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Carnot Reflexions sur la Metaphysique
du calcul infinitesimal Note sur les quantites
negatives: pp 217 to 252
A negative quantity taken per se,
has it seems been taken for
the subject of a definition:
a definition in the ordinary sense
of the word, definition viz. per
genus et differantiiam. But applied to
this subject the definition per
genus et differantiiam is self
contradictory and impossible. That
refers to a class of
real existence; this the to a class the existence of which is
by the supposition the existence
of which is unreal, purely fictitious.
A positive quantity is a
real entity: a negative quantity
is a fictitious entity: no fictitious
entity can belong
to any class of real entities:
not a proposition asserting that it
does is a self-contradictory
proposition.
What mode of exposition
therefore is it that is suitable
to the nature of a negative
quantity taken per se? The mode
termed by J.B. paraphrasis, of which
an explanation is given in the
Fragment on Government.
Of every fictitious entity it
being of the very essence not to
be real or to speak more strictly
its being of the very essence
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