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no E。 Similarly with the rest。 In all cases it is necessary to find
some common term other than the subjects of inquiry； to which the
syllogism establishing the false conclusion may relate； so that if
this premiss is converted； and the other remains as it is； the
syllogism will be ostensive by means of the same terms。 For the
ostensive syllogism differs from the reductio ad impossibile in
this： in the ostensive syllogism both remisses are laid down in
accordance with the truth； in the reductio ad impossibile one of the
premisses is assumed falsely。
These points will be made clearer by the sequel； when we discuss the
reduction to impossibility： at present this much must be clear； that
we must look to terms of the kinds mentioned whether we wish to use an
ostensive syllogism or a reduction to impossibility。 In the other
hypothetical syllogisms； I mean those which proceed by substitution；
or by positing a certain quality； the inquiry will be directed to
the terms of the problem to be proved…not the terms of the original
problem； but the new terms introduced； and the method of the inquiry
will be the same as before。 But we must consider and determine in
how many ways hypothetical syllogisms are possible。
Each of the problems then can be proved in the manner described； but
it is possible to establish some of them syllogistically in another
way； e。g。 universal problems by the inquiry which leads up to a
particular conclusion； with the addition of an hypothesis。 For if
the Cs and the Gs should be identical； but E should be assumed to
belong to the Gs only； then A would belong to every E： and again if
the Ds and the Gs should be identical； but E should be predicated of
the Gs only； it follows that A will belong to none of the Es。
Clearly then we must consider the matter in this way also。 The
method is the same whether the relation is necessary or possible。
For the inquiry will be the same； and the syllogism will proceed
through terms arranged in the same order whether a possible or a
pure proposition is proved。 We must find in the case of possible
relations； as well as terms that belong； terms which can belong though
they actually do not： for we have proved that the syllogism which
establishes a possible relation proceeds through these terms as
well。 Similarly also with the other modes of predication。
It is clear then from what has been said not only that all
syllogisms can be formed in this way； but also that they cannot be
formed in any other。 For every syllogism has been proved to be
formed through one of the aforementioned figures； and these cannot
be composed through other terms than the consequents and antecedents
of the terms in question： for from these we obtain the premisses and
find the middle term。 Consequently a syllogism cannot be formed by
means of other terms。
30
The method is the same in all cases； in philosophy； in any art or
study。 We must look for the attributes and the subjects of both our
terms； and we must supply ourselves with as many of these as possible；
and consider them by means of the three terms； refuting statements
in one way； confirming them in another； in the pursuit of truth
starting from premisses in which the arrangement of the terms is in
accordance with truth； while if we look for dialectical syllogisms
we must start from probable premisses。 The principles of syllogisms
have been stated in general terms； both how they are characterized and
how we must hunt for them； so as not to look to everything that is
said about the terms of the problem or to the same points whether we
are confirming or refuting； or again whether we are confirming of
all or of some； and whether we are refuting of all or some。 we must
look to fewer points and they must be definite。 We have also stated
how we must select with reference to everything that is； e。g。 about
good or knowledge。 But in each science the principles which are
peculiar are the most numerous。 Consequently it is the business of
experience to give the principles which belong to each subject。 I mean
for example that astronomical experience supplies the principles of
astronomical science： for once the phenomena were adequately
apprehended； the demonstrations of astronomy were discovered。
Similarly with any other art or science。 Consequently； if the
attributes of the thing are apprehended； our business will then be
to exhibit readily the demonstrations。 For if none of the true
attributes of things had been omitted in the historical survey； we
should be able to discover the proof and demonstrate everything
which admitted of proof； and to make that clear； whose nature does not
admit of proof。
In general then we have explained fairly well how we must select
premisses： we have discussed the matter accurately in the treatise
concerning dialectic。
31
It is easy to see that division into classes is a small part of
the method we have described： for division is； so to speak； a weak
syllogism； for what it ought to prove； it begs； and it always
establishes something more general than the attribute in question。
First； this very point had escaped all those who used the method of
division； and they attempted to persuade men that it was possible to
make a demonstration of substance and essence。 Consequently they did
not understand what it is possible to prove syllogistically by
division； nor did they understand that it was possible to prove
syllogistically in the manner we have described。 In demonstrations；
when there is a need to prove a positive statement； the middle term
through which the syllogism is formed must always be inferior to and
not comprehend the first of the extremes。 But division has a
contrary intention： for it takes the universal as middle。 Let animal
be the term signified by A； mortal by B； and immortal by C； and let
man； whose definition is to be got； be signified by D。 The man who
divides assumes that every animal is either mortal or immortal： i。e。
whatever is A is all either B or C。 Again； always dividing； he lays it
down that man is an animal； so he assumes A of D as belonging to it。
Now the true conclusion is that every D is either B or C； consequently
man must be either mortal or immortal； but it is not necessary that
man should be a mortal animal…this is begged： and this is what ought
to have been proved syllogistically。 And again； taking A as mortal
animal； B as footed； C as footless； and D as man； he assumes in the
same way that A inheres either in B or in C （for every mortal animal
is either footed or footless）； and he assumes A of D （for he assumed
man； as we saw； to be a mortal animal）； consequently it is necessary
that man should be either a footed or a footless animal； but it is not
necessary that man should be footed： this he assumes： and it is just
this again which he ought to have demonstrated。 Always dividing then
in this way it turns out that these logicians assume as middle the
universal term； and as extremes that which ought to have been the
subject of demonstration and the differentiae。 In conclusion； they
do not make it clear； and show it to be necessary； that this is man or
whatever the subject of inquiry may be： for they pursue the other
method altogether； never even suspecting the presence of the rich
supply of evidence which might be used。 It is clear that it is neither
possible to refute a statement by this method of division； nor to draw
a conc