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All syllogisms cannot have the same basic truths. This may be
shown first of all by the following dialectical considerations. (1)
Some syllogisms are true and some false: for though a true inference
is possible from false premisses, yet this occurs once only-I mean
if A for instance, is truly predicable of C, but B, the middle, is
false, both A-B and B-C being false; nevertheless, if middles are
taken to prove these premisses, they will be false because every
conclusion which is a falsehood has false premisses, while true
conclusions have true premisses, and false and true differ in kind.
Then again, (2) falsehoods are not all derived from a single identical
set of principles: there are falsehoods which are the contraries of
one another and cannot coexist, e.g. 'justice is injustice', and
'justice is cowardice'; 'man is horse', and 'man is ox'; 'the equal is
greater', and 'the equal is less.' From established principles we
may argue the case as follows, confining-ourselves therefore to true
conclusions. Not even all these are inferred from the same basic
truths; many of them in fact have basic truths which differ
generically and are not transferable; units, for instance, which are
without position, cannot take the place of points, which have
position.
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