1. _False Views of Syllogism arising from False Views of Judgment._--The false views of judgment, which we have been examining, have led to false views of inference. On the one hand, having reduced categorical judgments to an existential form, Brentano proposes to reform the syllogism, with the results that it must contain four terms, of which two are opposed and two appear twice; that, when it is negative, both premises are negative; and that, when it is affirmative, one premise, at least, is negative. In order to infer the universal affirmative that every professor is mortal because he is a man, Brentano's existential syllogism would run as follows:-- There is not a not-mortal man. There is not a not-human professor. :. There is not a non-mortal professor. On the other hand, if on the plan of Sigwart categorical universals were reducible to hypothetical, the same inference would be a pure hypothetical syllogism, thus:-- If anything is a man it is mortal. If anything is a professor it is a man. :. If anything is a professor it is mortal. But both these unnatural forms, which are certainly not analyses of any conscious process of categorical reasoning, break down at once, because they cannot explain those moods in the third figure, e.g. _Darapti_, which reason from universal premises to a particular conclusion. Thus, in order to infer that some wise men are good from the example of professors, Brentano's syllogism would be the following _non-sequitur_:-- There is not a not-good professor. There is not a not-wise professor. There is a wise good (_non-sequitur_). So Sigwart's syllogism would be the following _non-sequitur_:-- If anything is a professor, it is good. If anything is a professor, it is wise. Something wise is good (_non-sequitur_). But as by the admission of both logicians these reconstructions of _Darapti_ are illogical, it follows that their respective reductions of categorical universals to existentials and hypotheticals are false, because they do not explain an actual inference. Sigwart does not indeed shrink from this and greater absurdities; he reduces the first figure to the _modus ponens_ and the second to the _modus tollens_ of the hypothetical syllogism, and then, finding no place for the third figure, denies that it can infer necessity; whereas it really infers the necessary consequence of particular conclusions. But the crowning absurdity is that, if all universals were hypothetical, _Barbara_ in the first figure would become a purely hypothetical syllogism--a consequence which seems innocent enough until we remember that all universal affirmative conclusions in all sciences would with their premises dissolve into mere hypothesis. No logic can be sound which leads to the following analysis:-- If anything is a body it is extended. If anything is a planet it is a body. :. If anything is a planet it is extended.