Posterior Analytics   

was not subordinate to D, D-B false because if it had been true, the
conclusion too would have been true; but it is ex hypothesi false.
When the erroneous inference is in the second figure, both premisses
cannot be entirely false; since if B is subordinate to A, there can be
no middle predicable of all of one extreme and of none of the other,
as was stated before. One premiss, however, may be false, and it may
be either of them. Thus, if C is actually an attribute of both A and
B, but is assumed to be an attribute of A only and not of B, C-A
will be true, C-B false: or again if C be assumed to be attributable
to B but to no A, C-B will be true, C-A false.
We have stated when and through what kinds of premisses error will
result in cases where the erroneous conclusion is negative. If the
conclusion is affirmative, (a) (i) it may be inferred through the
'appropriate' middle term. In this case both premisses cannot be false
since, as we said before, C-B must remain unchanged if there is to
be a conclusion, and consequently A-C, the quality of which is
changed, will always be false. This is equally true if (ii) the middle
is taken from another series of predication, as was stated to be the
case also with regard to negative error; for D-B must remain
unchanged, while the quality of A-D must be converted, and the type of
error is the same as before.
(b) The middle may be inappropriate. Then (i) if D is subordinate to
A, A-D will be true, but D-B false; since A may quite well be
predicable of several terms no one of which can be subordinated to
another. If, however, (ii) D is not subordinate to A, obviously A-D,
since it is affirmed, will always be false, while D-B may be either
true or false; for A may very well be an attribute of no D, whereas
all B is D, e.g. no science is animal, all music is science. Equally
well A may be an attribute of no D, and D of no B. It emerges, then,
that if the middle term is not subordinate to the major, not only both
premisses but either singly may be false.
Thus we have made it clear how many varieties of erroneous inference
are liable to happen and through what kinds of premisses they occur,
in the case both of immediate and of demonstrable truths.

18

It is also clear that the loss of any one of the senses entails
the loss of 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