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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 third term by means of
the middle； the former proves the major to belong to the middle by
means of the third。 In the order of nature； syllogism through the
middle term is prior and better known； but syllogism through induction
is clearer to us。
24
We have an 'example' when the major term is proved to belong to
the middle by means of a term which resembles the third。 It ought to
be known both that the middle belongs to the third term； and that
the first belongs to that which resembles the third。 For example let A
be evil； B making war against neighbours； C Athenians against Thebans；
D Thebans against Phocians。 If then we wish to prove that to fight
with the Thebans is an evil； we must assume that to fight against
neighbours is an evil。 Evidence of this is obtained from similar
cases； e。g。 that the war against the Phocians was an evil to the
Thebans。 Since then to fight against neighbours is an evil； and to
fight against the Thebans is to fight against neighbours； it is
clear that to fight against the Thebans is an evil。 Now it is clear
that B belongs to C and to D （for both are cases of making war upon
one's neighbours） and that A belongs to D （for the war against the
Phocians did not turn out well for the Thebans）： but that A belongs to
B will be proved through D。 Similarly if the belief in the relation of
the middle term to the extreme should be produced by several similar
cases。 Clearly then to argue by example is neither like reasoning from
part to whole； nor like reasoning from whole to part； but rather
reasoning from part to part； when both particulars are subordinate
to the same term； and one of them is known。 It differs from induction；
because induction starting from all the particular cases proves （as we
saw） that the major term belongs to the middle； and does not apply the
syllogistic conclusion to the minor term； whereas argument by
example does make this application and does not draw its proof from
all the particular cases。
25
By reduction we mean an argument in which the first term clearly
belongs to the middle； but the relation of the middle to the last term
is uncertain though equally or more probable than the conclusion； or
again an argument in which the terms intermediate between the last
term and the middle are few。 For in any of these cases it turns out
that we approach more nearly to knowledge。 For example let A stand for
what can be taught； B for knowledge； C for justice。 Now it is clear
that knowledge can be taught： but it is uncertain whether virtue is
knowledge。 If now the statement BC is equally or more probable than
AC； we have a reduction： for we are nearer to knowledge； since we have
taken a new term； being so far without knowledge that A belongs to
C。 Or again suppose that the terms intermediate between B and C are
few： for thus too we are nearer knowledge。 For example let D stand for
squaring； E for rectilinear figure； F for circle。 If there were only
one term intermediate between E and F （viz。 that the circle is made
equal to a rectilinear figure by the help of lunules）； we should be
near to knowledge。 But when BC is not more probable than AC； and the
intermediate terms are not few； I do not call this reduction： nor
again when the statement BC is immediate： for such a statement is
knowledge。
26
An objection is a premiss contrary to a premiss。 It differs from a
premiss； because it may be particular； but a premiss either cannot
be particular at all or not in universal syllogisms。 An objection is
brought in two ways and through two figures； in two ways because every
objection is either universal or particular； by two figures because
objections are brought in opposition to the premiss； and opposites can
be proved only in the first and third figures。 If a man maintains a
universal affirmative； we reply with a universal or a particular
negative； the former is proved from the first figure； the latter
from the third。 For example let stand for there being a single
science； B for contraries。 If a man premises that contraries are
subjects of a single science； the objection may be either that
opposites are never subjects of a single science； and contraries are
opposites； so that we get the first figure； or that the knowable and
the unknowable are not subjects of a single science： this proof is
in the third figure： for it is true of C （the knowable and the
unknowable） that they are contraries； and it is false that they are
the subjects of a single science。
Similarly if the premiss objected to is negative。 For if a man
maintains that contraries are not subjects of a single science； we
reply either that all opposites or that certain contraries； e。g。
what is healthy and what is sickly； are subjects of the same
science： the former argument issues from the first； the latter from
the third figure。
In general if a man urges a universal objection he must frame his
contradiction with reference to the universal of the terms taken by
his opponent； e。g。 if a man maintains that contraries are not subjects
of the same science； his opponent must reply that there is a single
science of all opposites。 Thus we must have the first figure： for
the term which embraces the original subject becomes the middle term。
If the objection is particular； the objector must frame his
contradiction with reference to a term relatively to which the subject
of his opponent's premiss is universal； e。g。 he will point out that
the knowable and the unknowable are not subjects of the same
science： 'contraries' is universal relatively to these。 And we have
the third figure： for the particular term assumed is middle； e。g。
the knowable and the unknowable。 Premisses from which it is possible
to draw the contrary conclusion are what we start from when we try
to make objections。 Consequently we bring objections in these
figures only： for in them only are opposite syllogisms possible； since
the second figure cannot produce an affirmative conclusion。
Besides； an objection in the middle figure would require a fuller
argument； e。g。 if it should not be granted that A belongs to B；
because C does not follow B。 This can be made clear only by other
premisses。 But an objection ought not to turn off into other things；
but have its new premiss quite clear immediately。 For this reason also
this is the only figure from which proof by signs cannot be obtained。
We must consider