But, as things are, demonstration is not
transferable to another genus, with such exceptions as we have
mentioned of the application of geometrical demonstrations to theorems
in mechanics or optics, or of arithmetical demonstrations to those
of harmonics.
It is hard to be sure whether one knows or not; for it is hard to be
sure whether one's knowledge is based on the basic truths
appropriate to each attribute-the differentia of true knowledge. We
think we have scientific knowledge if we have reasoned from true and
primary premisses. But that is not so: the conclusion must be
homogeneous with the basic facts of the science.
10
I call the basic truths of every genus those clements in it the
existence of which cannot be proved. As regards both these primary
truths and the attributes dependent on them the meaning of the name is
assumed. The fact of their existence as regards the primary truths
must be assumed; but it has to be proved of the remainder, the
attributes. Thus we assume the meaning alike of unity, straight, and
triangular; but while as regards unity and magnitude we assume also
the fact of their existence, in the case of the remainder proof is
required.
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