Posterior Analytics   

regard ourselves as then only having full knowledge of the reason
why he came.
If, then, all causes and reasons are alike in this respect, and if
this is the means to full knowledge in the case of final causes such
as we have exemplified, it follows that in the case of the other
causes also full knowledge is attained when an attribute no longer
inheres because of something else. Thus, when we learn that exterior
angles are equal to four right angles because they are the exterior
angles of an isosceles, there still remains the question 'Why has
isosceles this attribute?' and its answer 'Because it is a triangle,
and a triangle has it because a triangle is a rectilinear figure.'
If rectilinear figure possesses the property for no further reason, at
this point we have full knowledge-but at this point our knowledge
has become commensurately universal, and so we conclude that
commensurately universal demonstration is superior.
(6) The more demonstration becomes particular the more it sinks into
an indeterminate manifold, while universal demonstration tends to
the simple and determinate. But objects so far as they are an
indeterminate manifold are unintelligible, so far as they are
determinate, intelligible: they are therefore intelligible rather in
so far as they are universal than in so far as they are particular.
From this it follows that universals are more demonstrable: but
since relative and correlative increase concomitantly, of the more
demonstrable there will be fuller demonstration. Hence the
commensurate and universal form, being more truly demonstration, is
the superior.
(7) Demonstration which teaches two things is preferable to
demonstration which teaches only one. He who possesses
commensurately universal demonstration knows the particular as well,
but he who possesses particular demonstration does not know the
universal. So that this is an additional reason for preferring
commensurately universal demonstration. And there is yet this
further argument:
(8) Proof becomes more and more proof of the commensurate
universal as its middle term approaches nearer to the basic truth, and
nothing is so near as the immediate premiss which is itself the
basic truth. If, then, proof from the basic truth is more accurate
than proof not so derived, demonstration which depends more closely on
it is more accurate than demonstration which is less closely
dependent. But commensurately universal demonstration is characterized
by this closer dependence, and is therefore superior. Thus, if A had
to be proved to inhere in D, and the middles were B and C, B being the
higher term would render the demonstration which it mediated the
more universal.
Some of these arguments, however, are dialectical. The clearest
indication of the precedence of commensurately universal demonstration
is as follows: if of two propositions, a prior and a posterior, we
have a grasp of the prior, we have a kind of knowledge-a potential
grasp-of the posterior as well. For example, if one knows that the
angles of all triangles are equal to two right angles, one knows in
a sense-potentially-that the isosceles' angles also are equal to two
right angles, even if one does not know that the isosceles is a
triangle; but to grasp this posterior proposition is by no means to
know the commensurate universal either potentially or actually.
Moreover, commensurately universal demonstration is through and
through intelligible; particular demonstration issues in
sense-perception.

25

The preceding arguments constitute our defence of the superiority of
commensurately universal to particular demonstration. That affirmative
demonstration excels negative may be shown as follows.
(1) We may assume the superiority ceteris paribus of the