together in order to investigate the relation of their predicates. Hence arises the third figure, in which accordingly the middle appears in both premisses as the subject. It is also here the tertium comparationis, 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 Falsche Spitzfinigkeit, § 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 brutes,"
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 the
