The nature and analysis of inference have been so fully treated in the
Introduction that here we may content ourselves with some points of
detail.
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_).