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necessary； but not everything which is necessary is a syllogism。
Consequently； though something results when certain propositions are
assumed； we must not try to reduce it directly； but must first state
the two premisses； then divide them into their terms。 We must take
that term as middle which is stated in both the remisses： for it is
necessary that the middle should be found in both premisses in all the
figures。
If then the middle term is a predicate and a subject of predication；
or if it is a predicate； and something else is denied of it； we
shall have the first figure： if it both is a predicate and is denied
of something； the middle figure： if other things are predicated of it；
or one is denied； the other predicated； the last figure。 For it was
thus that we found the middle term placed in each figure。 It is placed
similarly too if the premisses are not universal： for the middle
term is determined in the same way。 Clearly then； if the same term
is not stated more than once in the course of an argument； a syllogism
cannot be made： for a middle term has not been taken。 Since we know
what sort of thesis is established in each figure； and in which the
universal； in what sort the particular is described； clearly we must
not look for all the figures； but for that which is appropriate to the
thesis in hand。 If the thesis is established in more figures than one；
we shall recognize the figure by the position of the middle term。
33
Men are frequently deceived about syllogisms because the inference
is necessary； as has been said above； sometimes they are deceived by
the similarity in the positing of the terms； and this ought not to
escape our notice。 E。g。 if A is stated of B； and B of C： it would seem
that a syllogism is possible since the terms stand thus： but nothing
necessary results； nor does a syllogism。 Let A represent the term
'being eternal'； B 'Aristomenes as an object of thought'； C
'Aristomenes'。 It is true then that A belongs to B。 For Aristomenes as
an object of thought is eternal。 But B also belongs to C： for
Aristomenes is Aristomenes as an object of thought。 But A does not
belong to C： for Aristomenes is perishable。 For no syllogism was
made although the terms stood thus： that required that the premiss
AB should be stated universally。 But this is false； that every
Aristomenes who is an object of thought is eternal； since
Aristomenes is perishable。 Again let C stand for 'Miccalus'； B for
'musical Miccalus'； A for 'perishing to…morrow'。 It is true to
predicate B of C： for Miccalus is musical Miccalus。 Also A can be
predicated of B： for musical Miccalus might perish to…morrow。 But to
state A of C is false at any rate。 This argument then is identical
with the former； for it is not true universally that musical
Miccalus perishes to…morrow： but unless this is assumed； no
syllogism （as we have shown） is possible。
This deception then arises through ignoring a small distinction。 For
if we accept the conclusion as though it made no difference whether we
said 'This belong to that' or 'This belongs to all of that'。
34
Men will frequently fall into fallacies through not setting out
the terms of the premiss well； e。g。 suppose A to be health； B disease；
C man。 It is true to say that A cannot belong to any B （for health
belongs to no disease） and again that B belongs to every C （for
every man is capable of disease）。 It would seem to follow that
health cannot belong to any man。 The reason for this is that the terms
are not set out well in the statement； since if the things which are
in the conditions are substituted； no syllogism can be made； e。g。 if
'healthy' is substituted for 'health' and 'diseased' for 'disease'。
For it is not true to say that being healthy cannot belong to one
who is diseased。 But unless this is assumed no conclusion results；
save in respect of possibility： but such a conclusion is not
impossible： for it is possible that health should belong to no man。
Again the fallacy may occur in a similar way in the middle figure： 'it
is not possible that health should belong to any disease； but it is
possible that health should belong to every man； consequently it is
not possible that disease should belong to any man'。 In the third
figure the fallacy results in reference to possibility。 For health and
diseae and knowledge and ignorance； and in general contraries； may
possibly belong to the same thing； but cannot belong to one another。
This is not in agreement with what was said before： for we stated that
when several things could belong to the same thing； they could
belong to one another。
It is evident then that in all these cases the fallacy arises from
the setting out of the terms： for if the things that are in the
conditions are substituted； no fallacy arises。 It is clear then that
in such premisses what possesses the condition ought always to be
substituted for the condition and taken as the term。
35
We must not always seek to set out the terms a single word： for we
shall often have complexes of words to which a single name is not
given。 Hence it is difficult to reduce syllogisms with such terms。
Sometimes too fallacies will result from such a search； e。g。 the
belief that syllogism can establish that which has no mean。 Let A
stand for two right angles； B for triangle； C for isosceles
triangle。 A then belongs to C because of B： but A belongs to B without
the mediation of another term： for the triangle in virtue of its own
nature contains two right angles； consequently there will be no middle
term for the proposition AB； although it is demonstrable。 For it is
clear that the middle must not always be assumed to be an individual
thing； but sometimes a complex of words； as happens in the case
mentioned。
36
That the first term belongs to the middle； and the middle to the
extreme； must not be understood in the sense that they can always be
predicated of one another or that the first term will be predicated of
the middle in the same way as the middle is predicated of the last
term。 The same holds if the premisses are negative。 But we must
suppose the verb 'to belong' to have as many meanings as the senses in
which the verb 'to be' is used； and in which the assertion that a
thing 'is' may be said to be true。 Take for example the statement that
there is a single science of contraries。 Let A stand for 'there
being a single science'； an