(2) It has been proved that no conclusion follows if both
premisses are negative, but that one must be negative, the other
affirmative. So we are compelled to lay down the following
additional rule: as the demonstration expands, the affirmative
premisses must increase in number, but there cannot be more than one
negative premiss in each complete proof. Thus, suppose no B is A,
and all C is B. Then if both the premisses are to be again expanded, a
middle must be interposed. Let us interpose D between A and B, and E
between B and C. Then clearly E is affirmatively related to B and C,
while D is affirmatively related to B but negatively to A; for all B
is D, but there must be no D which is A. Thus there proves to be a
single negative premiss, A-D. In the further prosyllogisms too it is
the same, because in the terms of an affirmative syllogism the
middle is always related affirmatively to both extremes; in a negative
syllogism it must be negatively related only to one of them, and so
this negation comes to be a single negative premiss, the other
premisses being affirmative. If, then, that through which a truth is
proved is a better known and more certain truth, and if the negative
proposition is proved through the affirmative and not vice versa,
affirmative demonstration, being prior and better known and more
certain, will be superior.
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