e. true. Similarly (ii) if
the middle is taken from another series of predication; e.g. suppose D
to be not only contained within A as a part within its whole but
also predicable of all B. Then the premiss D-B must remain
unchanged, but the quality of A-D must be changed; so that D-B is
always true, A-D always false. Such error is practically identical
with that which is inferred through the 'appropriate' middle. On the
other hand, (b) if the conclusion is not inferred through the
'appropriate' middle-(i) when the middle is subordinate to A but is
predicable of no B, both premisses must be false, because if there
is to be a conclusion both must be posited as asserting the contrary
of what is actually the fact, and so posited both become false: e.g.
suppose that actually all D is A but no B is D; then if these
premisses are changed in quality, a conclusion will follow and both of
the new premisses will be false. When, however, (ii) the middle D is
not subordinate to A, A-D will be true, D-B false-A-D true because A
was not subordinate to D, D-B false because if it had been true, the
conclusion too would have been true; but it is ex hypothesi false.
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