The World as Will and Idea, Vol. II — Arthur Schopenhauer, trans. Haldane & Kemp

together in order to investigate the relation of their predicates. Hence arises the third Jlgure,in which accordingly the middle appears in both premisses as the subject It is also here the tertium corrvparationis, the measure which is applied to both the conceptions which are to be investigated, or, as it were, a chemical reagent, with which we test them both in order to learn from their relation to it what relation exists between themselves. Thus, then, the conclusion declares whether a relation of subject and predicate exists between the two, and to what extent this is the case. Accordingly, what exhibits itself in this figure is reflection concerning two properties which we are inclined to regard either as incompatible, or else as inseparable, and in order to decide this we attempt to make them the predicates of one subject in two judgments. From this it results either that both properties belong to the same thing, consequently their compatibility, or else that a thing has the one but not the other, consequently their separableness. The former in all moods with two affirmative premisses, the latter in all moods with one negative ; for example :

Some brutes can speak ;

All brutes are irrational :

Therefore some irrational beings can speak. According to Kant {Die Falscke SpUzfinigkeit, § 4) this inference would only be conclusive if we added in thought : " Therefore some irrational beings are brutes." But this seems to be here quite superfluous and by no means the natural process of thought. But in order to carry out the same process of thought directly by means of the first figure I must say :

" All brutes are irrational ;

Some beings that can speak are brute?," which is clearly not the natural course of thought; indeed the conclusion which would then follow, "Some beings that can speak are irrational," would have to be converted in order to preserve the conclusion which thep. 301 third figure gives of itself, and at which the whole course of thought has aimed. Let us take another example :

All alkalis float in water ;

All alkalis are metals :

Therefore some metals float in water. When this is transposed into the first figure the minor must be converted, and thus runs : " Some metals are alkalis." It therefore merely asserts that some metals lie

(QQ, in the sphere " alkalis," thus Wikan«.U ileum J , while our actual knowledge is that all alkalis lie in the sphere

/ Metal*. N.

"metals," thus: ( ^-v ] It follows that if the first figure is to be regarded as the only normal one, in order to think naturally we would have to think less than we know, and to think indefinitely while we know definitely. This assumption has too much against it Thus in general it must be denied that when we draw inferences in the second and third figures we tacitly convert a proposition. On the contrary, the third, and also the second, figure exhibits just as rational a process of thought as the first. Let us now consider another example of the other class of the third figure, in which the separableness of two predicates is the result ; on account of which one premiss must here be negative :

No Buddhist believes in a God ;

Some Buddhists are rational :

Therefore some rational beings do not believe in a God.

As in the examples given above the compatibility of two properties is the problem of reflection, now their separableness is its problem, which here also must be decided by comparing them with one subject and showingp. 302 that one of them is present in it without the other. Thus the end is directly attained, while by means of the first figure it could only be attained indirectly. For in order to reduce the syllogism to the first figure we must convert the minor, and therefore say : " Some rational beings are Buddhists," which would be only a faulty expression of its meaning, which really is: "Some Buddhists are yet certainly rational."

As the guiding principle of this figure I therefore give : for the affirmative moods: Ejusdem rei notce, modo sit altera universalis, sibi invicem sunt notce particulares ; and for the negative moods: Nota rei competens, notce eidem repugnanti, particulariter repugnat, modo sit altera universalis. Translated : If two predicates are affirmed of one subject, and at least one of them universally, they are also affirmed of each other particularly ; and, on the contrary, they are denied of each other particularly whenever one of them contradicts the subject of which the other is affirmed; provided always that either the contradiction or the affirmation be universal.