g. that
everything must be either affirmed or denied, and that a thing
cannot at the same time be and not be, and all other such
premisses:-the question is whether the same science deals with them as
with substance, or a different science, and if it is not one
science, which of the two must be identified with that which we now
seek.-It is not reasonable that these topics should be the object of
one science; for why should it be peculiarly appropriate to geometry
or to any other science to understand these matters? If then it
belongs to every science alike, and cannot belong to all, it is not
peculiar to the science which investigates substances, any more than
to any other science, to know about these topics.-And, at the same
time, in what way can there be a science of the first principles?
For we are aware even now what each of them in fact is (at least
even other sciences use them as familiar); but if there is a
demonstrative science which deals with them, there will have to be
an underlying kind, and some of them must be demonstrable attributes
and others must be axioms (for it is impossible that there should be
demonstration about all of them); for the demonstration must start
from certain premisses and be about a certain subject and prove
certain attributes. Therefore it follows that all attributes that
are proved must belong to a single class; for all demonstrative
sciences use the axioms.
But if the science of substance and the science which deals with
the axioms are different, which of them is by nature more
authoritative and prior? The axioms are most universal and are
principles of all things.
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