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contraries. And these belong to one science, whether they have or have
not one single meaning. Probably the truth is that they have not;
yet even if 'one' has several meanings, the other meanings will be
related to the primary meaning (and similarly in the case of the
contraries), even if being or unity is not a universal and the same in
every instance or is not separable from the particular instances (as
in fact it probably is not; the unity is in some cases that of
common reference, in some cases that of serial succession). And for
this reason it does not belong to the geometer to inquire what is
contrariety or completeness or unity or being or the same or the
other, but only to presuppose these concepts and reason from this
starting-point.--Obviously then it is the work of one science to
examine being qua being, and the attributes which belong to it qua
being, and the same science will examine not only substances but
also their attributes, both those above named and the concepts 'prior'
and 'posterior', 'genus' and 'species', 'whole' and 'part', and the
others of this sort.

We must state whether it belongs to one or to different sciences
to inquire into the truths which are in mathematics called axioms, and
into substance. Evidently, the inquiry into these also belongs to
one science, and that the science of the philosopher; for these truths
hold good for everything that is, and not for some special genus apart
from others. And all men use them, because they are true of being
qua being and each genus has being. But men use them just so far as to
satisfy their purposes; that is, as far as the genus to which their
demonstrations refer extends. Therefore since these truths clearly
hold good for all things qua being (for this is what is common to
them), to him who studies being qua being belongs the inquiry into
these as well. And for this reason no one who is conducting a
special inquiry tries to say anything about their truth or
falsity,-neither the geometer nor the arithmetician. Some natural
philosophers indeed have done so, and their procedure was intelligible
enough; for they thought that they alone were inquiring about the
whole of nature and about being. But since there is one kind of
thinker who is above even the natural philosopher (for nature is
only one particular genus of being), the discussion of these truths
also will belong to him whose inquiry is universal and deals with
primary substance. Physics also is a kind of Wisdom, but it is not the
first kind.-And the attempts of some of those who discuss the terms on
which truth should be accepted, are due to a want of training in
logic; for they should know these things already when they come to a
special study, and not be inquiring into them while they are listening
to lectures on it.
Evidently then it belongs to the philosopher, i.e. to him who is
studying the nature of all substance, to inquire also into the
principles of syllogism. But he who knows best about each genus must
be able to state the most certain principles of his subject, so that
he whose subject is existing things qua existing must be able to state
the most certain principles of all things. This is the philosopher,
and the most certain principle of all is that regarding which it is
impossible to be mistaken; for such a principle must be both the
best known (for all men may be mistaken about things which they do not
know), and non-hypothetical. For a principle which every one must have
who understands anything that is, is not a hypothesis; and that
which every one must know who knows anything, he must already have
when he comes to a special study. Evidently then such a principle is
the most certain of all; which principle this is, let us proceed to
say. It is, that the same attribute cannot at the same time belong and
not belong to the same subject and in the same respect; we must
presuppose, to guard against dialectical objections, any further
qualifications which might be added. This, then, is the most certain
of all principles, since it answers to the definition given above. For

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