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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 knowledge of the universal； but not
with a knowledge of the particulars； consequently his knowledge will
not be contrary to his ignorance。 The argument in the Meno that
learning is recollection may be criticized in a similar way。 For it
never happens that a man starts with a foreknowledge of the
particular； but along with the process of being led to see the general
principle he receives a knowledge of the particulars； by an act （as it
were） of recognition。 For we know some things directly； e。g。 that
the angles are equal to two right angles； if we know that the figure
is a triangle。 Similarly in all other cases。
By a knowledge of the universal then we see the particulars； but
we do not know them by the kind of knowledge which is proper to
them； consequently it is possible that we may make mistakes about
them； but not that we should have the knowledge and error that are
contrary to one another： rather we have the knowledge of the universal
but make a mistake in apprehending the particular。 Similarly in the
cases stated above。 The error in respect of the middle term is not
contrary to the knowledge obtained through the syllogism； nor is the
thought in respect of one middle term contrary to that in respect of
the other。 Nothing prevents a man who knows both that A belongs to the
whole of B； and that B again belongs to C； thinking that A does not
belong to C； e。g。 knowing that every mule is sterile and that this
is a mule； and thinking that this animal is with foal： for he does not
know that A belongs to C； unless he considers the two propositions
together。 So it is evident that if he knows the one and does not
know the other； he will fall into error。 And this is the relation of
knowledge of the universal to knowledge of the particular。 For we know
no sensible thing； once it has passed beyond the range of our
senses； even if we happen to have perceived it； except by means of the
universal and the possession of the knowledge which is proper to the
particular； but without the actual exercise of that knowledge。 For
to know is used in three senses： it may mean either to have
knowledge of the universal or to have knowledge proper to the matter
in hand or to exercise such knowledge： consequently three kinds of
error also are possible。 Nothing then prevents a man both knowing
and being mistaken about the same thing； provided that his knowledge
and his error are not contrary。 And this happens also to the man whose
knowledge is limited to each of the premisses and who has not
previously considered the particular question。 For when he thinks that
the mule is with foal he has not the knowledge in the sense of its
actual exercise； nor on the other hand has his thought caused an error
contrary t