The Complete Aristotle (eng.)

which alters a property changes.
Again, we can 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,
30
    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.
31
    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.
32
    All syllogisms cannot have the same basic truths. This may be
shown first of all by the following dialectical considerations. (1)
Some syllogisms are true and some false: for though a true
inference is possible from false premisses, yet this occurs once
only-I mean if A for instance, is truly predicable of C, but B, the
middle, is false, both A-B and B-C being false; nevertheless, if
middles are taken to prove these premisses, they will be false
because every conclusion which is a falsehood has false premisses,
while true conclusions have true premisses, and false and true
differ in kind. Then again, (2) falsehoods are not all derived from
a single identical set of principles: there are falsehoods which
are the contraries of one another and cannot coexist, e.g. ‘justice
is injustice’, and ‘justice is cowardice’; ‘man is