It is evident, then, that not everything demonstrable can be
defined. What then? Can everything definable be demonstrated, or
not? There is one of our previous arguments which covers this too.
Of a single thing qua single there is a single scientific knowledge.
Hence, since to know the demonstrable scientifically is to possess the
demonstration of it, an impossible consequence will follow:-possession
of its definition without its demonstration will give knowledge of the
demonstrable.
Moreover, the basic premisses of demonstrations are definitions, and
it has already been shown that these will be found indemonstrable;
either the basic premisses will be demonstrable and will depend on
prior premisses, and the regress will be endless; or the primary
truths will be indemonstrable definitions.
But if the definable and the demonstrable are not wholly the same,
may they yet be partially the same? Or is that impossible, because
there can be no demonstration of the definable? There can be none,
because definition is of the essential nature or being of something,
and all demonstrations evidently posit and assume the essential
nature-mathematical demonstrations, for example, the nature of unity
and the odd, and all the other sciences likewise.
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