Secondly, when one has taken one's differing pair of opposites and
assumed that the two sides exhaust the genus, and that the subject one
seeks to define is present in one or other of them, and one has
further verified its presence in one of them; then it does not
matter whether or not one knows all the other subjects of which the
differentiae are also predicated. For it is obvious that when by
this process one reaches subjects incapable of further differentiation
one will possess the formula defining the substance. Moreover, to
postulate that the division exhausts the genus is not illegitimate
if the opposites exclude a middle; since if it is the differentia of
that genus, anything contained in the genus must lie on one of the two
sides.
In establishing a definition by division one should keep three
objects in view: (1) the admission only of elements in the definable
form, (2) the arrangement of these in the right order, (3) the
omission of no such elements. The first is feasible because one can
establish genus and differentia through the topic of the genus, just
as one can conclude the inherence of an accident through the topic
of the accident.
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