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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 with that term which is subject in the hypothesis： for if it
is impossible that F should belong to B； the impossible conclusion
will disappear if B is eliminated。 Similarly when the syllogisms are
negative。
It is clear then that when the impossibility is not related to the
original terms； the false conclusion does not result on account of the
assumption。 Or perhaps even so it may sometimes be independent。 For if
it were laid down that A belongs not to B but to K； and that K belongs
to C and C to D； the impossible conclusion would still stand。
Similarly if one takes the terms in an ascending series。
Consequently since the impossibility results whether the first
assumption is suppressed or not； it would appear to be independent
of that assumption。 Or perhaps we ought not to understand the
statement that the false conclusion results independently of the
assumption； in the sense that if something else were supposed the
impossibility would result； but rather we mean that when the first
assumption is eliminated； the same impossibility results through the
remaining premisses； since it is not perhaps absurd that the same
false result should follow from several hypotheses； e。g。 that
parallels meet； both on the assumption that the interior angle is
greater than the exterior and on the assumption that a triangle
contains more than two right angles。
18
A false argument depends on the first false statement in it。 Every
syllogism is made out of two or more premisses。 If then the false
conclusion is drawn from two premisses； one or both of them must be
false： for （as we proved） a false syllogism cannot be drawn from two
premisses。 But if the premisses are more than two； e。g。 if C is
established through A and B； and these through D； E； F； and G； one
of these higher propositions must be false； and on this the argument
depends： for A and B are inferred by means of D； E； F； and G。
Therefore the conclusion and the error results from one of them。
19
In order to avoid having a syllogism drawn against us we must take
care； whenever an opponent asks us to admit the reason without the
conclusions； not to grant him the same term twice over in his
premisses； since we know that a syllogism cannot be drawn without a
middle term； and that term which is stated more than once is the
middle。 How we ought to watch the middle in reference to each
conclusion； is evident from our knowing what kind of thesis is
proved in each figure。 This will not escape us since we know how we
are maintaining the argument。
That which we urge men to beware of in their admissions； they
ought in attack to try to conceal。 This will be possible first； if；
instead of drawing the conclusions of preliminary syllogisms； they
take the necessary premisses and leave the conclusions in the dark；
secondly if instead of inviting assent to propositions which are
closely connected they take