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. And those who say mathematical number is first and go on
to generate one kind of substance after another and give different
principles for each, make the substance of the universe a mere
series of episodes (for one substance has no influence on another by
its existence or nonexistence), and they give us many governing
principles; but the world refuses to be governed badly.
'The rule of many is not good; one ruler let there be.'
Book XIII
1
WE have stated what is the substance of sensible things, dealing
in the treatise on physics with matter, and later with the substance
which has actual existence. Now since our inquiry is whether there
is or is not besides the sensible substances any which is immovable
and eternal, and, if there is, what it is, we must first consider what
is said by others, so that, if there is anything which they say
wrongly, we may not be liable to the same objections, while, if
there is any opinion common to them and us, we shall have no private
grievance against ourselves on that account; for one must be content
to state some points better than one's predecessors, and others no
worse.
Two opinions are held on this subject; it is said that the objects
of mathematics-i.e. numbers and lines and the like-are substances, and
again that the Ideas are substances. And (1) since some recognize
these as two different classes-the Ideas and the mathematical numbers,
and (2) some recognize both as having one nature, while (3) some
others say that the mathematical substances are the only substances,
we must consider first the objects of mathematics, not qualifying them
by any other characteristic-not asking, for instance, whether they are
in fact Ideas or not, or whether they are the principles and
substances of existing things or not, but only whether as objects of
mathematics they exist or not, and if they exist, how they exist
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