those things which the inferior term follows, e.g. take as subjects of
the predicate 'animal' what are really subjects of the predicate
'man'. It is necessary indeed, if animal follows man, that it should
follow all these also. But these belong more properly to the choice of
what concerns man. One must apprehend also normal consequents and
normal antecedents-, for propositions which obtain normally are
established syllogistically from premisses which obtain normally, some
if not all of them having this character of normality. For the
conclusion of each syllogism resembles its principles. We must not
however choose attributes which are consequent upon all the terms: for
no syllogism can be made out of such premisses. The reason why this is
so will be clear in the sequel.
28
If men wish to establish something about some whole, they must
look to the subjects of that which is being established (the
subjects of which it happens to be asserted), and the attributes which
follow that of which it is to be predicated. For if any of these
subjects is the same as any of these attributes, the attribute
originally in question must belong to the subject originally in
question. But if the purpose is to establish not a universal but a
particular proposition, they must look for the terms of which the
terms in question are predicable: for if any of these are identical,
the attribute in question must belong to some of the subject in
question. Whenever the one term has to belong to none of the other,
one must look to the consequents of the subject, and to those
attributes which cannot possibly be present in the predicate in
question: or conversely to the attributes which cannot possibly be
present in the subject, and to the consequents of the predicate. If
any members of these groups are identical, one of the terms in
question cannot possibly belong to any of the other. For sometimes a
syllogism in the first figure results, sometimes a syllogism in the
second. But if the object is to establish a particular negative
proposition, we must find antecedents of the subject in question and
attributes which cannot possibly belong to the predicate in
question. If any members of these two groups are identical, it follows
that one of the terms in question does not belong to some of the
other. Perhaps each of these statements will become clearer in the
following way. Suppose the consequents of A are designated by B, the
antecedents of A by C, attributes which cannot possibly belong to A by
D. Suppose again that the attributes of E are designated by F, the
antecedents of E by G, and attributes which cannot belong to E by H.
If then one of the Cs should be identical with one of the Fs, A must
belong to all E: for F belongs to all E, and A to all C,
consequently A belongs to all E. If C and G are identical, A must
belong to some of the Es: for A follows C, and E follows all G. If F
and D are identical, A will belong to none of the Es by a
prosyllogism: for since the negative proposition is convertible, and F
is identical with D, A will belong to none of the Fs, but F belongs to
all E. Again, if B and H are identical, A will belong to none of the
Es: for B will belong to all A, but to no E: for it was assumed to
be identical with H, and H belonged to none of the Es. If D and G
are identical, A will not belong to some of the Es: for it will not
belong to G, because it does not belong to D: but G falls under E:
consequently A will not belong to some of the Es. If B is identical
with G, there will be a converted syllogism: for E will belong to
all A since B belongs to A and E to B (for B was found to be identical
with G): but that A should belong to all E is not necessary, but it
must belong to some E because it is possible to convert the
universal statement into a particular.
It is clear then that in every proposition which requires proof we
must look to the aforesaid relations of the subject and predicate in
question: for all syllogisms proceed through these. But if we are
seeking consequents and antecedents we must look for those which are
KF rather than to F alone, and in reference to A we must look to KC
rather than to C alone. For if A belongs to KF, it belongs both to F
and to E: but if it does not follow KF, it may yet follow F. Similarly
we must consider the antecedents of A itself: for if a term follows
the primary antecedents, it will follow those also which are
subordinate, but if it does not follow the former, it may yet follow
the latter.
It is clear too that the inquiry proceeds through the three terms
and the two premisses, and that all the syllogisms proceed through the
aforesaid figures. For it is proved that A belongs to all E,
whenever an identical term is found among the Cs and Fs. This will
be the middle term; A and E will be the extremes. So the first
figure is formed. And A will belong to some E, whenever C and G are
apprehended to be the same. This is the last figure: for G becomes the
middle term. And A will belong to no E, when D and F are identical.
Thus we have both the first figure and the middle figure; the first,
because A belongs to no F, since the negative statement is
convertible, and F belongs to all E: the middle figure because D
belongs to no A, and to all E. And A will not belong to some E,
whenever D and G are identical. This is the last figure: for A will
belong to no G, and E will belong to all G. Clearly then all
syllogisms proceed through the aforesaid figures, and we must not
select consequents of all the terms, because no syllogism is
produced from them. For (as we saw) it is not possible at all to
establish a proposition from consequents, and it is not possible to
refute by means of a consequent of both the terms in question: for the
middle term must belong to the one, and not belong to the other.
It is clear too that other methods of inquiry by selection of middle
terms are useless to produce a syllogism, e.g. if the consequents of
the terms in question are identical, or if the antecedents of A are
identical with those attributes which cannot possibly belong to E,
or if those attributes are identical which cannot belong to either
term: for no syllogism is produced by means of these. For if the
consequents are identical, e.g. B and F, we have the middle figure
with both premisses affirmative: if the antecedents of A are identical
with attributes which cannot belong to E, e.g. C with H, we have the
first figure with its minor premiss negative. If attributes which
cannot belong to either term are identical, e.g. C and H, both
premisses are negative, either in the first or in the middle figure.
But no syllogism is possible in this way.
It is evident too that we must find out which terms in this
inquiry are identical, not which are different or contrary, first
because the object of our investigation is the middle term, and the
middle term must be
not diverse but identical. Secondly, wherever it
happens that a syllogism results from taking contraries or terms which
cannot belong to the same thing, all arguments can be reduced to the
aforesaid moods, e.g. if B and F are contraries or cannot belong to
the same thing. For if these are taken, a syllogism will be formed
to prove that A belongs to none of the Es, not however from the
premisses taken but in the aforesaid mood. For B will belong to all
A and to no E. Consequently B must be identical with one of the Hs.
Again, if B and G cannot belong to the same thing, it follows that A
will not belong to some of the Es: for then too we shall have the
middle figure: for B will belong to all A and to no G. Consequently
B must be identical with some of the Hs. For the fact that B and G
cannot belong to the same thing differs in no way from the fact that B
is identical with some of the Hs: for that includes everything which
cannot belong to E.
It is clear then that from the inquiries taken by themselves no
syllogism results; but if B and F are contraries B must be identical
with one of the Hs, and the syllogism results through these terms.
It turns out then that those who inquire in this manner are looking
gratuitously for some other way than the necessary way because they
have failed to observe the identity of the Bs with the Hs.
29
Syllogisms which lead to impossible conclusions are similar to
ostensive syllogisms; they also are formed by means of the consequents
and antecedents of the terms in question. In both cases the same
inquiry is involved. For what is proved ostensively may also be
concluded syllogistically per impossibile by means of the same
terms; and what is proved per impossibile may also be proved
ostensively, e.g. that A belongs to none of the Es. For suppose A to
belong to some E: then since B belongs to all A and A to some of the
Es, B will belong to some of the Es: but it was assumed that it
belongs to none. Again we may prove that A belongs to some E: for if A
belonged to none of the Es, and E belongs to all G, A will belong to
none of the Gs: but it was assumed to belong to all. Similarly with
the other propositions requiring proof. The proof per impossibile will
always and in all cases be from the consequents and antecedents of the
terms in question. Whatever the problem the same inquiry is
necessary whether one wishes to use an ostensive syllogism or a
reduction to impossibility. For both the demonstrations start from the
same terms, e.g. suppose it has been proved that A belongs to no E,
because it turns out that otherwise B belongs to some of the Es and
this is impossible-if now it is assumed that B belongs to no E and
to all A, it is clear that A will belong to no E. Again if it has been
proved by an ostensive syllogism that A belongs to no E, assume that A
belongs to some E and it will be proved per impossibile to belong to
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 examp
le 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