'But'-you
may say-'eliminate figure or limit, and the attribute vanishes.' True,
but figure and limit are not the first differentiae whose
elimination destroys the attribute. 'Then what is the first?' If it is
triangle, it will be in virtue of triangle that the attribute
belongs to all the other subjects of which it is predicable, and
triangle is the subject to which it can be demonstrated as belonging
commensurately and universally.
6
Demonstrative knowledge must rest on necessary basic truths; for the
object of scientific knowledge cannot be other than it is. Now
attributes attaching essentially to their subjects attach
necessarily to them: for essential attributes are either elements in
the essential nature of their subjects, or contain their subjects as
elements in their own essential nature. (The pairs of opposites
which the latter class includes are necessary because one member or
the other necessarily inheres.) It follows from this that premisses of
the demonstrative syllogism must be connexions essential in the
sense explained: for all attributes must inhere essentially or else be
accidental, and accidental attributes are not necessary to their
subjects.
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