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  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 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 Ari
stomenes 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', and B for things which are contrary to one

  another. Then A belongs to B, not in the sense that contraries are the

  fact of there being a single science of them, but in the sense that it

  is true to say of the contraries that there is a single science of

  them.

  It happens sometimes that the first term is stated of the middle,

  but the middle is not stated of the third term, e.g. if wisdom is

  knowledge, and wisdom is of the good, the conclusion is that there

  is knowledge of the good. The good then is not knowledge, though

  wisdom is knowledge. Sometimes the middle term is stated of the third,

  but the first is not stated of the middle, e.g. if there is a

  science of everything that has a quality, or is a contrary, and the

  good both is a contrary and has a quality, the conclusion is that

  there is a science of the good, but the good is not science, nor is

  that which has a quality or is a contrary, though the good is both

  of these. Sometimes neither the first term is stated of the middle,

  nor the middle of the third, while the first is sometimes stated of

  the third, and sometimes not: e.g. if there is a genus of that of

  which there is a science, and if there is a science of the good, we

  conclude that there is a genus of the good. But nothing is

  predicated of anything. And if that of which there is a science is a

  genus, and if there is a science of the good, we conclude that the

  good is a genus. The first term then is predicated of the extreme, but

  in the premisses one thing is not stated of another.

  The same holds good where the relation is negative. For 'that does

  not belong to this' does not always mean that 'this is not that',

  but sometimes that 'this is not of that' or 'for that', e.g. 'there is

  not a motion of a motion or a becoming of a becoming, but there is a

  becoming of pleasure: so pleasure is not a becoming.' Or again it

  may be said that there is a sign of laughter, but there is not a

  sign of a sign, consequently laughter is not a sign. This holds in the

  other cases too, in which the thesis is refuted because the genus is

  asserted in a particular way, in relation to the terms of the

  thesis. Again take the inference 'opportunity is not the right time:

  for opportunity belongs to God, but the right time does not, since

  nothing is useful to God'. We must take as terms opportunity-right

  time-God: but the premiss must be understood according to the case

  of the noun. For we state this universally without qualification, that

  the terms ought always to be stated in the nominative, e.g. man, good,

  contraries, not in oblique cases, e.g. of man, of a good, of

  contraries, but the premisses ought to be understood with reference to

  the cases of each term-either the dative, e.g. 'equal to
this', or the

  genitive, e.g. 'double of this', or the accusative, e.g. 'that which

  strikes or sees this', or the nominative, e.g. 'man is an animal',

  or in whatever other way the word falls in the premiss.

  37

  The expressions 'this belongs to that' and 'this holds true of that'

  must be understood in as many ways as there are different

  categories, and these categories must be taken either with or

  without qualification, and further as simple or compound: the same

  holds good of the corresponding negative expressions. We must consider

  these points and define them better.

  38

  A term which is repeated in the premisses ought to be joined to

  the first extreme, not to the middle. I mean for example that if a

  syllogism should be made proving that there is knowledge of justice,

  that it is good, the expression 'that it is good' (or 'qua good')

  should be joined to the first term. Let A stand for 'knowledge that it

  is good', B for good, C for justice. It is true to predicate A of B.

  For of the good there is knowledge that it is good. Also it is true to

  predicate B of C. For justice is identical with a good. In this way an

  analysis of the argument can be made. But if the expression 'that it

  is good' were added to B, the conclusion will not follow: for A will

  be true of B, but B will not be true of C. For to predicate of justice

  the term 'good that it is good' is false and not intelligible.

  Similarly if it should be proved that the healthy is an object of

  knowledge qua good, of goat-stag an object of knowledge qua not

  existing, or man perishable qua an object of sense: in every case in

  which an addition is made to the predicate, the addition must be

  joined to the extreme.

  The position of the terms is not the same when something is

  established without qualification and when it is qualified by some

  attribute or condition, e.g. when the good is proved to be an object

  of knowledge and when it is proved to be an object of knowledge that

  it is good. If it has been proved to be an object of knowledge without