[1061b]
[1]
and in others their commensurability or
incommensurability, and in others their ratios; yet nevertheless we
hold that there is one and the same science of all these things, viz.
geometry), so it is the same with regard to Being.For the study of its attributes in so
far as it is Being, and of its contrarieties1
qua Being, belongs to no other science than
Philosophy; for to physics one would assign the study of things not
qua Being but qua
participating in motion, while dialectics and sophistry deal with the
attributes of existing things, but not of things qua Being, nor do they treat of Being itself in so far as it is
Being.Therefore it
remains that the philosopher is the man who studies the things which
we have described, in so far as they are Being. And since everything
that is , although the term has several meanings, is so
described in virtue of some one common concept, and the same is true
of the contraries (since they can be referred to the primary
contrarieties and differences of Being), and since things of this kind
can fall under one science, the difficulty which we stated at the
beginning2 may be regarded as
solved3—I mean the problem as to
how there can be one science of several things which are different in
genus. Since even the mathematician uses the common
axioms only in a particular application, it will be the province of
Primary Philosophy to study the principles of these as well.4
[20]
That when equals are taken from equals the remainders are equal is
an axiom common to all quantities; but mathematics isolates a
particular part of its proper subject matter and studies it
separately; e.g. lines or angles or numbers or some other kind of
quantity, but not qua Being, but only in so far
as each of them is continuous in one, two or three dimensions. But
philosophy does not investigate particular things in so far as each of
them has some definite attribute, but studies that which
is , in so far as each particular thing is
.The same applies to
the science of physics as to mathematics, for physics studies the
attributes and first principles of things qua
in motion, and not qua Being; but Primary
Science, as we have said, deals with these things only in so far as
the subjects which underlie them are existent, and not in respect of
anything else. Hence we should regard both physics and mathematics as
subdivisions of Wisdom. There is a principle in
existing things about which we cannot make a mistake5; of
which, on the contrary, we must always realize the
truth—viz. that the same thing cannot at one and the same
time be and not be,
1 i.e., identity, otherness, etc.
3 Also the problem stated in ch. i. 3.
4 This chapter corresponds to Aristot. Met. 4.3.1-6, and answers the problem stated in Aristot. Met. 11.1.2.
5 This chapter corresponds to Aristot. Met. 4.3.7-4.31.
Aristotle. Aristotle in 23 Volumes, Vols.17, 18, translated by Hugh Tredennick. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1933, 1989.
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