But such a condition cannot be knowledge.
When the conclusion is necessary, the middle through which it was
proved may yet quite easily be non-necessary. You can in fact infer
the necessary even from a non-necessary premiss, just as you can infer
the true from the not true. On the other hand, when the middle is
necessary the conclusion must be necessary; just as true premisses
always give a true conclusion. Thus, if A is necessarily predicated of
B and B of C, then A is necessarily predicated of C. But when the
conclusion is nonnecessary the middle cannot be necessary either.
Thus: let A be predicated non-necessarily of C but necessarily of B,
and let B be a necessary predicate of C; then A too will be a
necessary predicate of C, which by hypothesis it is not.
To sum up, then: demonstrative knowledge must be knowledge of a
necessary nexus, and therefore must clearly be obtained through a
necessary middle term; otherwise its possessor will know neither the
cause nor the fact that his conclusion is a necessary connexion.
Either he will mistake the non-necessary for the necessary and believe
the necessity of the conclusion without knowing it, or else he will
not even believe it-in which case he will be equally ignorant, whether
he actually infers the mere fact through middle terms or the
reasoned fact and from immediate premisses.
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