Posterior Analytics   

the conclusion is necessary, the mediating link is a contingent
fact. Or again, if a man is without knowledge now, though he still
retains the steps of the argument, though there is no change in
himself or in the fact and no lapse of memory on his part; then
neither had he knowledge previously. But the mediating link, not being
necessary, may have perished in the interval; and if so, though
there be no change in him nor in the fact, and though he will still
retain the steps of the argument, yet he has not knowledge, and
therefore had not knowledge before. Even if the link has not
actually perished but is liable to perish, this situation is
possible and might occur. But such a condition cannot be knowledge.
When the conclusion is necessary, the middle through which it was
proved may yet quite easily be non-necessary. You can in fact infer
the necessary even from a non-necessary premiss, just as you can infer
the true from the not true. On the other hand, when the middle is
necessary the conclusion must be necessary; just as true premisses
always give a true conclusion. Thus, if A is necessarily predicated of
B and B of C, then A is necessarily predicated of C. But when the
conclusion is nonnecessary the middle cannot be necessary either.
Thus: let A be predicated non-necessarily of C but necessarily of B,
and let B be a necessary predicate of C; then A too will be a
necessary predicate of C, which by hypothesis it is not.
To sum up, then: demonstrative knowledge must be knowledge of a
necessary nexus, and therefore must clearly be obtained through a
necessary middle term; otherwise its possessor will know neither the
cause nor the fact that his conclusion is a necessary connexion.
Either he will mistake the non-necessary for the necessary and believe
the necessity of the conclusion without knowing it, or else he will
not even believe it-in which case he will be equally ignorant, whether
he actually infers the mere fact through middle terms or the
reasoned fact and from immediate premisses.
Of accidents that are not essential according to our definition of
essential there is no demonstrative knowledge; for since an
accident, in the sense in which I here speak of it, may also not
inhere, it is impossible to prove its inherence as a necessary
conclusion. A difficulty, however, might be raised as to why in
dialectic, if the conclusion is not a necessary connexion, such and
such determinate premisses should be proposed in order to deal with
such and such determinate problems. Would not the result be the same
if one asked any questions whatever and then merely stated one's
conclusion? The solution is that determinate questions have to be put,
not because the replies to them affirm facts which necessitate facts
affirmed by the conclusion, but because these answers are propositions
which if the answerer affirm, he must affirm the conclusion and affirm
it with truth if they are true.
Since it is just those attributes within every genus which are
essential and possessed by their respective subjects as such that
are necessary it is clear that both the conclusions and the
premisses of demonstrations which produce scientific knowledge are
essential. For accidents are not necessary: and, further, since
accidents are not necessary one does not necessarily have reasoned
knowledge of a conclusion drawn from them (this is so even if the
accidental premisses are invariable but not essential, as in proofs
through signs; for though the conclusion be actually essential, one
will not know it as essential nor know its reason); but to have
reasoned knowledge of a conclusion is to know it through its cause. We
may conclude that the middle must be consequentially connected with
the minor, and the major with the middle.

7

It follows that we cannot in demonstrating pass from one genus to
another. We cannot, for instance, prove geometrical truths by
arithmetic. For there are three elements in demonstration: (1) what is