On Interpretation

        A. Affirmation        B. Denial

               Man is just       Man is not just

                            \   /

                              X

                            /   \

             D. Denial             C. Affirmation

           Man is not not-just     Man is not-just



Here 'is' and 'is not' are added either to 'just' or to 'not-just'.

This then is the proper scheme for these propositions, as has been

said in the Analytics. The same rule holds good, if the subject is

distributed. Thus we have the table:



         A'. Affirmation               B'. Denial

        Every man is just           Not every man is just

                             \   /

                               X

         D'. Denial          /   \     C'. Affirmation

   Not every man is not-just        Every man is not-just

Yet here it is not possible, in the same way as in the former case,

that the propositions joined in the table by a diagonal line should

both be true; though under certain circumstances this is the case.

  We have thus set out two pairs of opposite propositions; there are

moreover two other pairs, if a term be conjoined with 'not-man', the

latter forming a kind of subject. Thus:



              A."                            B."

        Not-man is just               Not-man is not just

                               \   /

-                                X

              D."              /   \         C."

        Not-man is not not-just       Not-man is not-just



  This is an exhaustive enumeration of all the pairs of opposite

propositions that can possibly be framed. This last group should

remain distinct from those which preceded it, since it employs as

its subject the expression 'not-man'.

  When the verb 'is' does not fit the structure of the sentence (for

instance, when the verbs 'walks', 'enjoys health' are used), that

scheme applies, which applied when the word 'is' was added.

  Thus we have the propositions: 'every man enjoys health', 'every man

does-not-enjoy-health', 'all that is not-man enjoys health', 'all that

is not-man does-not-enjoy-health'. We must not in these propositions

use the expression 'not every man'. The negative must be attached to

the word 'man', for the word 'every' does not give to the subject a

universal significance, but implies that, as a subject, it is

distributed. This is plain from the following pairs: 'man enjoys

health', 'man does not enjoy health'; 'not-man enjoys health', 'not

man does not enjoy health'. These propositions differ from the

former in being indefinite and not universal in character. Thus the

adjectives 'every' and no additional significance except that the

subject, whether in a positive or in a negative sentence, is

distributed. The rest of the sentence, therefore, will in each case be

the same.

  Since the contrary of the proposition 'every animal is just' is

'no animal is just', it is plain that these two propositions will

never both be true at the same time or with reference to the same

subject. Sometimes, however, the contradictories of these contraries

will both be true, as in the instance before us: the propositions 'not

every animal is just' and 'some animals are just' are both true.

  Further, the proposition 'no man is just' follows from the

proposition 'every man is not just' and the proposition 'not every man

is not just', which is the opposite of 'every man is not-just',

follows from the proposition 'some men are just'; for if this be true,

there must be some just men.

  It is evident, also, that when the subject is individual, if a

question is asked and the negative answer is the true one, a certain

positive proposition is also true. Thus, if the question were asked

Socrates wise?' and the negative answer were the true one, the

positive inference 'Then Socrates is unwise' is correct. But no such

inference is correct in the case of universals, but rather a

negative proposition. For instance, if to the question 'Is every man

wise?' the answer is 'no', the inference 'Then every man is unwise' is

false. But under these circumstances the inference 'Not every man is

wise' is correct. This last is the contradictory, the former the

contrary. Negative expressions, which consist of an indefinite noun or

predicate, such as 'not-man' or 'not-just', may seem to be denials

containing neither noun nor verb in the proper sense of the words. But

they are not. For a denial must always be either true or false, and he

that uses the expression 'not man', if nothing more be added, is not

nearer but rather further from making a true or a false statement than

he who uses the expression 'man'.

  The propositions 'everything that is not man is just', and the

contradictory of this, are not equivalent to any of the other

propositions; on the other hand, the proposition 'everything that is

not man is not just' is equivalent to the proposition 'nothing that is

not man is just'.

  The conversion of the position of subject and predicate in a

sentence involves no difference in its meaning. Thus we say 'man is

white' and 'white is man'. If these were not equivalent, there would

be more than one contradictory to the same proposition, whereas it has

been demonstrated' that each proposition has one proper

contradictory and one only. For of the proposition 'man is white'

the appropriate contradictory is 'man is not white', and of the

proposition 'white is man', if its meaning be different, the

contradictory will either be 'white is not not-man' or 'white is not

man'. Now the former of these is the contradictory of the

proposition 'white is not-man', and the latter of these is the

contradictory of the proposition 'man is white'; thus there will be

two contradictories to one proposition.

  It is evident, therefore, that the inversion of the relative

position of subject and predicate does not affect the sense of

affirmations and denials.

                                11



  There is no unity about an affirmation or denial which, either

positively or negatively, predicates one thing of many subjects, or

many things of the same subject, unless that which is indicated by the

many is really some one thing. do not apply this word 'one' to those

things which, though they have a single recognized name, yet do not

combine to form a unity. Thus, man may be an animal, and biped, and

domesticated, but these three predicates combine to form a unity. On

the other hand, the predicates 'white', 'man', and 'walking' do not

thus combine. Neither, therefore, if these three form the subject of

an affirmation, nor if they form its predicate, is there any unity

about that affirmation. In both cases the unity is linguistic, but not

real.

  If therefore the dialectical question is a request for an answer,

i.e. either for the admission of a premiss or for the admission of one

of two contradictories-and the premiss is itself always one of two

contradictories-the answer to such a question as contains the above

predicates cannot be a single proposition. For as I have explained

in the Topics, question is not a single one, even if the answer

asked for is true.

  At the same time it is plain that a question of the form 'what is

it?' is not a dialectical question, for a dialectical questioner

must by the form of his question give his opponent the chance of

announcing one of two alternatives, whichever he wishes. He must

therefore put the question into a more definite form, and inquire,

e.g.. whether man has such and such a characteristic or not.

  Some combinations of predicates are such that the separate

predicates unite to form a single predicate. Let us consider under

what conditions this is and is not possible. We may either state in

two separate propositions that man is an animal and that man is a

biped, or we may combine the two, and state that man is an animal with

two feet. Similarly we may use 'man' and 'white' as separate

predicates, or unite them into one. Yet if a man is a shoemaker and is

also good, we cannot construct a composite proposition and say that he

is a good shoemaker. For if, whenever two separate predicates truly

belong to a subject, it follows that the predicate resulting from

their combination also truly belongs to the subject, many absurd

results ensue. For instance, a man is man and white. Therefore, if

predicates may always be combined, he is a white man. Again, if the

predicate 'white' belongs to him, then the combination of that

predicate with the former composite predicate will be permissible.

Thus it will be right to say that he is a white man so on

indefinitely. Or, again, we may combine the predicates 'musical',

'white', and 'walking', and these may be combined many times.

Similarly we may say that Socrates is Socrates and a man, and that

therefore he is the man Socrates, or that Socrates is a man and a

biped, and that therefore he is a two-footed man. Thus it is

manifest that if man states unconditionally that predicates can always

be combined, many absurd consequences ensue.

  We will now explain what ought to be laid down.

  Those predicates, and terms forming the subject of predication,

which are accidental either to the same subject or to one another,

do not combine to form a unity. Take the proposition 'man is white

of complexion and musical'. Whiteness and being musical do not

coalesce to form a unity, for they belong only accidentally to the

same subject. Nor yet, if it were true to say that that which is white

is musical, would the terms 'musical' and 'white' form a unity, for it

is only incidentally that that which is musical is white; the

combination of the two will, therefore, not form a unity.

  Thus, again, whereas, if a man is both good and a shoemaker, we

cannot combine the two propositions and say simply that he is a good

shoemaker, we are, at the same time, able to combine the predicates

'animal' and 'biped' and say that a man is an animal with two feet,

for these predicates are not accidental.

  Those predicates, again, cannot form a unity, of which the one is

implicit in the other: thus we cannot combine the predicate 'white'

again and again with that which already contains the notion 'white',

nor is it right to call a man an animal-man or a two-footed man; for

the notions 'animal' and 'biped' are implicit in the word 'man'. On

the other hand, it is possible to predicate a term simply of any one

instance, and to say that some one particular man is a man or that

some one white man is a white man.

  Yet this is not always possible: indeed, when in the adjunct there

is some opposite which involves a contradiction, the predication of

the simple term is impossible. Thus it is not right to call a dead man

a man. When, however, this is not the case, it is not impossible.

  Yet the facts of the case might rather be stated thus: when some

such opposite elements are present, resolution is never possible,

but when they are not present, resolution is nevertheless not always

possible. Take the proposition 'Homer is so-and-so', say 'a poet';

does it follow that Homer is, or does it not? The verb 'is' is here

used of Homer only incidentally, the proposition being that Homer is a

poet, not that he is, in the independent sense of the word.

  Thus, in the case of those predications which have within them no

contradiction when the nouns are expanded into definitions, and

wherein the predicates belong to the subject in their own proper sense

and not in any indirect way, the individual may be the subject of

the simple propositions as well as of the composite. But in the case

of that which is not, it is not true to say that because it is the

object of opinion, it is; for the opinion held about it is that it

is not, not that it is.



                                12



  As these distinctions have been made, we must consider the mutual

relation of those affirmations and denials which assert or deny

possibility or contingency, impossibility or necessity: for the

subject is not without difficulty.

  We admit that of composite expressions those are contradictory

each to each which have the verb 'to be' its positive and negative

form respectively. Thus the contradictory of the proposition 'man

is' is 'man is not', not 'not-man is', and the contradictory of 'man

is white' is 'man is not white', not 'man is not-white'. For

otherwise, since either the positive or the negative proposition is

true of any subject, it will turn out true to say that a piece of wood

is a man that is not white.

  Now if this is the case, in those propositions which do not

contain the verb 'to be' the verb which takes its place will

exercise the same function. Thus the contradictory of 'man walks' is

'man does not walk', not 'not-man walks'; for to say 'man walks'

merely equivalent to saying 'man is walking'.

  If then this rule is universal, the contradictory of 'it may be'

is may not be', not 'it cannot be'.

  Now it appears that the same thing both may and may not be; for

instance, everything that may be cut or may walk may also escape

cutting and refrain from walking; and the reason is that those

things that have potentiality in this sense are not always actual.

In such cases, both the positive and the negative propositions will be

true; for that which is capable of walking or of being seen has also a

potentiality in the opposite direction.

  But since it is impossible that contradictory propositions should

both be true of the same subject, it follows that' it may not be' is

not the contradictory of 'it may be'. For it is a logical

consequence of what we have said, either that the same predicate can

be both applicable and inapplicable to one and the same subject at the

same time, or that it is not by the addition of the verbs 'be' and

'not be', respectively, that positive and negative propositions are

formed. If the former of these alternatives must be rejected, we

must choose the latter.

  The contradictory, then, of 'it may be' is 'it cannot be'. The

same rule applies to the proposition 'it is contingent that it

should be'; the contradictory of this is 'it is not contingent that it

should be'. The similar propositions, such as 'it is necessary' and

'it is impossible', may be dealt with in the same manner. For it comes

about that just as in the former instances the verbs 'is' and 'is not'

were added to the subject-matter of the sentence 'white' and 'man', so

here 'that it should be' and 'that it should not be' are the

subject-matter and 'is possible', 'is contingent', are added. These

indicate that a certain thing is or is not possible, just as in the

former instances 'is' and 'is not' indicated that certain things

were or were not the case.

  The contradictory, then, of 'it may not be' is not 'it cannot be',

but 'it cannot not be', and the contradictory of 'it may be' is not

'it may not be', but cannot be'. Thus the propositions 'it may be' and

'it may not be' appear each to imply the other: for, since these two

propositions are not contradictory, the same thing both may and may

not be. But the propositions 'it may be' and 'it cannot be' can

never be true of the same subject at the same time, for they are

contradictory. Nor can the propositions 'it may not be' and 'it cannot

not be' be at once true of the same subject.

  The propositions which have to do with necessity are governed by the

same principle. The contradictory of 'it is necessary that it should

be', is not 'it is necessary that it should not be,' but 'it is not

necessary that it should be', and the contradictory of 'it is

necessary that it should not be' is 'it is not necessary that it

should not be'.

  Again, the contradictory of 'it is impossible that it should be'

is not 'it is impossible that it should not be' but 'it is not

impossible that it should be', and the contradictory of 'it is

impossible that it should not be' is 'it is not impossible that it

should not be'.

  To generalize, we must, as has been stated, define the clauses 'that

it should be' and 'that it should not be' as the subject-matter of the

propositions, and in making these terms into affirmations and

denials we must combine them with 'that it should be' and 'that it

should not be' respectively.

  We must consider the following pairs as contradictory propositions:



   It may be.              It cannot be.

   It is contingent.       It is not contingent.

   It is impossible.       It is not impossible.

   It is necessary.        It is not necessary.

   It is true.             It is not true.

                                13



  Logical sequences follow in due course when we have arranged the

propositions thus. From the proposition 'it may be' it follows that it

is contingent, and the relation is reciprocal. It follows also that it

is not impossible and not necessary.

    From the proposition 'it may not be' or 'it is contingent that

it should not be' it follows that it is not necessary that it should

not be and that it is not impossible that it should not be. From the

proposition 'it cannot be' or 'it is not contingent' it follows that

it is necessary that it should not be and that it is impossible that

it should be. From the proposition 'it cannot not be' or 'it is not

contingent that it should not be' it follows that it is necessary that

it should be and that it is impossible that it should not be.

    Let us consider these statements by the help of a table:



           A.                       B.

   It may be.                   It cannot be.

   It is contingent.            It is not contingent.

   It is not impossible         It is impossible that it

     that it should be.           should be.

   It is not necessary          It is necessary that it

     that it should be.           should not be.



           C.                       D.

   It may not be.               It cannot not be.

   It is contingent that it     It is not contingent that

     should not be.               it should not be.

   It is not impossible         It is impossible thatit

     that it should not be.       should not be.

   It is not necessary that     It is necessary that it

     it should not be.            should be.



  Now the propositions 'it is impossible that it should be' and 'it is

not impossible that it should be' are consequent upon the propositions

'it may be', 'it is contingent', and 'it cannot be',  'it is not

contingent', the contradictories upon the contradictories. But there

is inversion. The negative of the proposition 'it is impossible' is

consequent upon the proposition 'it may be' and the corresponding

positive in the first case upon the negative in the second. For 'it is

impossible' is a positive proposition and 'it is not impossible' is

negative.

  We must investigate the relation subsisting between these

propositions and those which predicate necessity. That there is a

distinction is clear. In this case, contrary propositions follow

respectively from contradictory propositions, and the contradictory

propositions belong to separate sequences. For the proposition 'it

is not necessary that it should be' is not the negative of 'it is

necessary that it should not be', for both these propositions may be

true of the same subject; for when it is necessary that a thing should

not be, it is not necessary that it should be. The reason why the

propositions predicating necessity do not follow in the same kind of

sequence as the rest, lies in the fact that the proposition 'it is

impossible' is equivalent, when used with a contrary subject, to the

proposition 'it is necessary'. For when it is impossible that a

thing should be, it is necessary, not that it should be, but that it

should not be, and when it is impossible that a thing should not be,

it is necessary that it should be. Thus, if the propositions

predicating impossibility or non-impossibility follow without change

of subject from those predicating possibility or non-possibility,

those predicating necessity must follow with the contrary subject; for

the propositions 'it is impossible' and 'it is necessary' are not

equivalent, but, as has been said, inversely connected.

  Yet perhaps it is impossible that the contradictory propositions

predicating necessity should be thus arranged. For when it is

necessary that a thing should be, it is possible that it should be.

(For if not, the opposite follows, since one or the other must follow;

so, if it is not possible, it is impossible, and it is thus impossible

that a thing should be, which must necessarily be; which is absurd.)

  Yet from the proposition 'it may be' it follows that it is not

impossible, and from that it follows that it is not necessary; it

comes about therefore that the thing which must necessarily be need

not be; which is absurd. But again, the proposition 'it is necessary

that it should be' does not follow from the proposition 'it may be',

nor does the proposition 'it is necessary that it should not be'.

For the proposition 'it may be' implies a twofold possibility,

while, if either of the two former propositions is true, the twofold

possibility vanishes. For if a thing may be, it may also not be, but

if it is necessary that it should be or that it should not be, one

of the two alternatives will be excluded. It remains, therefore,

that the proposition 'it is not necessary that it should not be'

follows from the proposition 'it may be'. For this is true also of

that which must necessarily be.

  Moreover the proposition 'it is not necessary that it should not be'

is the contradictory of that which follows from the proposition 'it

cannot be'; for 'it cannot be' is followed by 'it is impossible that

it should be' and by 'it is necessary that it should not be', and

the contradictory of this is the proposition 'it is not necessary that

it should not be'. Thus in this case also contradictory propositions

follow contradictory in the way indicated, and no logical

impossibilities occur when they are thus arranged.

  It may be questioned whether the proposition 'it may be' follows

from the proposition 'it is necessary that it should be'. If not,

the contradictory must follow, namely that it cannot be, or, if a

man should maintain that this is not the contradictory, then the

proposition 'it may not be'.

  Now both of these are false of that which necessarily is. At the

same time, it is thought that if a thing may be cut it may also not be

cut, if a thing may be it may also not be, and thus it would follow

that a thing which must necessarily be may possibly not be; which is

false. It is evident, then, that it is not always the case that that

which may be or may walk possesses also a potentiality in the other

direction. There are exceptions. In the first place we must except

those things which possess a potentiality not in accordance with a

rational principle, as fire possesses the potentiality of giving out

heat, that is, an irrational capacity. Those potentialities which

involve a rational principle are potentialities of more than one

result, that is, of contrary results; those that are irrational are

not always thus constituted. As I have said, fire cannot both heat and

not heat, neither has anything that is always actual any twofold

potentiality. Yet some even of those potentialities which are

irrational admit of opposite results. However, thus much has been said

to emphasize the truth that it is not every potentiality which

admits of opposite results, even where the word is used always in

the same sense.

  But in some cases the word is used equivocally. For the term

'possible' is ambiguous, being used in the one case with reference

to facts, to that which is actualized, as when a man is said to find

walking possible because he is actually walking, and generally when

a capacity is predicated because it is actually realized; in the other

case, with reference to a state in which realization is

conditionally practicable, as when a man is said to find walking

possible because under certain conditions he would walk. This last

sort of potentiality belongs only to that which can be in motion,

the former can exist also in the case of that which has not this

power. Both of that which is walking and is actual, and of that

which has the capacity though not necessarily realized, it is true

to say that it is not impossible that it should walk (or, in the other

case, that it should be), but while we cannot predicate this latter

kind of potentiality of that which is necessary in the unqualified

sense of the word, we can predicate the former.

  Our conclusion, then, is this: that since the universal is

consequent upon the particular, that which is necessary is also

possible, though not in every sense in which the word may be used.

  We may perhaps state that necessity and its absence are the

initial principles of existence and non-existence, and that all else

must be regarded as posterior to these.

  It is plain from what has been said that that which is of

necessity is actual. Thus, if that which is eternal is prior,

actuality also is prior to potentiality. Some things are actualities

without potentiality, namely, the primary substances; a second class

consists of those things which are actual but also potential, whose

actuality is in nature prior to their potentiality, though posterior

in time; a third class comprises those things which are never

actualized, but are pure potentialities.

                                14



  The question arises whether an affirmation finds its contrary in a

denial or in another affirmation; whether the proposition 'every man

is just' finds its contrary in the proposition 'no man is just', or in

the proposition 'every man is unjust'. Take the propositions

'Callias is just', 'Callias is not just', 'Callias is unjust'; we have

to discover which of these form contraries.

  Now if the spoken word corresponds with the judgement of the mind,

and if, in thought, that judgement is the contrary of another, which

pronounces a contrary fact, in the way, for instance, in which the

judgement 'every man is just' pronounces a contrary to that pronounced

by the judgement 'every man is unjust', the same must needs hold

good with regard to spoken affirmations.

  But if, in thought, it is not the judgement which pronounces a

contrary fact that is the contrary of another, then one affirmation

will not find its contrary in another, but rather in the corresponding

denial. We must therefore consider which true judgement is the

contrary of the false, that which forms the denial of the false

judgement or that which affirms the contrary fact.

  Let me illustrate. There is a true judgement concerning that which

is good, that it is good; another, a false judgement, that it is not

good; and a third, which is distinct, that it is bad. Which of these

two is contrary to the true? And if they are one and the same, which

mode of expression forms the contrary?

  It is an error to suppose that judgements are to be defined as

contrary in virtue of the fact that they have contrary subjects; for

the judgement concerning a good thing, that it is good, and that

concerning a bad thing, that it is bad, may be one and the same, and

whether they are so or not, they both represent the truth. Yet the

subjects here are contrary. But judgements are not contrary because

they have contrary subjects, but because they are to the contrary

effect.

  Now if we take the judgement that that which is good is good, and

another that it is not good, and if there are at the same time other

attributes, which do not and cannot belong to the good, we must

nevertheless refuse to treat as the contraries of the true judgement

those which opine that some other attribute subsists which does not

subsist, as also those that opine that some other attribute does not

subsist which does subsist, for both these classes of judgement are of

unlimited content.

  Those judgements must rather be termed contrary to the true

judgements, in which error is present. Now these judgements are

those which are concerned with the starting points of generation,

and generation is the passing from one extreme to its opposite;

therefore error is a like transition.

  Now that which is good is both good and not bad. The first quality

is part of its essence, the second accidental; for it is by accident

that it is not bad. But if that true judgement is most really true,

which concerns the subject's intrinsic nature, then that false

judgement likewise is most really false, which concerns its

intrinsic nature. Now the judgement that that is good is not good is a

false judgement concerning its intrinsic nature, the judgement that it

is bad is one concerning that which is accidental. Thus the

judgement which denies the true judgement is more really false than

that which positively asserts the presence of the contrary quality.

But it is the man who forms that judgement which is contrary to the

true who is most thoroughly deceived, for contraries are among the

things which differ most widely within the same class. If then of

the two judgements one is contrary to the true judgement, but that

which is contradictory is the more truly contrary, then the latter, it

seems, is the real contrary. The judgement that that which is good

is bad is composite. For presumably the man who forms that judgement

must at the same time understand that that which is good is not good.

  Further, the contradictory is either always the contrary or never;

therefore, if it must necessarily be so in all other cases, our

conclusion in the case just dealt with would seem to be correct. Now

where terms have no contrary, that judgement is false, which forms the

negative of the true; for instance, he who thinks a man is not a man

forms a false judgement. If then in these cases the negative is the

contrary, then the principle is universal in its application.

  Again, the judgement that that which is not good is not good is

parallel with the judgement that that which is good is good. Besides

these there is the judgement that that which is good is not good,

parallel with the judgement that that that is not good is good. Let us

consider, therefore, what would form the contrary of the true

judgement that that which is not good is not good. The judgement

that it is bad would, of course, fail to meet the case, since two true

judgements are never contrary and this judgement might be true at

the same time as that with which it is connected. For since some

things which are not good are bad, both judgements may be true. Nor is

the judgement that it is not bad the contrary, for this too might be

true, since both qualities might be predicated of the same subject. It

remains, therefore, that of the judgement concerning that which is not

good, that it is not good, the contrary judgement is that it is

good; for this is false. In the same way, moreover, the judgement

concerning that which is good, that it is not good, is the contrary of

the judgement that it is good.

  It is evident that it will make no difference if we universalize the

positive judgement, for the universal negative judgement will form the

contrary. For instance, the contrary of the judgement that

everything that is good is good is that nothing that is good is

good. For the judgement that that which is good is good, if the

subject be understood in a universal sense, is equivalent to the

judgement that whatever is good is good, and this is identical with

the judgement that everything that is good is good. We may deal

similarly with judgements concerning that which is not good.

  If therefore this is the rule with judgements, and if spoken

affirmations and denials are judgements expressed in words, it is

plain that the universal denial is the contrary of the affirmation

about the same subject. Thus the propositions 'everything good is

good', 'every man is good', have for their contraries the propositions

'nothing good is good', 'no man is good'. The contradictory

propositions, on the other hand, are 'not everything good is good',

'not every man is good'.

  It is evident, also, that neither true judgements nor true

propositions can be contrary the one to the other. For whereas, when

two propositions are true, a man may state both at the same time

without inconsistency, contrary propositions are those which state

contrary conditions, and contrary conditions cannot subsist at one and

the same time in the same subject.





                            THE END

.