Barnes Jonathan. Truth, etc

Подождите немного. Документ загружается.

460 When is a Syllogism not a Syllogism?

Suppose that there is a certain form of argument, which takes us validly from

premisses of this sort to a conclusion of that sort; and suppose that we wish to

determine whether arguments of that form are, in virtue of having that form,

syllogisms. How might the question be resolved? According to Alexander and

his friends, arguments of that form are syllogisms if and only if an argument of

that form may be a scientiﬁc proof. There will, of course, be innumerably many

syllogisms of that form which are not proofs—syllogisms with false premisses,

for example. Alexander does not make the absurd claim that an argument is a

syllogism only if it is a proof; but he does claim that any syllogism must either

be probative or else have probative siblings: every syllogism is valid in virtue

of having a structure in virtue of which some probative arguments are valid.

A syllogism is a tool, and a tool is deﬁned by its function: if a screw-driver

is a tool for screwing and unscrewing, and this item can’t screw or unscrew,

then it is not a screw-driver. Or in Alexander’s words:

The measure of any tool is its usefulness with regard to what is shown or produced

by it—and if it is no longer useful, it is not even a tool. For an adze which is of no

use to a carpenter is no longer an adze, except homonymously.

(in APr 164.31–165.2)²⁶

Or again:

A syllogism is a tool; for the utility of a syllogism is to make evident, by way of known

and evident items, something which is thought not to be known. … What does not

provide the utility of a syllogism is not a syllogism at all. For if a syllogism is a tool,

and every tool is useful, then a syllogism is useful. … And that a tool is useful is clear:

in the case of all tools we see that when they can no longer provide their proper

utility they no longer exist—for no one would call anything a lyre if it can’t be used

for making music nor an adze if can’t be used for carpentry. If you persist in calling

by the same word items which have lost their utility, you speak homonymously—as

when we talk of painted or sculpted items and speak of a stone hand. So something

which does not preserve the utility of a syllogism is no longer a syllogism.

(in Top 9.22–10.6)²⁷

An argumentative form which has no probative utility is not just a useless

sort of syllogism—it is no sort of syllogism at all. If you insist on calling

²⁶ παντὸς γὰρ ὀργάνου μέτρον ἡ χρεία πρὸς τὸ ὑπ᾿ αὐτοῦ δεικνύμενόν τε καὶ γινόμενον·

τὸ δὲ μηκέτι χρήσιμον οὐδ᾿ ἂν ὄργανον εἴη· τὸ γὰρ ἄχρηστον σκέπαρνον τῷ τέκτονι οὐκέτι

σκέπαρνον ἀλλ᾿ ἢ ὁμωνύμως.

²⁷ … ὄργανόν ἐστιν ὁ συλλογισμός. ἔστι γὰρ πρὸς τὸ φανερόν τι ποιῆσαι μὴ δοκοῦν

εἶναι γνώριμον διά τινων γνωρίμων τε καὶ φανερῶν ἡ τοῦ συλλογισμοῦ χρεία. ... ὁ δὲ μὴ

παρεχόμενος τὴν τοῦ συλλογισμοῦ χρείαν λόγος οὐδὲ συλλογισμός. εἰ γὰρ ὁ συλλογισμὸς

The Use of Logic 461

some non-probative forms of argument syllogistic, then you merely use the

word ‘syllogistic’ in a different sense. Hands and feet are tools for grasping

andforwalkingwith;andifapieceofstone—apartofasculpture,say—is

nonetheless called a hand or a foot, then the words ‘hand’ and ‘foot’ are used

in different senses.

Alexander’s reference to stone hands alludes to an Aristotelian common-

place. So, for example,

it is impossible that an item of any sort whatsoever should be a hand—for example,

a bronze or a stone item—except homonymously, like a painted doctor.

(PA 640b35–641a1)²⁸

But the commonplace is at best a half-truth; and its application to syllogisms

is dubious.

Alexander, like Aristotle before him, offers a variety of cases in which an off-

colour so-and-so is allegedly called a so-and-so only homonymously: rusted

adzes, severed limbs, painted ladies, dead parrots, toy chain-saws, … But

the cases are not all alike. Consider the adze. True, adzes are now rarities;

but my neighbour Bernard has several specimens in his workshop—he

inherited them from his grandfather, who was an Alsatian. They are no

longer serviceable, and some of them are irredeemably rusted. Nonetheless,

they are adzes; and they are adzes in exactly the sense in which working adzes

are adzes. If I say: ‘Here are a couple of adzes, one of them in good working

order and the other hopelessly blunted’, I have not made a weak pun or

indulged in a zeugma. An item which no longer functions as an adze does

not thereby cease to be an adze.

In the same way, a dead parrot is a parrot. When the Norwegian blue

ﬁnally fell off its perch, what lay on the bottom of the cage was a parrot—and

a parrot in the ordinary sense of the word ‘parrot’, the sense in which the

word applied to the bird before it dropped off. So too, in an Oxford museum,

there is a dodo—a real dodo, though not a real live dodo.

ὄργανον, πᾶν δὲ ὄργανον χρήσιμον, ὁ συλλογισμὸς χρήσιμος· ... ὅτι δὲ τὸ ὄργανον χρήσιμον,

δῆλον· ἐν πᾶσι γὰρ τοῖς ὀργάνοις ὁρῶμεν ὅταν μὴ τὴν οἰκείαν χρείαν παρέχεσθαι δύνηται

ἀναιρούμενα αὐτά. οὔτε γὰρ λύραν ἄν τις εἴποι ᾗ οὐχ οἷόν τε μουσικῶς χρῆσθαι, οὔτε

σκέπαρνον ᾧ μὴ τεκτονικῶς· ὁ γὰρ καὶ τὰ ἐκπίπτοντα τῆς χρείας ἔτι λέγων τῷ αὐτῷ

ὀνόματι ὁμωνύμως λέγει, ὡς καὶ τὰ γεγραμμένα ἢ πεπλασμένα ὡς χεῖρα τὴν λιθίνην. οὐδὲ

συλλογισμὸς οὖν ἔτι εἴη ἂν ὁ μὴ τὴν χρείαν σώζων τὴν τοῦ συλλογισμοῦ.

²⁸ ἔτι δ᾿ ἀδύνατον εἶναι χεῖρα ὁπωσοῦν διακειμένην, οἷον χαλκῆν ἢ ξυλίνην, πλὴν ὁμων-

ύμως, ὥσπερ τὸν γεγραμμένον ἰατρόν.

462 When is a Syllogism not a Syllogism?

Of course, if you are a parrot-fancier or a carpenter you will need to be able

to distinguish between serviceable adzes and adzes which no longer function,

between working parrots and parrots which are no more. But there is no

particular difﬁculty about that—and if there were, the task would become not

a jot easier were we to legislate a double sense for the words ‘adze’ and ‘parrot’.

Again, the portrait of a blinking idiot is not a blinking idiot—it is not a

blinking idiot in any sense of the phrase ‘blinking idiot’. Magritte illustrated

that banal fact. As for a portrayed or painted idiot, he is an idiot—and an

idiot in the ordinary sense of the word. No painting, not even a Holbein,

is qualiﬁed to be a monarch; but one of the items portrayed by Holbein is

Henry VIII—and he was a king, and not homonymously.

Toy chain-saws are different: they are not chain-saws—no more than

decoy ducks are ducks or false noses noses. But that is not because they are

chain-saws in a different sense of the word ‘chain-saw’: it is because they are

toy chain-saws, and, as a general rule, toy so-and-sos are not so-and-sos. The

sense of ‘chain-saw’ in the phrase ‘toy chain-saw’ is its ordinary sense.

In some cases, Alexander himself takes that sort of line. For example,

certain arguments—he says—are called, perhaps with propriety, ‘rhetorical

syllogisms’;

but such arguments are not syllogisms in the strict sense: they are rhetorical syllogisms,

the phrase being taken as a whole.

(in Top 9.14–15)²⁹

A rhetorical syllogism—according to Alexander—is like a false nose: it is not

useless—any more than a false nose is useless; but it is not a syllogism—any

more than a false nose is a nose. The word ‘syllogism’ has the same sense

in ‘rhetorical syllogism’ as it has in ‘probative syllogism’. There is no special

sense of ‘syllogism’ in which the word is specially true of rhetorical syllogisms;

and it would be entirely absurd to invent such a sense.

Another and more interesting false nose will poke into a later part of

the discussion. But enough of them for the nonce. For even were Alex-

ander right about adzes, why imagine that syllogisms are in the same

case? Why, in other words, imagine that the term ‘syllogism’ is a func-

tional term, on a level with ‘adze’ or ‘parrot’? So far as I can see, there

is no reason, in ordinary Greek, to think that the word ‘συλλογισ-

μός’ means, or somehow must mean, ‘argument useful in such-and-such

²⁹ οὐδὲ οἱ τοιοῦτοι κυρίως συλλογισμοί, ἀλλὰ τὸ ὅλον ῥητορικοὶ συλλογισμοί.

Modal Logic 463

a way’; nor does Aristotle’s celebrated deﬁnition of the syllogism indic-

ate or presuppose that syllogisms are essentially functional items. To be

sure, it may be important for a philosopher to be able to distinguish

between syllogisms which are serviceable (to one end or another) and

syllogisms which are not. But to do so is not particularly difﬁcult; and

any difﬁculty there may be is not one whit eased by stipulating that an

argument be called a syllogism only if it is useful in a certain way or

ways.

The utilitarian view of logic which makes syllogisms tools and not objects

of contemplation in their own right is a stipulative view inasmuch as it

depends upon—or consists in—a decision to limit the use of a certain term

in a certain way. Some may think it a harmless stipulation, others a pernicious

stipulation; and I have heard it called a philistine stipulation. In any event,

it is surely a pointless stipulation; for Alexander and his friends could easily

have expressed their utilitarianism without it. They could have said: ‘You

should include a given type of syllogism in your logic if and only if it is useful

for proof.’

Nevertheless, the stipulation, and the utilitarianism which it proclaims,

are not triﬂing terminological decisions: they have consequences for the

study of logic. The rest of this chapter will look at three such con-

sequences, different in kind from one another and also different in their

signiﬁcance.

MODAL LOGIC

One striking difference between the predicative syllogistic which Aristotle

presents in the Prior Analytics and Stoic syllogistic (so far as we know

it) is this: Aristotle considers modal syllogisms, the Stoics do not. We do

not know why the Stoics, who certainly had some interest in the general

phenomenon of modality, did not concern themselves with modal logic; but

at the end of antiquity Boethius thought it appropriate to indicate why his

own essay on hypothetical syllogisms apparently omitted certain varieties of

inference:

I have judged it superﬂuous to inquire into the number of <propositions> determ-

ined as to their quantity, since conditionals determined in that way are not normally

propounded. And in much the same way hypothetical propositions are not expressed

in terms of necessity or in terms of contingency—rather, it is those which signify

464 When is a Syllogism not a Syllogism?

being the case which are chieﬂy introduced for use in inferences. All of them, to be

sure, mean to maintain a necessary connection—those which signify being the case,

those to which necessity is added, and those to which a predication of possibility is

afﬁxed (for these apply to the terms).

(hyp syll i ix 3)³⁰

What Boethius means is less than plain. He clearly states that modalized

hypothetical propositions are not used, or only rarely; and it is plausible to

think that he drew the consequence that modal hypothetical logic is pointless.

Yet the last parenthetical sentence of the passage suggests a far stronger thesis:

modal operators apply to terms and not to propositions, so that while there

may in principle be a modal logic of terms or a modal predicative syllogistic,

there cannot in principle be a modal logic of propositions or a modal

hypothetical syllogistic.

However that may be, modal predicative syllogistic was certainly developed

by the Peripatetics. The modal logic of the Analytics is by far the most

complicated and technically intricate part of Aristotle’s syllogistic; and its

exposition occupies about three times as much space as the exposition

of the non-modal syllogistic. The modal exposition turns about apodictic

propositions, or propositions which say that necessarily such-and-such, and

problematic propositions, or propositions which say that possibly such-and-

such. It elaborates apodictic syllogisms, every component proposition of

which is apodictic, and problematic syllogisms, every component of which is

problematic; and it elaborates mixed syllogisms, or syllogisms the constituent

members of which have different modalities or no modality.

Not everyone appreciated modal syllogistic. It is not mentioned in Apuleius’

On Interpretation. It is not mentioned in Galen’s Introduction to Logic.Tobe

sure, those two little works are introductory handbooks, and modal syllogistic

is horribly difﬁcult. But if you would not expect them to expound the ins and

outs of mixed modalities, you would expect a reference to modal syllogisms

or at least some sort of promissory note. After all, Galen observes more than

once in the Introduction that the syllogisms he is discussing are ‘useful for

proof’; and at the end of the text he states that

³⁰ atque ideo supervacaneum iudicavi determinatarum secundum quantitatem propositionum quaer-

ere multitudinem, cum determinatae conditionales proponi non soleant. fere autem hypotheticae

propositiones ne per necessitatem quidem vel per contingens enuntiantur, sed illae maximae in usum

collectionis deducuntur quae inesse signiﬁcant. omnes vero necessariam tenere consequentiam volunt, et

quae inesse signiﬁcant, et quibus necessitas additur, et quibus praedicatio possibilitatis aptatur (haec

enim terminis applicantur).—For ‘collectionis’themanuscriptshave‘collocutionis’; for ‘applicantur’

editors have preferred the singular ‘applicatur’.

Modal Logic 465

in introductions to logic, none of the useful items should be omitted—but it is not

necessary to refute the superﬂuous items.

(inst log xix 5)³¹

If he took modal syllogisms to be instruments of proof, then how could he

have failed to notice their existence in the Introduction?

There is a pertinent piece of evidence. It is third-hand; but it seems to

be trustworthy. In a work On Medicine, Moses Maimonides cited a passage

from al-Farabi’s commentary on the Prior Analytics, which in turn refers to

Galen’s On Proof. Since the text is not well known, I shall cite it in full.

All this has been explained by al-Farabi, namely that Galen rejected possible syllogisms

and mixed syllogisms and limited himself to non-modal syllogisms, which are called

hyparctic syllogisms; and that what is useful in medicine and in the majority of the

arts are possible syllogisms and mixed syllogisms. Listen, then, to al-Farabi on the

subject. In his long commentary on the Book of Syllogisms, at the beginning of his

commentary on Aristotle’s introduction to the possible and to possible syllogisms, he

says this. al-Farabi says:

Matters do not stand here as Galen the doctor thought. In the book which

he entitled Book of Proof he remarks that the study of the possible and of the

syllogisms generated from it is superﬂuous. But if there is anyone who ought to

have studied possible syllogisms, it is Galen, the doctor: in the book entitled Book

of Proof he ought to have concentrated all his attention on possible syllogisms

inasmuch as he claims that he has composed his Book of Proof in order for it

to be of use in medicine. The syllogisms which medicine uses in its account of

the parts of the art of medicine and the syllogisms which it uses to grasp the

hidden diseases and their causes in each case in which it seeks a cure—all these

are possible syllogisms, and there is no necessity at all in them (save in some cases

which are pretty well extraneous to the art of medicine). For that reason, in the

book which he entitled Book of Proof he ought to have spoken above all else

about possible syllogisms alone, and not about hyparctic syllogisms. For if in the

book he restricted himself to hyparctic syllogisms on the ground that they would

be useful for proofs, in fact the hyparctic forms are not appropriate to proofs; for

proofs do not come about in matter of that sort but only in necessary forms.

End of the citation from al-Farabi.³²

The last sentence of the citation is scarcely coherent, and it may be suspected

that the text once read: ‘… only in necessary or possible forms’. Perhaps

³¹ κατὰ γὰρ τὰς εἰσαγωγὰς αὐτῶν οὐδὲν δεῖ τῶν χρησίμων παραλείπεσθαι, τοὺς δ᾿

ἐλέγχους τῶν περιττῶν μὴ λέγεσθαι.

³² Marwan Rashed generously made me a French translation of Maimonides’ text. A fragment

of the citation is printed in a Latin version in I. von M

uller, Galens Werk vom wissenschaftlichen

Beweis, p. 424.

466 When is a Syllogism not a Syllogism?

the notice has suffered further and less evident damage in the course of its

transmission; and certainly it would be rash to try to construct any of Galen’s

Greek on its base. But there is no intrinsic reason to doubt that the sentiment

which the passage transmits was Galen’s sentiment.

al-Farabi makes it clear that Galen rejected problematic syllogistic. The

text also reports that On Proof restricted itself to ‘hyparctic’ or non-modal

syllogisms; and although al-Farabi does not explicitly say that Galen regarded

apodictic syllogistic and mixed modal syllogistic as superﬂuous, it is odds on

that he took the same attitude to them as he took to problematic syllogistic.

Thus the Introduction to Logic is neither coy nor misleading when it refrains

from mentioning modal logic: Galen did not mention it there because he

took it to be useless.

Modal arguments are useless for proof, and therefore there are no modal

syllogisms. al-Farabi found Galen’s attitude bizarre: medicine is a science

of contingencies; problematic syllogistic is concerned with the contingent;

and yet Galen, the leading doctor and medical theorist of his age, rejected

problematic syllogistic.

The view of problematic syllogistic at which al-Farabi here hints was

traditional. When he introduces the part of his modal syllogistic which deals

with problematic propositions, Aristotle says this:

Let us observe that being possible is said in two senses—in one sense, coming

about for the most part and not necessarily (e.g. that men go grey, or grow, or

decline, or in general what holds by nature … ); and in another sense what is

indeterminate.

(APr 32b4–10)³³

Alexander comments thus:

He omits to exhibit the syllogisms in the ﬁgures in connexion with the latter sort

of possibility not because it cannot be done but because it is useless—thereby

indicating to us that in this subject we should only take up and elaborate what is

useful for items which will be proved and omit the useless even if it allows certain

combinations.

(in APr 164.23–27)³⁴

³³ … λέγωμεν ὅτι τὸ ἐνδέχεσθαι κατὰ δύο λέγεται τρόπους, ἕνα μὲν τὸ ὡς ἐπὶ τὸ πολὺ

γίνεσθαι καὶ διαλείπειν τὸ ἀναγκαῖον, οἷον τὸ πολιοῦσθαι ἄνθρωπον ἢ τὸ αὐξάνεσθαι ἢ

φθίνειν, ἢ ὅλως τὸ πεφυκὸς ὑπάρχειν ..., ἄλλον δὲ τὸ ἀόριστον ...

³⁴ …παραιτεῖται τὴν ἐπὶ τοῦ τοιούτου ἐνδεχομένου δεῖξιν τῶν κατὰ τὰ σχήματα συλλο-

γισμῶν, οὐχ ὡς οὐ δυναμένην γενέσθαι, ἀλλ᾿ ὡς ἄχρηστον, ἐνδεικνύμενος ἡμῖν ὅτι δεῖ τὸ

Modal Logic 467

Aristotle does not discuss arguments which use indeterminate possibility

because such arguments cannot be used to prove anything. As for the former

sort of possibility, which is identiﬁed with what holds for the most part,

he promises that he will discuss the other sort because there are many arts which are

conjectural and which syllogize on the basis of this sort of possibility—medicine, for

example, and navigation, and gymnastics. But also and more generally, everything

which is adopted on the basis of deliberation is shown by way of this sort of possibility.

(in APr 165.8–11)³⁵

There are problematic syllogisms in the case of the ﬁrst sort of possibility

inasmuch as some sciences prove problematic propositions of that kind: prob-

lematic syllogisms will embody proofs in medicine, and in navigation. (What

gymnastical proofs Alexander might have in mind I do not care to guess.)

Alexander is not inventing: he is merely paraphrasing and illustrating the

Aristotelian text on which he is commenting:

There is no knowledge and there are no probative syllogisms about the indeterminate

cases, since the middle term is disorderly; but of what holds by nature there are—and

indeed our arguments and inquiries concern what is possible in this sense. As for the

other sense, it is indeed possible for there to be syllogisms, but they are not usually

looked for.

(APr 32b18–22)³⁶

According to Aristotle, there are two senses of ‘possible’. Problematic syllo-

gisms may be constructed around each of the senses; but in fact we generally

restrict ourselves to the ﬁrst sense—the sense with respect to which there are

probative syllogisms. Alexander takes a harder line: there are no probative

arguments which use problematic propositions of the indeterminate or dis-

orderly sort; so there are no syllogisms which use such propositions; so the

study of arguments involving indeterminate possibility has no place in logic.

In any event, Alexander—like Aristotle before him and al-Farabi after

him—thinks that there are probative problematic syllogisms. He thinks

εὔχρηστον ἐν τῇδε τῇ πραγματείᾳ πρὸς τὰ δειχθησόμενα μόνον λαμβάνειν τε καὶ ἐξεργάζεσθαι,

τὸ δ᾿ ἄχρηστον, εἰ καὶ ἔχοι τινὰ συμπλοκήν, παραιτεῖσθαι.

³⁵ περὶ δὲ τοῦ ἑτέρου ἐρεῖν ἐπαγγέλλεται ὅτι πολλαὶ τέχναι στοχαστικαὶ οὖσαι ἐκ τοῦ

οὕτως ἐνδεχομένου τὸ προκείμενον συλλογίζονται, ὡς ἰατρική, κυβερνητική, γυμναστική·

ἀλλὰ καὶ ὅλως τὰ ἐκ τοῦ βουλεύεσθαι λαμβανόμενα διὰ τοῦ τοιούτου ἐνδεχομένου δείκνυται.

³⁶ ἐπιστήμη δὲ καὶ συλλογισμὸς ἀποδεικτικὸς τῶν μὲν ἀορίστων οὐκ ἔστι διὰ τὸ ἄτακτον

εἶναι τὸ μέσον, τῶν δὲ πεφυκότων ἔστι, καὶ σχεδὸν οἱ λόγοι καὶ αἱ σκέψεις γίνονται περὶ

τῶν οὕτως ἐνδεχομένων· ἐκείνων δ᾿ ἐγχωρεῖ μὲν γενέσθαι συλλογισμόν, οὐ μὴν εἴωθέ γε

ζητεῖσθαι.

468 When is a Syllogism not a Syllogism?

that problematic syllogistic has a scientiﬁc application. Now that notion of

the applicability of problematic syllogistic suggests a general thesis about

Peripatetic modal logic. Modal syllogistic, as I have said, contains three

types of syllogism: there are problematic syllogisms, there are apodictic

syllogisms, and there are mixed syllogisms. Aristotle appears to tell us that

problematic syllogisms will serve those sciences whose matter holds only for

the most part—that is to say, the majority of the sciences which concern

the world below the moon. It is therefore natural to suppose that apodictic

syllogisms are designed to provide proofs for those sciences whose matter

is necessary and unvarying—for the mathematical sciences, and for any

science which treats the supralunary regions. There is no obvious scientiﬁc

domain for mixed syllogisms, in which some constituents have one modality

and some another; but an ingenious interpreter will recall that Aristotle

recognizes the existence of certain subordinate sciences: thus optics, for

example, stands under the mathematical science of geometry, to which it

adds certain contingent axioms of its own—and the ingenious interpreter

will conjecture that just as its subject-matter is a mixture of mathematics and

empirically observable fact, so its logic will be a mixture of the necessary and

the possible.

That general view about the application of modal syllogistic is not sketched

by Aristotle himself; and Alexander says less on the matter than we might

have hoped. Nonetheless, it is reasonable to think that it was an orthodox

Peripatetic view: after all, any orthodox Peripatetic must do two things—he

must accept and appreciate some version of Aristotle’s modal syllogistic, and

he must uphold the doctrine that an item is a syllogism only insofar as it is

useful, and hence only insofar as it can be used to frame a probative syllogism.

To advance the view which I have just sketched is the obvious way—perhaps

the only way—of doing those two things.

Why did Galen reject modal syllogistic? Before that question is addressed,

another Galenic text may be introduced.

ALOGICALTHEOREM

It is the only passage in Galen’s surviving works which mentions modal syllo-

gisms. It is a perplexing passage. It occurs in a section of the treatise on Simple

Drugs in which Galen is concerned to argue that certain substances—the

oak-gall and the safﬂower—are useful for purging the body of excessive

phlegm.

A Logical Theorem 469

At this point in the argument I should like to recall a logical theorem which was

shown in the work On Proof and which is useful in the present context. The theorem

is this. Some proofs conclude that of necessity this holds of that, others that it possibly

holds; and of these latter, some transform into holding of necessity when they follow

necessary principles—and that is so in the case which we have just proved. For

the phlegm-like juice which is contained in oak-gall and safﬂower cannot be shown

evidently—rather, it is what is possible or likely or contingent which holds of the argu-

ment. But since we have shown that attraction depends on similarity of essence … ,

then since what is purged is phlegm, what attracts it must necessarily be phlegm-like.

(simp med temp xi 612–613)³⁷

Galen appears to be saying this: ‘There are problematic syllogisms and there

are apodictic syllogisms. I have just proved, by a problematic syllogism, that

it is possible (or perhaps probable) that gall and safﬂower are phlegm-like.

But I know a logical theorem which enables me to transform the problematic

conclusion into an apodictic conclusion, and hence to afﬁrm that necessarily

gall and safﬂower are phlegm-like.’

At ﬁrst sight, that is embarrassing. First, according to the testimony of

al-Farabi, Galen denied that there are any problematic syllogisms (and also,

in all probability, that there are any apodictic syllogisms). Secondly, he

would need a magical rather than a logical theorem to infer necessity from

possibility. Must we blush for Galen and move on?

Perhaps things are not quite what they seem.

First, Galen says that he cannot ‘show evidently’ that gall and safﬂower

are phlegm-like—that is to say, their phlegmatic character is not revealed

by smelling or tasting or otherwise perceiving them. But Galen can pro-

duce—and has produced—an argument in favour of the thesis that gall and

safﬂower are phlegm-like. He does not set the argument out formally; but it

may decently be presented thus:

Gall and safﬂower attract phlegm.

What attracts phlegm is phlegm-like.

³⁷ βούλομαι δὲ ἐπεὶ κατὰ τούτου τοῦ λόγου γέγονα, καί τινος θεωρήματος ἀναμνῆσαι

λογικοῦ, δεδειγμένου κᾄν τοῖς Περὶ ἀποδείξεως ὑπομνήμασιν, εἴς τε τὰ παρόντα χρησίμου.

ἔστι δὲ τὸ θεώρημα τοιόνδε. τῶν ἀποδείξεων αἱ μὲν ὡς ἐξ ἀνάγκης ὑπάρχει τόδε τῷδε

περαίνουσιν, αἱ δὲ ὡς ὑπάρχειν ἐνδέχεται. τούτων δὲ αὐτῶν μεταπίπτουσί τινες εἰς τὸ ἐξ

ἀνάγκης ὑπάρχειν ὅταν ἀναγκαίαις ἀρχαῖς ἕπωνται, καθάπερ καὶ ἐν αὐτῷ τούτῳ τῷ νῦν

ἡμῖν ἀποδεδειγμένῳ. ἐν γὰρ τῷ κόκκῳ καὶ τῷ κνίκῳ τὸν φλεγματώδη περιεχόμενον χυμὸν

ἐναργῶς μὲν οὐκ ἔστι δεῖξαι, τὸ δυνατὸν δὲ καὶ εἰκὸς καὶ ἐνδεχόμενον ὑπάρχει τῷ λόγῳ.

ἀλλ᾿ ἐπειδὴ καὶ τὰς ὁλκὰς ταῖς τῶν οὐσιῶν ὁμοιότησιν ἐδείξαμεν γίγνεσθαι, ... ἐπεὶ τοίνυν τὸ

καθαιρόμενόν ἐστι φλέγμα, πάντως δή που καὶ τὸ ἕλκον ἀνάγκη φλεγματῶδες ὑπάρχειν.