The Complete Aristotle (eng.)

a corresponding portion of knowledge, and that, since
we learn either by induction or by demonstration, this knowledge
cannot be acquired. Thus demonstration develops from universals,
induction from particulars; but since it is possible to familiarize
the pupil with even the so-called mathematical abstractions only
through induction-i.e. only because each subject genus possesses,
in virtue of a determinate mathematical character, certain
properties which can be treated as separate even though they do not
exist in isolation-it is consequently impossible to come to grasp
universals except through induction. But induction is impossible
for those who have not sense-perception. For it is sense-perception
alone which is adequate for grasping the particulars: they cannot
be objects of scientific knowledge, because neither can universals
give us knowledge of them without induction, nor can we get it
through induction without sense-perception.
19
    Every syllogism is effected by means of three terms. One kind of
syllogism serves to prove that A inheres in C by showing that A
inheres in B and B in C; the other is negative and one of its
premisses asserts one term of another, while the other denies one
term of another. It is clear, then, that these are the fundamentals
and so-called hypotheses of syllogism. Assume them as they have
been stated, and proof is bound to follow-proof that A inheres in C
through B, and again that A inheres in B through some other middle
term, and similarly that B inheres in C. If our reasoning aims at
gaining credence and so is merely dialectical, it is obvious that
we have only to see that our inference is based on premisses as
credible as possible: so that if a middle term between A and B is
credible though not real, one can reason through it and complete a
dialectical syllogism. If, however, one is aiming at truth, one
must be guided by the real connexions of subjects and attributes.
Thus: since there are attributes which are predicated of a subject
essentially or naturally and not coincidentally-not, that is, in
the sense in which we say ‘That white (thing) is a man’, which is
not the same mode of predication as when we say ‘The man is white’:
the man is white not because he is something else but because he is
man, but the white is man because ‘being white’ coincides with
‘humanity’ within one substratum-therefore there are terms such as
are naturally subjects of predicates. Suppose, then, C such a term
not itself attributable to anything else as to a subject, but the
proximate subject of the attribute B—i.e. so that B-C is immediate;
suppose further E related immediately to F, and F to B. The first
question is, must this series terminate, or can it proceed to
infinity? The second question is as follows: Suppose nothing is
essentially predicated of A, but A is predicated primarily of H and
of no intermediate prior term, and suppose H similarly related to G
and G to B; then must this series also terminate, or can it too
proceed to infinity? There is this much difference between the
questions: the first is, is it possible to start from that which is
not itself attributable to anything else but is the subject of
attributes, and ascend to infinity? The second is the problem
whether one can start from that which is a predicate but not itself
a subject of predicates, and descend to infinity? A third question
is, if the extreme terms are fixed, can there be an infinity of
middles? I mean this: suppose for example that A inheres in C and B
is intermediate between them, but between B and A there are other
middles, and between these again fresh middles; can these proceed
to infinity or can they not? This is the equivalent of inquiring,
do demonstrations proceed to infinity, i.e. is everything
demonstrable? Or do ultimate subject and primary attribute limit
one another?
    I hold that the same questions arise with regard to negative
conclusions and premisses: viz. if A is attributable to no B, then
either this predication will be primary, or there will be an
intermediate term prior to B to which a is not attributable-G, let
us say, which is attributable to all B-and there may still be
another term H prior to G, which is attributable to all G. The same
questions arise, I say, because in these cases too either the
series of prior terms to which a is not attributable is infinite or
it terminates.
    One cannot ask the same questions in the case of reciprocating
terms, since when subject and