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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 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
of the terms； so error may arise in our thought about them； e。g。 if it
is possible that the same predicate should belong to more than one
subject immediately； but although knowing the one； a man may forget
the other and think the opposite true。 Suppose that A belongs to B and
to C in virtue of their nature； and that B and C belong to all D in
the same way。 If then a man thinks that A belongs to all B； and B to
D； but A to no C； and C to all D； he will both know and not know the
same thing in respect of the same thing。 Again if a man were to make a
mistake about the members of a single series； e。g。 suppose A belongs
to B； B to C； and C to D； but some one thinks that A belongs to all B；
but to no C： he will both know that A belongs to D； and think that
it does not。 Does he then maintain after this simply that what he
knows； he does not think？ For he knows in a way that A belongs to C
through B； since the part is included in the whole； so that what he
knows in a way； this he maintains he does not think at all： but that
is impossible。
In the former case； where the middle term does not belong to the
same series； it is not possible to think both the premisses with
reference to each of the two middle terms： e。g。 that A belongs to
all B； but to no C； and both B and C belong to all D。 For it turns out
that the first premiss of the one syllogism is either wholly or
partially contrary to the first premiss of the other。 For if he thinks
that A belongs to everything to which B belongs； and he knows that B
belongs to D； then he knows that A belongs to D。 Consequently if again
he thinks that A belongs to nothing to which C belongs； he thinks that
A does not belong to some of that to which B belongs； but if he thinks
that A belongs to everything to which B belongs； and again thinks that
A does not belong to some of that to which B belongs； these beliefs
are wholly or partially contrary。 In this way then it is not
possible to think； but nothing prevents a man thinking one premiss
of each syllogism of both premisses of one of the two syllogisms： e。g。
A belongs to all B； and B to D； and again A belongs to no C。 An
error of this kind is similar to the error into which we fall
concerning particulars： e。g。 if A belongs to all B； and B to all C；
A will belong to all C。 If then a man knows that A belongs to
everything to which B belongs； he knows that A belongs to C。 But
nothing prevents his being ignorant that C exists； e。g。 let A stand
for two right angles； B for triangle； C for a particular diagram of
a triangle。 A man might think that C did not exist； though he knew
that every triangle contains two right angles； consequently he will
know and not know the same thing at the same time。 For the
expression 'to know that every triangle has its angles equal to two
right angles' is ambiguous； meaning to have the knowledge either of
the universal or of the particulars。 Thus then he knows that C
contains two right angles with a