Various Works

by Aristotle

  qualification, we must put as middle term 'that which is', but if we

  add the qualification 'that it is good', the middle term must be 'that

  which is something'. Let A stand for 'knowledge that it is something',

  B stand for 'something', and C stand for 'good'. It is true to

  predicate A of B: for ex hypothesi there is a science of that which is

  something, that it is something. B too is true of C: for that which

  C represents is something. Consequently A is true of C: there will

  then be knowledge of the good, that it is good: for ex hypothesi the

  term 'something' indicates the thing's special nature. But if

  'being' were taken as middle and 'being' simply were joined to the

  extreme, not 'being something', we should not have had a syllogism

  proving that there is knowledge of the good, that it is good, but that

  it is; e.g. let A stand for knowledge that it is, B for being, C for

  good. Clearly then in syllogisms which are thus limited we must take

  the terms in the way stated.

  39

  We ought also to exchange terms which have the same value, word

  for word, and phrase for phrase, and word and phrase, and always

  take a word in preference to a phrase: for thus the setting out of the

  terms will be easier. For example if it makes no difference whether we

  say that the supposable is not the genus of the opinable or that the

  opinable is not identical with a particular kind of supposable (for

  what is meant is the same in both statements), it is better to take as

  the terms the supposable and the opinable in preference to the

  phrase suggested.

  40

  Since the expressions 'pleasure is good' and 'pleasure is the

  good' are not identical, we must not set out the terms in the same

  way; but if the syllogism is to prove that pleasure is the good, the

  term must be 'the good', but if the object is to prove that pleasure

  is good, the term will be 'good'. Similarly in all other cases.

  41

  It is not the same, either in fact or in speech, that A belongs to

  all of that to which B belongs, and that A belongs to all of that to

  all of which B belongs: for nothing prevents B from belonging to C,

  though not to all C: e.g. let B stand for beautiful, and C for

  white. If beauty belongs to something white, it is true to say that

  beauty belongs to that which is white; but not perhaps to everything

  that is white. If then A belongs to B, but not to everything of

  which B is predicated, then whether B belongs to all C or merely

  belongs to C, it is not necessary that A should belong, I do not say

  to all C, but even to C at all. But if A belongs to everything of

  which B is truly stated, it will follow that A can be said of all of

  that of all of which B is said. If however A is said of that of all of

  which B may be said, nothing prevents B belonging to C, and yet A

  not belonging to all C or to any C at all. If then we take three terms

  it is clear that the expression 'A is said of all of which B is

  said' means this, 'A is said of all the things of which B is said'.

  And if B is said of all of a third term, so also is A: but if B is not

  said of all of the third term, there is no necessity that A should

  be said of all of it.

  We must not suppose that something absurd results through setting

  out the terms: for we do not use the existence of this particular

  thing, but imitate the geometrician who says that 'this line a foot

  long' or 'this straight line' or 'this line without breadth' exists

  although it does not, but does not use the diagrams in the sense

  that he reasons from them. For in general, if two things are not

  related as whole to part and part to whole, the prover does not

  prove from them, and so no syllogism a is formed. We (I mean the

  learner) use the process of setting out terms like perception by

  sense, not as though it were impossible to demonstrate without these

  illustrative terms, as it is to demonstrate without the premisses of

  the syllogism.

  42

  We should not forget that in the same syllogism not all

  conclusions are reached through one figure, but one through one

  figure, another through another. Clearly then we must analyse

  arguments in accordance with this. Since not every problem is proved

  in every figure, but certain problems in each figure, it is clear from

  the conclusion in what figure the premisses should be sought.

  43

  In reference to those arguments aiming at a definition which have

  been directed to prove some part of the definition, we must take as

  a term the point to which the argument has been directed, not the

  whole definition: for so we shall be less likely to be disturbed by

  the length of the term: e.g. if a man proves that water is a drinkable

  liquid, we must take as terms drinkable and water.

  44

  Further we must not try to reduce hypothetical syllogisms; for

  with the given premisses it is not possible to reduce them. For they

  have not been proved by syllogism, but assented to by agreement. For

  instance if a man should suppose that unless there is one faculty of

  contraries, there cannot be one science, and should then argue that

  not every faculty is of contraries, e.g. of what is healthy and what

  is sickly: for the same thing will then be at the same time healthy

  and sickly. He has shown that there is not one faculty of all

  contraries, but he has not proved that there is not a science. And yet

  one must agree. But the agreement does not come from a syllogism,

  but from an hypothesis. This argument cannot be reduced: but the proof

  that there is not a single faculty can. The latter argument perhaps

  was a syllogism: but the former was an hypothesis.

  The same holds good of arguments which are brought to a conclusion

  per impossibile. These cannot be analysed either; but the reduction to

  what is impossible can be analysed since it is proved by syllogism,

  though the rest of the argument cannot, because the conclusion is

  reached from an hypothesis. But these differ from the previous

  arguments: for in the former a preliminary agreement must be reached

  if one is to accept the conclusion; e.g. an agreement that if there is

  proved to be one faculty of contraries, then contraries fall under the

  same science; whereas in the latter, even if no preliminary

  agreement has been made, men still accept the reasoning, because the

  falsity is patent, e.g. the falsity of what follows from the

  assumption that the diagonal is commensurate, viz. that then odd

  numbers are equal to evens.

  Many other arguments are brought to a conclusion by the help of an

  hypothesis; these we ought to consider and mark out clearly. We

  shall describe in the sequel their differences, and the various ways

  in which hypothetical arguments are formed: but at present this much

  must be clear, that it is not possible to resolve such arguments

  into the figures. And we have explained the reason.

  45

  Whatever problems are proved in more than one figure, if they have

  been established in one figure by syllogism, can be red
uced to another

  figure, e.g. a negative syllogism in the first figure can be reduced

  to the second, and a syllogism in the middle figure to the first,

  not all however but some only. The point will be clear in the

  sequel. If A belongs to no B, and B to all C, then A belongs to no

  C. Thus the first figure; but if the negative statement is

  converted, we shall have the middle figure. For B belongs to no A, and

  to all C. Similarly if the syllogism is not universal but

  particular, e.g. if A belongs to no B, and B to some C. Convert the

  negative statement and you will have the middle figure.

  The universal syllogisms in the second figure can be reduced to

  the first, but only one of the two particular syllogisms. Let A belong

  to no B and to all C. Convert the negative statement, and you will

  have the first figure. For B will belong to no A and A to all C. But

  if the affirmative statement concerns B, and the negative C, C must be

  made first term. For C belongs to no A, and A to all B: therefore C

  belongs to no B. B then belongs to no C: for the negative statement is

  convertible.

  But if the syllogism is particular, whenever the negative

  statement concerns the major extreme, reduction to the first figure

  will be possible, e.g. if A belongs to no B and to some C: convert the

  negative statement and you will have the first figure. For B will

  belong to no A and A to some C. But when the affirmative statement

  concerns the major extreme, no resolution will be possible, e.g. if

  A belongs to all B, but not to all C: for the statement AB does not

  admit of conversion, nor would there be a syllogism if it did.

  Again syllogisms in the third figure cannot all be resolved into the

  first, though all syllogisms in the first figure can be resolved

  into the third. Let A belong to all B and B to some C. Since the

  particular affirmative is convertible, C will belong to some B: but

  A belonged to all B: so that the third figure is formed. Similarly

  if the syllogism is negative: for the particular affirmative is

  convertible: therefore A will belong to no B, and to some C.

  Of the syllogisms in the last figure one only cannot be resolved

  into the first, viz. when the negative statement is not universal: all

  the rest can be resolved. Let A and B be affirmed of all C: then C can

  be converted partially with either A or B: C then belongs to some B.

  Consequently we shall get the first figure, if A belongs to all C, and

  C to some of the Bs. If A belongs to all C and B to some C, the

  argument is the same: for B is convertible in reference to C. But if B

  belongs to all C and A to some C, the first term must be B: for B

  belongs to all C, and C to some A, therefore B belongs to some A.

  But since the particular statement is convertible, A will belong to

  some B. If the syllogism is negative, when the terms are universal

  we must take them in a similar way. Let B belong to all C, and A to no

  C: then C will belong to some B, and A to no C; and so C will be

  middle term. Similarly if the negative statement is universal, the

  affirmative particular: for A will belong to no C, and C to some of

  the Bs. But if the negative statement is particular, no resolution

  will be possible, e.g. if B belongs to all C, and A not belong to some

  C: convert the statement BC and both premisses will be particular.

  It is clear that in order to resolve the figures into one another

  the premiss which concerns the minor extreme must be converted in both

  the figures: for when this premiss is altered, the transition to the

  other figure is made.

  One of the syllogisms in the middle figure can, the other cannot, be

  resolved into the third figure. Whenever the universal statement is

  negative, resolution is possible. For if A belongs to no B and to some

  C, both B and C alike are convertible in relation to A, so that B

  belongs to no A and C to some A. A therefore is middle term. But

  when A belongs to all B, and not to some C, resolution will not be

  possible: for neither of the premisses is universal after conversion.

  Syllogisms in the third figure can be resolved into the middle

  figure, whenever the negative statement is universal, e.g. if A

  belongs to no C, and B to some or all C. For C then will belong to

  no A and to some B. But if the negative statement is particular, no

  resolution will be possible: for the particular negative does not

  admit of conversion.

  It is clear then that the same syllogisms cannot be resolved in

  these figures which could not be resolved into the first figure, and

  that when syllogisms are reduced to the first figure these alone are

  confirmed by reduction to what is impossible.

  It is clear from what we have said how we ought to reduce

  syllogisms, and that the figures may be resolved into one another.

  46

  In establishing or refuting, it makes some difference whether we

  suppose the expressions 'not to be this' and 'to be not-this' are

  identical or different in meaning, e.g. 'not to be white' and 'to be

  not-white'. For they do not mean the same thing, nor is 'to be

  not-white' the negation of 'to be white', but 'not to be white'. The

  reason for this is as follows. The relation of 'he can walk' to 'he

  can not-walk' is similar to the relation of 'it is white' to 'it is

  not-white'; so is that of 'he knows what is good' to 'he knows what is

  not-good'. For there is no difference between the expressions 'he

  knows what is good' and 'he is knowing what is good', or 'he can walk'

  and 'he is able to walk': therefore there is no difference between

  their contraries 'he cannot walk'-'he is not able to walk'. If then

  'he is not able to walk' means the same as 'he is able not to walk',

  capacity to walk and incapacity to walk will belong at the same time

  to the same person (for the same man can both walk and not-walk, and

  is possessed of knowledge of what is good and of what is not-good),

  but an affirmation and a denial which are opposed to one another do

  not belong at the same time to the same thing. As then 'not to know

  what is good' is not the same as 'to know what is not good', so 'to be

  not-good' is not the same as 'not to be good'. For when two pairs

  correspond, if the one pair are different from one another, the

  other pair also must be different. Nor is 'to be not-equal' the same

  as 'not to be equal': for there is something underlying the one,

  viz. that which is not-equal, and this is the unequal, but there is

  nothing underlying the other. Wherefore not everything is either equal

  or unequal, but everything is equal or is not equal. Further the

  expressions 'it is a not-white log' and 'it is not a white log' do not

  imply one another's truth. For if 'it is a not-white log', it must

  be a log: but that which is not a white log need not be a log at

  all. Therefore it is clear that 'it is not-good' is not the denial

  of 'it is good'. If then every single statement may truly be said to

  be either an affirmation or a negation, if it is not a negation

  clearly it must in a sense be an affirmation. But every affirmation
r />   has a corresponding negation. The negation then of 'it is not-good' is

  'it is not not-good'. The relation of these statements to one

  another is as follows. Let A stand for 'to be good', B for 'not to

  be good', let C stand for 'to be not-good' and be placed under B,

  and let D stand for not to be not-good' and be placed under A. Then

  either A or B will belong to everything, but they will never belong to

  the same thing; and either C or D will belong to everything, but

  they will never belong to the same thing. And B must belong to

  everything to which C belongs. For if it is true to say 'it is a

  not-white', it is true also to say 'it is not white': for it is

  impossible that a thing should simultaneously be white and be

  not-white, or be a not-white log and be a white log; consequently if

  the affirmation does not belong, the denial must belong. But C does

  not always belong to B: for what is not a log at all, cannot be a

  not-white log either. On the other hand D belongs to everything to

  which A belongs. For either C or D belongs to everything to which A

  belongs. But since a thing cannot be simultaneously not-white and

  white, D must belong to everything to which A belongs. For of that

  which is white it is true to say that it is not not-white. But A is

  not true of all D. For of that which is not a log at all it is not

  true to say A, viz. that it is a white log. Consequently D is true,

  but A is not true, i.e. that it is a white log. It is clear also

  that A and C cannot together belong to the same thing, and that B

  and D may possibly belong to the same thing.

  Privative terms are similarly related positive ter terms respect

  of this arrangement. Let A stand for 'equal', B for 'not equal', C for

  'unequal', D for 'not unequal'.

  In many things also, to some of which something belongs which does

  not belong to others, the negation may be true in a similar way,

  viz. that all are not white or that each is not white, while that each