Supposing we are to prove that does not inhere in B, we
have to assume that it does inhere, and further that B inheres in C,
with the resulting inference that A inheres in C. This we have to
suppose a known and admitted impossibility; and we then infer that A
cannot inhere in B. Thus if the inherence of B in C is not questioned,
A's inherence in B is impossible.
The order of the terms is the same in both proofs: they differ
according to which of the negative propositions is the better known,
the one denying A of B or the one denying A of C. When the falsity
of the conclusion is the better known, we use reductio ad
impossible; when the major premiss of the syllogism is the more
obvious, we use direct demonstration. All the same the proposition
denying A of B is, in the order of being, prior to that denying A of
C; for premisses are prior to the conclusion which follows from
them, and 'no C is A' is the conclusion, 'no B is A' one of its
premisses. For the destructive result of reductio ad impossibile is
not a proper conclusion, nor are its antecedents proper premisses.
On the contrary: the constituents of syllogism are premisses related
to one another as whole to part or part to whole, whereas the
premisses A-C and A-B are not thus related to one another.
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