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. But they must
predicate of every subject the affirmation or the negation of every
attribute. For it is absurd if of each subject its own negation is
to be predicable, while the negation of something else which cannot be
predicated of it is not to be predicable of it; for instance, if it is
true to say of a man that he is not a man, evidently it is also true
to say that he is either a trireme or not a trireme. If, then, the
affirmative can be predicated, the negative must be predicable too;
and if the affirmative is not predicable, the negative, at least, will
be more predicable than the negative of the subject itself. If,
then, even the latter negative is predicable, the negative of
'trireme' will be also predicable; and, if this is predicable, the
affirmative will be so too.
Those, then, who maintain this view are driven to this conclusion,
and to the further conclusion that it is not necessary either to
assert or to deny. For if it is true that a thing is a man and a
not-man, evidently also it will be neither a man nor a not-man. For to
the two assertions there answer two negations, and if the former is
treated as a single proposition compounded out of two, the latter also
is a single proposition opposite to the former.
Again, either the theory is true in all cases, and a thing is both
white and not-white, and existent and non-existent, and all other
assertions and negations are similarly compatible or the theory is
true of some statements and not of others
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