The just are not unhappy (negative). The just are not-recognized (affirmative). ∴ Some not-recognized are not unhappy (negative).

Here the minor being the infinite term “not-recognized” in the conclusion, must be the same term also in the minor premise. Schuppe, however, who is a fertile creator of quasi-syllogisms, has managed to invent some examples from two negative premises of a different kind:—

(1)(2)(3)
 No M is P. No M is P. No P is M.
 S is not P. S is not M. S is not M.
∴ Neither S nor M is P.∴ S may be P.∴ S may be P.

But (1) concludes with a mere repetition, (2) and (3) with a contingent “may be,” which, as Aristotle says, also “may not be,” and therefore nihil certo colligitur. The same answer applies to Schuppe’s supposed syllogisms from two particular premises:—

(1)(2)
 Some M is P. Some M is P.
 Some S is M. Some M is S.
∴ Some S may be P.∴ Some S may be P.

The only difference between these and the previous examples (2) and (3) is that, while those break the rule against two negative premises, these break that against undistributed middle. Equally fallacious are two other attempts of Schuppe to produce syllogisms from invalid moods:—

(1) 1st Fig.(2) 2nd Fig.
 All M is P. P is M.
 No S is M. S is M.
∴ S may be P.∴ S is partially identical with P.

In the first the fallacy is the indifferent contingency of the conclusion caused by the non-sequitur from a negative premise to an affirmative conclusion; while the second is either a mere repetition of the premises if the conclusion means “S is like P in being M,” or, if it means “S is P,” a non-sequitur on account of the undistributed middle. It must not be thought that this trifling with logical rules has no effect. The last supposed syllogism, namely, that having two affirmative premises and entailing an undistributed middle in the second figure, is accepted by Wundt under the title “Inference by Comparison” (Vergleichungsschluss), and is supposed by him to be useful for abstraction and subsidiary to induction, and by Bosanquet to be useful for analogy. Wundt, for example, proposes the following premises:—

Gold is a shining, fusible, ductile, simple body.
Metals are shining, fusible, ductile, simple bodies.

But to say from these premises, “Gold and metal are similar in what is signified by the middle term,” is a mere repetition of the premises; to say, further, that “Gold may be a metal” is a non-sequitur, because, the middle being undistributed, the logical conclusion is the contingent “Gold may or may not be a metal,” which leaves the question quite open, and therefore there is no syllogism. Wundt, who is again followed by Bosanquet, also supposes another syllogism in the third figure, under the title of “Inference by Connexion” (Verbindungsschluss), to be useful for induction. He proposes, for example, the following premises:—