The Complete Aristotle (eng.)

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 as far as possible those that are not
connected by middle terms. For example suppose that A is to be
inferred to be true of F, B, C, D, and E being middle terms. One
ought then to ask whether A belongs to B, and next whether D
belongs to E, instead of asking whether B belongs to C; after that
he may ask whether B belongs to C, and so on. If the syllogism is
drawn through one middle term, he ought to begin with that: in this
way he will most likely deceive his opponent.
20
    Since we know when a syllogism can be formed and how its terms
must be related, it is clear when refutation will be possible and
when impossible. A refutation is possible whether everything is
conceded, or the answers alternate (one, I mean, being affirmative,
the other negative). For as has been shown a syllogism is possible
whether the terms are related in affirmative propositions or one
proposition is affirmative, the other negative: consequently, if
what is laid down is contrary to the conclusion, a refutation must
take place: for a refutation is a syllogism which establishes the
contradictory. But if nothing is conceded, a refutation is
impossible: for no syllogism is possible (as we saw) when all the
terms are negative: therefore no refutation is possible. For if a
refutation were possible, a syllogism must be possible; although if
a syllogism is possible it does not follow that a refutation is
possible. Similarly refutation is not possible if nothing is
conceded universally: since the fields of refutation and syllogism
are defined in the same way.
21
    It sometimes happens that just as we are deceived in the
arrangement