The third case is that in which we place two judgments 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 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. [Alkalis and Metals overlapping circles] Figure 1 [Metals circle with Alkalis circle inside it] Figure 2