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Aristotle

"Posterior Analytics"


It is also clear that when A inheres in B, this can be
demonstrated if there is a middle term. Further, the 'elements' of
such a conclusion are the premisses containing the middle in question,
and they are identical in number with the middle terms, seeing that
the immediate propositions-or at least such immediate propositions
as are universal-are the 'elements'. If, on the other hand, there is
no middle term, demonstration ceases to be possible: we are on the way
to the basic truths. Similarly if A does not inhere in B, this can
be demonstrated if there is a middle term or a term prior to B in
which A does not inhere: otherwise there is no demonstration and a
basic truth is reached. There are, moreover, as many 'elements' of the
demonstrated conclusion as there are middle terms, since it is
propositions containing these middle terms that are the basic
premisses on which the demonstration rests; and as there are some
indemonstrable basic truths asserting that 'this is that' or that
'this inheres in that', so there are others denying that 'this is
that' or that 'this inheres in that'-in fact some basic truths will
affirm and some will deny being.


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