Posterior Analytics   

predicate A of G without falsehood, and G of B; for to feel pleasure
is to relax, and to relax is to change. So the conclusion can be drawn
through middles which are different, i.e. not in the same series-yet
not so that neither of these middles is predicable of the other, for
they must both be attributable to some one subject.
A further point worth investigating is how many ways of proving
the same conclusion can be obtained by varying the figure,

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There is no knowledge by demonstration of chance conjunctions; for
chance conjunctions exist neither by necessity nor as general
connexions but comprise what comes to be as something distinct from
these. Now demonstration is concerned only with one or other of
these two; for all reasoning proceeds from necessary or general
premisses, the conclusion being necessary if the premisses are
necessary and general if the premisses are general. Consequently, if
chance conjunctions are neither general nor necessary, they are not
demonstrable.

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Scientific knowledge is not possible through the act of
perception. Even if perception as a faculty is of 'the such' and not
merely of a 'this somewhat', yet one must at any rate actually
perceive a 'this somewhat', and at a definite present place and
time: but that which is commensurately universal and true in all cases
one cannot perceive, since it is not 'this' and it is not 'now'; if it
were, it would not be commensurately universal-the term we apply to
what is always and everywhere. Seeing, therefore, that
demonstrations are commensurately universal and universals
imperceptible, we clearly cannot obtain scientific knowledge by the
act of perception: nay, it is obvious that even if it were possible to
perceive that a triangle has its angles equal to two right angles,
we should still be looking for a demonstration-we should not (as
some say) possess knowledge of it; for perception must be of a
particular, whereas scientific knowledge involves the recognition of
the commensurate universal. So if we were on the moon, and saw the
earth shutting out the sun's light, we should not know the cause of
the eclipse: we should perceive the present fact of the eclipse, but
not the reasoned fact at all, since the act of perception is not of
the commensurate universal. I do not, of course, deny that by watching
the frequent recurrence of this event we might, after tracking the
commensurate universal, possess a demonstration, for the
commensurate universal is elicited from the several groups of
singulars.
The commensurate universal is precious because it makes clear the
cause; so that in the case of facts like these which have a cause
other than themselves universal knowledge is more precious than
sense-perceptions and than intuition. (As regards primary truths there
is of course a different account to be given.) Hence it is clear
that knowledge of things demonstrable cannot be acquired by
perception, unless the term perception is applied to the possession of
scientific knowledge through demonstration. Nevertheless certain
points do arise with regard to connexions to be proved which are
referred for their explanation to a failure in sense-perception: there
are cases when an act of vision would terminate our inquiry, not
because in seeing we should be knowing, but because we should have
elicited the universal from seeing; if, for example, we saw the
pores in the glass and the light passing through, the reason of the
kindling would be clear to us because we should at the same time see
it in each instance and intuit that it must be so in all instances.

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