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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。
23
It is clear then how the terms are related in conversion； and in
respect of being in a higher degree objects of aversion or of
desire。 We must now state that not only dialectical and
demonstrative syllogisms are formed by means of the aforesaid figures；
but also rhetorical syllogisms and in general any form of
persuasion； however it may be presented。 For every belief comes either
through syllogism or from induction。
Now induction； or rather the syllogism which springs out of
induction； consists in establishing syllogistically a relation between
one extreme and the middle by means of the other extreme； e。g。 if B is
the middle term between A and C； it consists in proving through C that
A belongs to B。 For this is the manner in which we make inductions。
For example let A stand for long…lived； B for bileless； and C for
the particular long…lived animals； e。g。 man； horse； mule。 A then
belongs to the whole of C： for whatever is bileless is long…lived。 But
B also （'not possessing bile'） belongs to all C。 If then C is
convertible with B； and the middle term is not wider in extension；
it is necessary that A should belong to B。 For it has already been
proved that if two things belong to the same thing； and the extreme is
convertible with one of them； then the other predicate will belong
to the predicate that is converted。 But we must apprehend C as made up
of all the particulars。 For induction proceeds through an
enumeration of all the cases。
Such is the syllogism which establishes the first and immediate
premiss： for where there is a middle term the syllogism proceeds
through the middle term； when there is no middle term； through
induction。 And in a way induction is opposed to syllogism： for the
latter proves the major term to belong to the thir