2. _Quasi-syllogisms._--Besides reconstructions of the syllogistic fabric, we find in recent logic attempts to extend the figures of the syllogism beyond the syllogistic rules. An old error that we may have a valid syllogism from merely negative premises (_ex omnibus negativis_), long ago answered by Alexander and Boethius, is now revived by Lotze, Jevons and Bradley, who do not perceive that the supposed second negative is really an affirmative containing a "not" which can only be carried through the syllogism by separating it from the copula and attaching it to one of the extremes, thus:-- 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 | :. S may be P. | :. S may be P. is 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:--