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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 to his knowledge： for the error contrary to the knowledge
of the universal would be a syllogism。
But he who thinks the essence of good is the essence of bad will
think the same thing to be the essence of good and the essence of bad。
Let A stand for the essence of good and B for the essence of bad；
and again C for the essence of good。 Since then he thinks B and C
identical； he will think that C is B； and similarly that B is A；
consequently that C is A。 For just as we saw that if B is true of
all of which C is true； and A is true of all of which B is true； A
is true of C； similarly with the word 'think'。 Similarly also with the
word 'is'； for we saw that if C is the same as B； and B as A； C is the
same as A。 Similarly therefore with 'opine'。 Perhaps then this is
necessary if a man will grant the first point。 But presumably that
is false； that any one could suppose the essence of good to be the
essence of bad； save incidentally。 For it is possible to think this in
many different ways。 But we must consider this matter better。
22
Whenever the extremes are convertible it is necessary that the
middle should be convertible with both。 For if A belongs to C
through B； then if A and C are convertible and C belongs everything to
which A belongs； B is convertible with A； and B belongs to
everything to which A belongs； through C as middle； and C is
convertible with B through A as middle。 Similarly if the conclusion is
negative； e。g。 if B belongs to C； but A does not belong to B；
neither will A belong to C。 If then B is convertible with A； C will be
convertible with A。 Suppose B does not belong to A； neither then
will C： for ex hypothesi B belonged to all C。 And if C is
convertible with B； B is convertible also with A； for C is said of
that of all of which B is said。 And if C is convertible in relation to
A and to B； B also is convertible in relation to A。 For C belongs to
that to which B belongs： but C does not belong to that to which A
belongs。 And this alone starts from the conclusion； the preceding
moods do not do so as in the affirmative syllogism。 Again if A and B
are convertible； and similarly C and D； and if A or C must belong to
anything whatever； then B and D will be such that one or other belongs
to anything whatever。 For since B belongs to that to which A
belongs； and D belongs to that to which C belongs； and since A or C
belongs to everything； but not together； it is clear that B or D
belongs to everything； but not together。 For example if that which
is uncreated is incorruptible and that which is incorruptible is
uncreated； it is necessary that what is created should be
corruptible and what is corruptible should have been created。 For
two syllogisms have been put together。 Again if A or B belongs to
everything and if C or D belongs to everything； but they cannot belong
together； then when A and C are convertible B and D are convertible。
For if B does not belong to something to which D belongs； it is
clear that A belongs to it。 But if A then C： for they are convertible。
Therefore C and D belong together。 But this is impossible。 When A
belongs to the whole of B and to C and is affirmed of nothing else；
and B also belongs to all C； it is necessary that A and B should be
convertible： for since A is said of B and C only； and B is affirmed
both of itself and of C； it is clear that B will be said of everything
of which A is said； except A itself。 Again when A and B belong to
the whole of C； and C is convertible with B； it is necessary that A
should belong to all B： for since A belongs to all C； and C to B by
conversion； A will belong to all B。
When； of two opposites A and B； A is preferable to B； and
similarly D is preferable to C； then if A and C together are
preferable to B and D together； A must be preferable to D。 For A is an
object of desire to the same extent as B is an object of aversion；
since they are opposites： and C is similarly related to D； since
they also are opposites。 If then A is an object of desire to the
same extent as D； B is an object of aversion to the same extent as C
（since each is to the same extent as each…the one an object of
aversion； the other an object of desire）。 Therefore both A and C
together； and B and D together； will be equally objects of desire or
aversion。 But since A and C are preferable to B and D； A cannot be
equally desirable with D； for then B along with D would be equally
desirable with A along with C。 But if D is preferable to A； then B
must be less an object of aversion than C： for the less is opposed
to the less。 But the greater good and lesser evil are preferable to
the lesser good and greater evil： the whole BD then is preferable to
the whole AC。 But ex hypothesi this is not so。 A then is preferable to
D； and C consequently is less an object of aversion than B。 If then
every lover in virtue of his love would prefer A； viz。 that the
beloved should be such as to grant a favour； and yet should not
grant it （for which C stands）； to the beloved's granting the favour
（represented by D） without being such as to grant it （represented by
B）； it is clear that A （being of such a nature） is preferable to
granting the favour。 To receive affection then is preferable in love
to sexual intercourse。 Love then is more dependent on friendship
than on intercourse。 And if it is most dependent on receiving
affection； then this is its end。 Intercourse then either is not an end
at all or is an end relative to the further end； the receiving of
affection。 And indeed the same is true of the other desires and arts。