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possible to refute a statement by this method of division； nor to draw
a conclusion about an accident or property of a thing； nor about its
genus； nor in cases in which it is unknown whether it is thus or thus；
e。g。 whether the diagonal is incommensurate。 For if he assumes that
every length is either commensurate or incommensurate； and the
diagonal is a length； he has proved that the diagonal is either
incommensurate or commensurate。 But if he should assume that it is
incommensurate； he will have assumed what he ought to have proved。
He cannot then prove it： for this is his method； but proof is not
possible by this method。 Let A stand for 'incommensurate or
commensurate'； B for 'length'； C for 'diagonal'。 It is clear then that
this method of investigation is not suitable for every inquiry； nor is
it useful in those cases in which it is thought to be most suitable。
From what has been said it is clear from what elements
demonstrations are formed and in what manner； and to what points we
must look in each problem。
32
Our next business is to state how we can reduce syllogisms to the
aforementioned figures： for this part of the inquiry still remains。 If
we should investigate the production of the syllogisms and had the
power of discovering them； and further if we could resolve the
syllogisms produced into the aforementioned figures； our original
problem would be brought to a conclusion。 It will happen at the same
time that what has been already said will be confirmed and its truth
made clearer by what we are about to say。 For everything that is
true must in every respect agree with itself First then we must
attempt to select the two premisses of the syllogism （for it is easier
to divide into large parts than into small； and the composite parts
are larger than the elements out of which they are made）； next we must
inquire which are universal and which particular； and if both
premisses have not been stated； we must ourselves assume the one which
is missing。 For sometimes men put forward the universal premiss； but
do not posit the premiss which is contained in it； either in writing
or in discussion： or men put forward the premisses of the principal
syllogism； but omit those through which they are inferred； and
invite the concession of others to no purpose。 We must inquire then
whether anything unnecessary has been assumed； or anything necessary
has been omitted； and we must posit the one and take away the other；
until we have reached the two premisses： for unless we have these；
we cannot reduce arguments put forward in the way described。 In some
arguments it is easy to see what is wanting； but some escape us； and
appear to be syllogisms； because something necessary results from what
has been laid down； e。g。 if the assumptions were made that substance
is not annihilated by the annihilation of what is not substance； and
that if the elements out of which a thing is made are annihilated；
then that which is made out of them is destroyed： these propositions
being laid down； it is necessary that any part of substance is
substance； this has not however been drawn by syllogism from the
propositions assumed； but premisses are wanting。 Again if it is
necessary that animal should exist； if man does； and that substance
should exist； if animal does； it is necessary that substance should
exist if man does： but as yet the conclusion has not been drawn
syllogistically： for the premisses are not in the shape we required。
We are deceived in such cases because something necessary results from
what is assumed； since the syllogism also is necessary。 But that which
is necessary is wider than the syllogism： for every syllogism is
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