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  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

  primary and most universal, e.g. in reference to E we must look to

  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