, I think, often supposed that the last two of the three propositions must

be maintained. That is to say, predications in one of the four Aristotelian

styles are the only matter of Aristotelian syllogistic, and the subjects of such

predications are determined by quantiﬁers. And it is often supposed, in

addition, that you simply cannot say ‘Every Socrates’ or ‘Some Socrates’ or

anything else of the sort; for such phrases—given that ‘Socrates’ is a singular

term—are nonsense, ungrammatical nonsense.

So we must reject the ﬁrst of the three propositions, and insist that singular

subjects cannot feature in Aristotelian syllogisms. To say that is to go against

a considerable number of texts: it is not an interpretation of Aristotle but

a correction. Nonetheless, it may be held to correct him in an Aristotelian

way. For despite certain asides in the Analytics and elsewhere, the ofﬁcial

doctrine of the Posterior Analytics denies that singular truths can be proved;

and although that doctrine does not entail that singular subjects cannot

162 Predicates and Subjects

appear in non-probative syllogisms, nothing much will be lost—and nothing

at all will be lost to demonstrative theory—if singular subjects are banned

from the syllogistic altogether.

Having gone that far, why not go a little further? Why not maintain that

singular sentences do not manifest, as such, the structure of Aristotelian pre-

dication? Did not Frege truly claim that there is a fundamental difference—a

fundamental logical difference—between

Jeoffry is grey

and

All cats are grey in the dark?

The former sentence has (among other forms) the form characteristic of

singular propositions which logicians customarily represent by a formula

such as

F(a).

‘F’ represents a one-placed predicate and ‘a’ a singular term; so that ‘F(a)’

might represent ‘is grey(Jeoffry)’—which is just a funny way of writing

‘Jeoffry is grey’. The latter sentence—

All cats are grey in the dark

—has (among other forms) the form characteristic of universal propositions.

Logicians usually represent it by something equivalent to this:

Take anything whatever, if F(it), then G(it).

So:

Take anything you like, if it’s a cat then it’s grey in the dark.

Aristotelian logic does not, and cannot, distinguish between those two forms

of proposition. That is the invisible worm in the bud, the Achilles’ heel, the

hinc illae lacrimae, of traditional syllogistic.

Now there can be no doubt but that it is a far far better thing to be a

Fregean in logic than to be an Aristotelian. And there may be a dozen good

reasons for abandoning Aristotelian syllogistic, reasons which have nothing

to do with singular propositions. But a stubborn Aristotelian will not sell the

pass at the ﬁrst appearance of a singular subject.

If propositions with singular subjects are to be accommodated within

Aristotelian logic, then either we must ﬁnd quantiﬁers for singular subjects or

else unquantiﬁed propositions—and another style, or other styles, of predic-

ation—must be allowed into the syllogistic. At ﬁrst blush, the latter option

is the more inviting: after all, no one is forbidden to make additions to Aris-

totelian syllogistic; and it would not be difﬁcult to invent rules which specify

the logical relations among different sorts of singular proposition and between

Singular Predication 163

singular propositions on the one hand and quantiﬁed Aristotelian propositions

on the other. But to do that is hardly to accommodate singular subjects within

Aristotelian logic: it is to accommodate Aristotelian logic to singular subjects.

So it is the former option—that of ﬁnding quantiﬁers for singular sub-

jects—which the stubborn Aristotelian must take. And he might ﬁrst appeal

to a passage in the Analytics where Aristotle considers a couple of sophistical

arguments, which he refutes by urging that each has a false premiss. (The

arguments themselves need not detain us.) In the ﬁrst case he says that

It is false to claim that every thinkable Aristomenes exists forever.

(APr 47b28–29)⁷³

In the second case he says that

It is not universally true that Mikkalos is musical.

(APr 47b35–36)⁷⁴

In the ﬁrst case Aristotle seems prepared to afﬁx a quantiﬁer to something

which might perhaps be a singular term, namely ‘thinkable Aristomenes’;

and in the second case he seems prepared to allow that a proposition with a

singular subject might somehow be universally true.

Alexander’s commentary on the passage is disappointing insofar as he does

not take up the quantiﬁcational question. But at the end of his remarks he

observes, casually enough, that

‘universally Mikkalos is musical’ means ‘every Mikkalos is musical’.

(in APr 352.25–26)⁷⁵

Apparently he sees nothing untoward in that sentence—which he simply

declares to be false.

Philoponus takes a different line from Alexander on the case of Mikkalos,

and he does not think that anything like ‘Every Mikkalos is musical’

is involved. On the case of Aristomenes—where Alexander says nothing

pertinent to the present point—he has this to say:

When I say

The thinkable Aristomenes,

I indicate the very thinkable form of Aristomenes; but if I say

⁷³ τοῦτο δὲ ψεῦδος, τὸ ἀξιοῦν πάντα τὸν διανοητὸν ᾿Αριστομένην ἀεὶ εἶναι.

⁷⁴ οὐ γὰρ ἀληθὲς καθόλου, Μίκκαλος μουσικός ...

⁷⁵ τὸ γὰρ καθόλου Μίκκαλος μουσικὸς τὴν πᾶς Μίκκαλος μουσικὸς σημαίνει.

164 Predicates and Subjects

Every thinkable Aristomenes,

I mean nothing other than

All the individual Aristomeneses who happen to be thinkable

—and of them it is not true to say that they exist forever.

(in APr 326.6–10)⁷⁶

So Philoponus, like Alexander, ﬁnds nothing untoward in fastening a quan-

tiﬁer to a proper name.

But Philoponus fastens a plural quantiﬁer to his proper name, and he

puts the proper name itself in the plural: presumably, by ‘all the individual

Aristomeneses’ he meant something like ‘everyone who is called by the name

‘Aristomenes’’. Whether or not that is a good way of dealing with Aristotle’s

sophism, it is of no interest in the present context; for although

Every item called ‘Jeoffry’ is grey

is an impeccably formed predicative sentence, it is not equivalent to

Jeoffry is grey.

For on Philoponus’ understanding, it is about a plurality of cats and not, or

not uniquely, about Christopher Smart’s best friend.

Alexander’s view of Mikkalos is more promising. For it suggests that we

might construe singular terms as though they were general. Why not, for

example, print the word ‘aristotle’ with a little a, and suppose that ‘Aristotle

wrote the Analytics’ is equivalent to—or perhaps short for—‘Every aristotle

wrote the Analytics’? As for the general term ‘aristotle’, that is perfectly

intelligible: ‘aristotle’ is true of an item if and only if that item is Aristotle.

Such a line of thought has something going for it. For example, it might

invoke the fact that, in Greek, proper names regularly take the deﬁnite article:

‘ὁΣωκράτης’ is good Greek for ‘Socrates’. Why not construe the deﬁnite

article there as a universal quantiﬁer?

Well, in ‘ὁΣωκράτης’ the article is in fact better taken as a demonstrat-

ive—like the Latin ‘ille’in‘Hector ille’. (Something similar is true of the

comparable use of the deﬁnitive article in German, say, or in Italian.) And

even if we swallow a quantiﬁcational article for ‘Socrates’, and for proper

names in general, we shall not do so for pronouns or for singular phrases such

as ‘the sun’ and ‘the moon’. If

Every aristotle shall be extolled

⁷⁶ ὅταν μὲν γὰρ εἴπω ὁ διανοητὸς ᾿Αριστομένης, αὐτὸ τὸ διανοητὸν εἶδος τοῦ ᾿Αριστομένους

δηλῶ· ἐὰν δὲ εἴπω πᾶς διανοητὸς ᾿Αριστομένης, οὐδὲν ἕτερον λέγω ἢ πάντες οἱ καθ ᾿ ἕκαστα

᾿Αριστομένεις οἷς συμβέβηκε τὸ διανοητοῖς εἶναι. διὸ οὐκ ἀληθὲς ἐπὶ τούτων εἰπεῖν ὅτι ἀεί

εἰσιν.

Singular Predication 165

is as good as

Every valley shall be exalted,

the same can hardly be said for

Every the sun shall be extinguished.

Moreover, even if ingenuity could make something out of ‘every the sun’, the

effort is hardly worthwhile. For there is another—and a more familiar—line

of thought which is more enticing.

It too transforms singular terms into general terms; but it does so by

preﬁxing them with some such formula as ‘item which is the same as’. Thus

‘Aristotle’ is replaced by ‘item which is the same as Aristotle’, ‘you’ by ‘item

which is the same as you’, ‘the sun’ by ‘item which is the same as the sun’, and

so on. Singular sentences, thus treated, turn at once into indeﬁnite sentences;

and so they may then be regarded as particular predications—or, of course,

you may attach quantiﬁers to them.

There is nothing mysterious about the general term ‘item which is the same

as Aristotle’: it is true of an object if and only if that object is the same as Aris-

totle—that is to say, it is true of Aristotle and of him alone. In general, ‘item

which is the same as A’ is true of all and only those objects which are identical

with A—that is to say, it is true of A and of A alone. Then the propositions

Aristotle is wise

Some item identical with Aristotle is wise

Every item identical with Aristotle is wise

turn out to be equivalent to one another. And that equivalence is all that

an Aristotelian needs in order to accommodate singular subjects within his

syllogistic.

Of course, there is no need to replace ‘Aristotle’ by ‘item which is the same

as Aristotle’. Rather, the sentence

Aristotle is wise

itself is—among other things—an A-predication; for it predicates ‘wise’

universally and afﬁrmatively of ‘an item which is the same as Aristotle’.

In traditional manuals of logic, the paradigm example of a syllogism in

Barbara was often this:

All men are mortal

Socrates is a man

Therefore: Socrates is mortal

Reﬁned Aristotelians have urged that the traditional paradigm is not a case of

Barbara at all: all three component propositions of a syllogism in Barbara must

166 Predicates and Subjects

be A-predications, but the second premiss and the conclusion of the paradigm

are not A-predications. Aristotelians of yet more exquisite reﬁnement may

now welcome the paradigm back into the Aristotelian fold.

An audacious conclusion now huffs at the gate: whether or not de Saussure

was right about grammar, Frege was wrong about logic—wrong insofar as

he suggested that subjects and predicates should be banished from logic.

For singular predications are not, as Frege perhaps thought, the invisible

worm of Aristotelian syllogistic; and the traditional obsession with subjects

and predicates does not imply that singular propositions cannot ﬁnd a place

within traditional logic.

But of course, Frege was not wrong, and nothing in the preceding argument

implies that he was wrong. If the sentence

Jeoffry is grey

has the form of an Aristotelian A-predication, it also has the form ‘F(a)’,

which is the characteristically singular form of singular sentences. That form is

something which Aristotelian syllogistic does not and cannot recognize. Con-

sequently—and this is the underlying force of Frege’s criticism—Aristotelian

syllogistic will be unable to account for the validity of any syllogisms

which turn about the peculiarities of that particular singular form. For

example, Aristotelian syllogistic cannot accommodate the simple inference

from

Jeoffry is grey

Something is grey.

And if Aristotelian logic cannot accommodate that inference, it is evid-

ently less potent—immeasurably less potent—than its admirers have sup-

posed.

I say that Aristotelian logic cannot accommodate the simple inference. It

will be answered that the inference can be reformulated as a syllogism in

Darapti, thus:

Every Jeoffry is grey.

Every Jeoffry is a thing.

Therefore, some thing is grey.

Well, you can do that if you like; and with enough ingenuity you will

be able to do similar and more complicated things for similar and more

Singular Predication 167

complicated cases.⁷⁷ But does that show that Aristotelian syllogistic can, after

all, accommodate the inferences? What are the rules of the game?

However that may be, treating singular sentences as A-predications does

not suddenly transform Aristotelian syllogistic into modern predicate logic.

But at least it enables Aristotelian syllogistic to formulate proofs which

conclude to a singular truth. And that is not nothing.

⁷⁷ Corine Besson forced me to take note of this point.

3. What is a Connector?

SENTENTIAL CONNECTIVES

The symbolisms of contemporary logic contain certain expressions called

propositional connectives or, perhaps better, sentential connectives. A sen-

tential connective is an expression which, when suitably concatenated with

one or more sentences, makes a sentence. For example, the symbol ‘⊃’isa

sentential connective: inscribe it between any pair of sentences and the result

is a sentence. Or again, ‘¬’ is a sentential connective: inscribe it before any

sentence and the result is a sentence.

Natural languages, English among them, also contain sentential connect-

ives. For example, the word ‘if ’ is a sentential connective: utter ‘if ’ followed

by a pair of sentences (of an appropriate sort) and the result is a sentence.

The word ‘if ’, like the symbol ‘⊃’,takestwosentencestotango.English

also contains expressions which, like the symbol ‘¬’, take a single sentence to

make a sentence. For example, write ‘perhaps’ followed by a sentence—or in

the middle of a sentence—and the result is a sentence. So too ‘mercifully’, or

‘necessarily’. And there are complex expressions with the same construction,

among them ‘It is not the case that’. Fastidious anglophones will not call

such items connectives (for they do not connect one thing to another); and

perhaps they are better named sentential adverbs, or ‘adsentences’. But that

is a matter of taste.

In the standard symbolisms of logic, every connective takes a ﬁxed and

determinate number of sentences to make a sentence. In English, there are

connectives which take an indeterminate number of sentences. ‘and’ is the

most obvious example: from ‘and’ and the twenty-six sentences ‘A’, ‘B’, …,

‘Z’, you may make the sentence:

A, B, …, Y, and Z.

Or ‘or’:

Let him go, let him tarry, let him sink, or let him swim.

Sentential Connectives 169

But some English connectives—‘if ’ and ‘because’, for example—are resol-

utely bigamous. Again, in the symbolisms of standard logic, the sentences

which connectives connect are indicative sentences, sentences which have

a truth-value (or perhaps sentences which express propositions which have

a truth-value). In English, connectives may conjoin sentences of any vari-

ety—imperatives and subjunctives, optatives and interrogatives.

An expression is identiﬁed as a sentential connective inasmuch as it can

take a number of sentences and make a sentence. It does not follow, and it is

not true, that sentential connectives can connect nothing but sentences. Even

in the symbolisms of logic, sentential connectives may connect items which

are not sentences. In the formula

(∀x)(Fx ⊃ Gx)

the sentential connective ‘⊃’ links ‘Fx’ and ‘Gx’, which are not sentences.

(True, logicians call such things ‘open sentences’. But an open sentence

is a Bombay duck.) In English, sentential connectives connect all sorts of

non-sentential items. Verbs, for example, and verbal phrases: ‘You’ve gone

and done it’. Names: ‘Sampras and Agassi met in the ﬁnal’. Other nominal

phrases: ‘The good, the bad, and the ugly’. Or adverbs: ‘They ran silently

and very fast’. And so on—connectives may even connect connectives: ‘He

dined if and when he pleased’. Those examples put together items of the same

syntactical sort; but connectives may also connect items of different sorts—a

name and a pronoun: ‘My husband and I …’; a sentence and an adverb: ‘He

went to the conference, if reluctantly’.

Or do sentential connectives really do such varied work? The word ‘and’

certainly appears in ‘They ran silently and very fast’, and in that sentence it

seems to connect a couple of adverbs. But why think that it is the sentential

‘and’? Why not suppose that it is a homonymous adverbial connective? The

answer, I suppose, is this: the sense of ‘and’ in

They ran silently and very fast

is fully determined by the sense it bears when it connects sentences. Roughly

speaking, you understand the ‘and’ in

They ran silently and very fast

inasmuch as, ﬁrst, you know that the sentence is synonymous with

They ran silently and they ran very fast,

and, secondly, you understand the sense of ‘and’ in that latter sentence. More

generally, you understand the construction