The Complete Aristotle (eng.)

contradiction through
other premisses, or to assume it in the way suggested in the
Topics. Since there are three oppositions to affirmative
statements, it follows that opposite statements may be assumed as
premisses in six ways; we may have either universal affirmative and
negative, or universal affirmative and particular negative, or
particular affirmative and universal negative, and the relations
between the terms may be reversed; e.g. A may belong to all B and
to no C, or to all C and to no B, or to all of the one, not to all
of the other; here too the relation between the terms may be
reversed. Similarly in the third figure. So it is clear in how many
ways and in what figures a syllogism can be made by means of
premisses which are opposed.
    It is clear too that from false premisses it is possible to draw
a true conclusion, as has been said before, but it is not possible
if the premisses are opposed. For the syllogism is always contrary
to the fact, e.g. if a thing is good, it is proved that it is not
good, if an animal, that it is not an animal because the syllogism
springs out of a contradiction and the terms presupposed are either
identical or related as whole and part. It is evident also that in
fallacious reasonings nothing prevents a contradiction to the
hypothesis from resulting, e.g. if something is odd, it is not odd.
For the syllogism owed its contrariety to its contradictory
premisses; if we assume such premisses we shall get a result that
contradicts our hypothesis. But we must recognize that contraries
cannot be inferred from a single syllogism in such a way that we
conclude that what is not good is good, or anything of that sort
unless a self-contradictory premiss is at once assumed, e.g. ‘every
animal is white and not white’, and we proceed ‘man is an animal’.
Either we must introduce the contradiction by an additional
assumption, assuming, e.g., that every science is supposition, and
then assuming ‘Medicine is a science, but none of it is
supposition’ (which is the mode in which refutations are made), or
we must argue from two syllogisms. In no other way than this, as
was said before, is it possible that the premisses should be really
contrary.
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    To beg and assume the original question is a species of failure
to demonstrate the problem proposed; but this happens in many ways.
A man may not reason syllogistically at all, or he may argue from
premisses which are less known or equally unknown, or he may
establish the antecedent by means of its consequents; for
demonstration proceeds from what is more certain and is prior. Now
begging the question is none of these: but since we get to know
some things naturally through themselves, and other things by means
of something else (the first principles through themselves, what is
subordinate to them through something else), whenever a man tries
to prove what is not self-evident by means of itself, then he begs
the original question. This may be done by assuming what is in
question at once; it is also possible to make a transition to other
things which would naturally be proved through the thesis proposed,
and demonstrate it through them, e.g. if A should be proved through
B, and B through C, though it was natural that C should be proved
through A: for it turns out that those who reason thus are proving
A by means of itself. This is what those persons do who suppose
that they are constructing parallel straight lines: for they fail
to see that they are assuming facts which it is impossible to
demonstrate unless the parallels exist. So it turns out that those
who reason thus merely say a particular thing is, if it is: in this
way everything will be self-evident. But that is impossible.
    If then it is uncertain whether A belongs to C, and also whether
A belongs to B, and if one should assume that A does belong to B,
it is not yet clear whether he begs the original question, but it
is evident that he is not demonstrating: for what is as uncertain
as the question to be answered cannot be a principle of a
demonstration. If however B is so related to C that they are
identical, or if they are plainly convertible, or the one belongs
to the other, the original question is begged. For one might
equally well prove that A belongs to B through those terms if they
are convertible. But if they are not convertible, it is the fact
that they are not that prevents such a demonstration, not the
method of demonstrating. But if one were to make the conversion,
then he