The Complete Aristotle (eng.)

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