The Complete Aristotle (eng.)

would be doing what we have described and effecting a
reciprocal proof with three propositions.
    Similarly if he should assume that B belongs to C, this being as
uncertain as the question whether A belongs to C, the question is
not yet begged, but no demonstration is made. If however A and B
are identical either because they are convertible or because A
follows B, then the question is begged for the same reason as
before. For we have explained the meaning of begging the question,
viz. proving that which is not self-evident by means of itself.
    If then begging the question is proving what is not self-evident
by means of itself, in other words failing to prove when the
failure is due to the thesis to be proved and the premiss through
which it is proved being equally uncertain, either because
predicates which are identical belong to the same subject, or
because the same predicate belongs to subjects which are identical,
the question may be begged in the middle and third figures in both
ways, though, if the syllogism is affirmative, only in the third
and first figures. If the syllogism is negative, the question is
begged when identical predicates are denied of the same subject;
and both premisses do not beg the question indifferently (in a
similar way the question may be begged in the middle figure),
because the terms in negative syllogisms are not convertible. In
scientific demonstrations the question is begged when the terms are
really related in the manner described, in dialectical arguments
when they are according to common opinion so related.
17
    The objection that ‘this is not the reason why the result is
false’, which we frequently make in argument, is made primarily in
the case of a reductio ad impossibile, to rebut the proposition
which was being proved by the reduction. For unless a man has
contradicted this proposition he will not say, ‘False cause’, but
urge that something false has been assumed in the earlier parts of
the argument; nor will he use the formula in the case of an
ostensive proof; for here what one denies is not assumed as a
premiss. Further when anything is refuted ostensively by the terms
ABC, it cannot be objected that the syllogism does not depend on
the assumption laid down. For we use the expression ‘false cause’,
when the syllogism is concluded in spite of the refutation of this
position; but that is not possible in ostensive proofs: since if an
assumption is refuted, a syllogism can no longer be drawn in
reference to it. It is clear then that the expression ‘false cause’
can only be used in the case of a reductio ad impossibile, and when
the original hypothesis is so related to the impossible conclusion,
that the conclusion results indifferently whether the hypothesis is
made or not. The most obvious case of the irrelevance of an
assumption to a conclusion which is false is when a syllogism drawn
from middle terms to an impossible conclusion is independent of the
hypothesis, as we have explained in the Topics. For to put that
which is not the cause as the cause, is just this: e.g. if a man,
wishing to prove that the diagonal of the square is incommensurate
with the side, should try to prove Zeno’s theorem that motion is
impossible, and so establish a reductio ad impossibile: for Zeno’s
false theorem has no connexion at all with the original assumption.
Another case is where the impossible conclusion is connected with
the hypothesis, but does not result from it. This may happen
whether one traces the connexion upwards or downwards, e.g. if it
is laid down that A belongs to B, B to C, and C to D, and it should
be false that B belongs to D: for if we eliminated A and assumed
all the same that B belongs to C and C to D, the false conclusion
would not depend on the original hypothesis. Or again trace the
connexion upwards; e.g. suppose that A belongs to B, E to A and F
to E, it being false that F belongs to A. In this way too the
impossible conclusion would result, though the original hypothesis
were eliminated. But the impossible conclusion ought to be
connected with the original terms: in this way it will depend on
the hypothesis, e.g. when one traces the connexion downwards, the
impossible conclusion must be connected with that term which is
predicate in the hypothesis: for if it is impossible that A should
belong to D, the false conclusion will no longer result after A has
been eliminated. If one traces the connexion upwards, the
impossible conclusion must be connected