(c) It may occur when both premisses are false; e.g. supposing A
atomically connected with both C and B, if it be then assumed that
no C is and all B is C, both premisses are false.
(d) It is also possible when one is false. This may be either
premiss indifferently. A-C may be true, C-B false-A-C true because A
is not an attribute of all things, C-B false because C, which never
has the attribute A, cannot be an attribute of B; for if C-B were
true, the premiss A-C would no longer be true, and besides if both
premisses were true, the conclusion would be true. Or again, C-B may
be true and A-C false; e.g. if both C and A contain B as genera, one
of them must be subordinate to the other, so that if the premiss takes
the form No C is A, it will be false. This makes it clear that whether
either or both premisses are false, the conclusion will equally be
false.
In the second figure the premisses cannot both be wholly false;
for if all B is A, no middle term can be with truth universally
affirmed of one extreme and universally denied of the other: but
premisses in which the middle is affirmed of one extreme and denied of
the other are the necessary condition if one is to get a valid
inference at all.
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