40.

41.

fect syllogism of the extremes. I call that the middle which is both itself contained in something else (i.e. the major), and has something else contained in it, and which also becomes middle by its position; and the extremes are (1st) that which is itself contained in another (the minor is contained in' or is subject to the middle), and (2nd) that in which another (the middle) is contained.

For if A is predicated of all B, and B of all C, A is necessarily predicated of all C.2

Prior Analytics I. 4, § 15.

And it is clear also that all the syllogisms in it (i.e. the first figure) are perfect; for they are all perfectly proved by the premisses originally assumed, and it is clear that all the kinds of propositions are proved by this figure viz. the universal affirmative, and the universal negative, and the particular affirmative and the particular negative. Now I call such figure the first,

Prior Analytics I. 5, §§ 1-4.

When the same predicate belongs to all of one term,

1e.g. in the formula, 'A is predicated of B and B of C,' B is 'middle by its position.' Vide note on (41.)

2

All B is A,

All C is B ;

... All C is A.

The other mode indicated above

that called celarent:

(ἐν ὅλῳ τῷ πρώτῳ . . . μὴ εἶναι) is

e.g. No arbitrary interference with the natural course of production is defensible,

Protection is such an arbitrary interference;

.. Protection is indefensible.

3 πάντα τὰ προβλήματα.

and to none of another, or to all or none of both,' I call such figure the second, and I call the middle in it

/cal

that which is predicated of both terms, and the extremes the terms of which the middle is stated, the major term that which is situated towards (i.e. nearest to) the middle, and the minor that which is furthest from the middle, and the middle is placed outside the extremes, but first in position.

2

There will then in no way be a perfect syllogism ia this figure; but there will be a valid one, both when the terms are universal, and when they are not universal. If they are universal, there will be a syllogism when the middle belongs to the whole of one extreme, and to none of the other; to whichever of the two the

1 The above seems the only possible meaning of ἢ ἑκατέρῳ παντὶ ἢ undevi, though it is hard to see the sense, the moods apparently indicated (A A A and E E E) being both illegitimate. Apparently, Aristotle intends to give a general description of all the moods that would come under the second figure, whether legitimate or not; but his enumeration is not complete, for he makes no mention of the moods with particular premisses, two of which (festino, baroko) are legitimate. Cf. (43), in which there is a description of the third figure, identical-mutatis mutandis-with this. There also the description is too general to include the legitimate moods only, and too confined to include all conceivable moods.

2 Aristotle seems to refer to his way of stating the premisses: 'A is predicated of all B and no C.' In this formula we see that the major term B is placed nearest the middle A, and the minor term C farthest away. The words that follow describe the position of the middle in the same formula, not between the extremes, as in the first figure, but before them. The expression is clearly meant to be contrasted with the companion description of the middle term in the third figure, τίθεται δὲ τὸ μέσον ἔξω μὲν τῶν ἄκρων, ἔσχατον δὲ τῇ féσei (43), as well as with that of the middle in the first figure, d kal τῇ θέσει γίνεται μέσον (39). The use of μέν and δέ in these cases seems to be to point the contrast between the first clause which agreesand the second clause which disagrees with the parallel statement,

negative sign be affixed; and in no other way. For let M be predicated of no N and of all X. Then, since the negative proposition is convertible, N will belong to no M; but M was assumed to belong to all X: therefore N belongs to no X; for this has been shown before." Again, if M belongs to all N and no X, N will also belong to no X.3 For if no X is M, no M will be X;

which is a syllogism in celarent of the first figure. As a concrete example of this syllogism we may cite :

(A) No metals are compound bodies,

(B) Brass is a compound body;

.. Brass is not a metal.

By conversion of (A) we get a syllogism in celarent thus:
No compound bodies are metals,

Brass is a compound body;

.. Brass is not a metal.

2 i.e. in discussing the first figure (Pri. Anal. I. 4. 3). This mood stated in the second figure is :

All N is M,

No X is M;

.. No X is N.

The conclusion, however, which Aristotle gives is, according to Bekker's text, and apparently all his MSS., 'No N is X.' We follow Mr. Magrath's second edition, and read TE Tò N instead of TO E TO N, since Aristotle himself, after getting as the conclusion of his first-figure syllogism, τὸ Ξ οὐδενὶ τῷ Ν ὑπάρξει, takes the trouble to convert it, to bring it into harmony with his former conclusion. σvλλoyiσuds at the end of this section seems to be used in its original sense of drawing a conclusion or inference, rather than in that usual to Aristotle. As a concrete example, we may cite:

(A) All fishes are oviparous,
(B) Whales are not oviparous;

(C) .. Whales are not fishes.

but M belonged to all N... X will belong to no N, for the first figure has again been produced. But since the negative is convertible, neither will N belong to any X, so that there will be the same conclusion drawn.

Prior Analytics I. 5, § 16.

It is clear then from what has been said, both that if the terms are related to one another, as was stated, a syllogism arises of necessity; and if there is a syllogism, the terms must be so related. And it is evident also that all the syllogisms in this figure are imperfect (for they are all perfected by the addition of certain assumptions, which either are inherent in the terms of necessity, or are added as hypotheses; as when we prove per impossibile): also that no affirmative conclusion is drawn by this figure, but they are all negative, both the universal and the particular.2

1

Prior Analytics I. 6, §§ 1, 2.

But if one predicate belongs to the whole of some thing, and another predicate belongs to none of the same thing; or if both predicates belong to the whole

By conversion of (B) we get:

(B') No oviparous things are whales,
(A) All fishes are oviparous;

(C'). No fishes are whales.

celarent

of the

1st figure.

And by conversion of (C') we get (C) again, 'no whales are fishes,' or whales are not fishes.'

1 Cf. note 2, page 22.

2 The truth of this rule follows directly from the general syllogistic laws: 1st, that the middle must be distributed; 2nd, that if one premiss be negative, the conclusion must be negative (vid. Jevons' Elementary Logic, pp. 127, 128; Fowler's Deductive Logic,

C

42.

43.

or to none of the thing;1 I call such figure the third, and I call that of which both the predicates are stated the middle, and I call the things predicated the extremes; the major extreme that farthest from the middle, and the minor that nearest; and the middle is placed outside the extremes, but last in position.2 There is no perfect syllogism in this figure either, but there will be a valid one, both when the terms are universal, and when they are not universal, with regard to the middle. If they are universal, when both P and R belong to all S, it follows of necessity that P will belong to some R; for since the affirmative is convertible, S will belong to some R; so that since P belongs to all S, and S to some R, P must necessarily belong to some R. For a syllogism is formed by the first figure.3

pp. 92, 93, &c. &c.). For as in both premisses the middle term is predicate, it can only be distributed in a negative premiss; and if there be a negative premiss, the conclusion must be also negative. 1 Vide note 1, page 15.

2 i.e. in the phrase P and R belong to, or are predicated of, S; P being the major, R the minor, and S the middle. Cf. note 2, page 15. 3 This is the mood represented by darapti—

(A) All S is P,

(B) All S is R;

.. Some R is P.

Or to reduce it to the first figure, converting (B)—

The principal use of the third figure is to prove exceptions to a general rule; for instance:

Plato's Republic is highly aristocratic in its aims,

Plato's Republic is a system of communism;

.. Some systems of communism are highly aristocratic in their aims.