On Interpretation

                               8



  An affirmation or denial is single, if it indicates some one fact

about some one subject; it matters not whether the subject is

universal and whether the statement has a universal character, or

whether this is not so. Such single propositions are: 'every man is

white', 'not every man is white';'man is white','man is not white';

'no man is white', 'some men are white'; provided the word 'white' has

one meaning. If, on the other hand, one word has two meanings which do

not combine to form one, the affirmation is not single. For

instance, if a man should establish the symbol 'garment' as

significant both of a horse and of a man, the proposition 'garment

is white' would not be a single affirmation, nor its opposite a single

denial. For it is equivalent to the proposition 'horse and man are

white', which, again, is equivalent to the two propositions 'horse

is white', 'man is white'. If, then, these two propositions have

more than a single significance, and do not form a single proposition,

it is plain that the first proposition either has more than one

significance or else has none; for a particular man is not a horse.

  This, then, is another instance of those propositions of which

both the positive and the negative forms may be true or false

simultaneously.



                                 9



  In the case of that which is or which has taken place, propositions,

whether positive or negative, must be true or false. Again, in the

case of a pair of contradictories, either when the subject is

universal and the propositions are of a universal character, or when

it is individual, as has been said,' one of the two must be true and

the other false; whereas when the subject is universal, but the

propositions are not of a universal character, there is no such

necessity. We have discussed this type also in a previous chapter.

  When the subject, however, is individual, and that which is

predicated of it relates to the future, the case is altered. For if

all propositions whether positive or negative are either true or

false, then any given predicate must either belong to the subject or

not, so that if one man affirms that an event of a given character

will take place and another denies it, it is plain that the

statement of the one will correspond with reality and that of the

other will not. For the predicate cannot both belong and not belong to

the subject at one and the same time with regard to the future.

  Thus, if it is true to say that a thing is white, it must

necessarily be white; if the reverse proposition is true, it will of

necessity not be white. Again, if it is white, the proposition stating

that it is white was true; if it is not white, the proposition to

the opposite effect was true. And if it is not white, the man who

states that it is making a false statement; and if the man who

states that it is white is making a false statement, it follows that

it is not white. It may therefore be argued that it is necessary

that affirmations or denials must be either true or false.

  Now if this be so, nothing is or takes place fortuitously, either in

the present or in the future, and there are no real alternatives;

everything takes place of necessity and is fixed. For either he that

affirms that it will take place or he that denies this is in

correspondence with fact, whereas if things did not take place of

necessity, an event might just as easily not happen as happen; for the

meaning of the word 'fortuitous' with regard to present or future

events is that reality is so constituted that it may issue in either

of two opposite directions. Again, if a thing is white now, it was

true before to say that it would be white, so that of anything that

has taken place it was always true to say 'it is' or 'it will be'. But

if it was always true to say that a thing is or will be, it is not

possible that it should not be or not be about to be, and when a thing

cannot not come to be, it is impossible that it should not come to be,

and when it is impossible that it should not come to be, it must

come to be. All, then, that is about to be must of necessity take

place. It results from this that nothing is uncertain or fortuitous,

for if it were fortuitous it would not be necessary.

  Again, to say that neither the affirmation nor the denial is true,

maintaining, let us say, that an event neither will take place nor

will not take place, is to take up a position impossible to defend. In

the first place, though facts should prove the one proposition

false, the opposite would still be untrue. Secondly, if it was true to

say that a thing was both white and large, both these qualities must

necessarily belong to it; and if they will belong to it the next

day, they must necessarily belong to it the next day. But if an

event is neither to take place nor not to take place the next day, the

element of chance will be eliminated. For example, it would be

necessary that a sea-fight should neither take place nor fail to

take place on the next day.

  These awkward results and others of the same kind follow, if it is

an irrefragable law that of every pair of contradictory

propositions, whether they have regard to universals and are stated as

universally applicable, or whether they have regard to individuals,

one must be true and the other false, and that there are no real

alternatives, but that all that is or takes place is the outcome of

necessity. There would be no need to deliberate or to take trouble, on

the supposition that if we should adopt a certain course, a certain

result would follow, while, if we did not, the result would not

follow. For a man may predict an event ten thousand years

beforehand, and another may predict the reverse; that which was

truly predicted at the moment in the past will of necessity take place

in the fullness of time.

  Further, it makes no difference whether people have or have not

actually made the contradictory statements. For it is manifest that

the circumstances are not influenced by the fact of an affirmation

or denial on the part of anyone. For events will not take place or

fail to take place because it was stated that they would or would

not take place, nor is this any more the case if the prediction

dates back ten thousand years or any other space of time. Wherefore,

if through all time the nature of things was so constituted that a

prediction about an event was true, then through all time it was

necessary that that should find fulfillment; and with regard to all

events, circumstances have always been such that their occurrence is a

matter of necessity. For that of which someone has said truly that

it will be, cannot fail to take place; and of that which takes

place, it was always true to say that it would be.

  Yet this view leads to an impossible conclusion; for we see that

both deliberation and action are causative with regard to the

future, and that, to speak more generally, in those things which are

not continuously actual there is potentiality in either direction.

Such things may either be or not be; events also therefore may

either take place or not take place. There are many obvious

instances of this. It is possible that this coat may be cut in half,

and yet it may not be cut in half, but wear out first. In the same

way, it is possible that it should not be cut in half; unless this

were so, it would not be possible that it should wear out first. So it

is therefore with all other events which possess this kind of

potentiality. It is therefore plain that it is not of necessity that

everything is or takes place; but in some instances there are real

alternatives, in which case the affirmation is no more true and no

more false than the denial; while some exhibit a predisposition and

general tendency in one direction or the other, and yet can issue in

the opposite direction by exception.

  Now that which is must needs be when it is, and that which is not

must needs not be when it is not. Yet it cannot be said without

qualification that all existence and non-existence is the outcome of

necessity. For there is a difference between saying that that which

is, when it is, must needs be, and simply saying that all that is must

needs be, and similarly in the case of that which is not. In the case,

also, of two contradictory propositions this holds good. Everything

must either be or not be, whether in the present or in the future, but

it is not always possible to distinguish and state determinately which

of these alternatives must necessarily come about.

  Let me illustrate. A sea-fight must either take place to-morrow or

not, but it is not necessary that it should take place to-morrow,

neither is it necessary that it should not take place, yet it is

necessary that it either should or should not take place to-morrow.

Since propositions correspond with facts, it is evident that when in

future events there is a real alternative, and a potentiality in

contrary directions, the corresponding affirmation and denial have the

same character.

  This is the case with regard to that which is not always existent or

not always nonexistent. One of the two propositions in such

instances must be true and the other false, but we cannot say

determinately that this or that is false, but must leave the

alternative undecided. One may indeed be more likely to be true than

the other, but it cannot be either actually true or actually false. It

is therefore plain that it is not necessary that of an affirmation and

a denial one should be true and the other false. For in the case of

that which exists potentially, but not actually, the rule which

applies to that which exists actually does not hold good. The case

is rather as we have indicated.



                                10



  An affirmation is the statement of a fact with regard to a

subject, and this subject is either a noun or that which has no

name; the subject and predicate in an affirmation must each denote a

single thing. I have already explained' what is meant by a noun and by

that which has no name; for I stated that the expression 'not-man' was

not a noun, in the proper sense of the word, but an indefinite noun,

denoting as it does in a certain sense a single thing. Similarly the

expression 'does not enjoy health' is not a verb proper, but an

indefinite verb. Every affirmation, then, and every denial, will

consist of a noun and a verb, either definite or indefinite.

  There can be no affirmation or denial without a verb; for the

expressions 'is', 'will be', 'was', 'is coming to be', and the like

are verbs according to our definition, since besides their specific

meaning they convey the notion of time. Thus the primary affirmation

and denial are 'as follows: 'man is', 'man is not'. Next to these,

there are the propositions: 'not-man is', 'not-man is not'. Again we

have the propositions: 'every man is, 'every man is not', 'all that is

not-man is', 'all that is not-man is not'. The same classification

holds good with regard to such periods of time as lie outside the

present.

  When the verb 'is' is used as a third element in the sentence, there

can be positive and negative propositions of two sorts. Thus in the

sentence 'man is just' the verb 'is' is used as a third element,

call it verb or noun, which you will. Four propositions, therefore,

instead of two can be formed with these materials. Two of the four, as

regards their affirmation and denial, correspond in their logical

sequence with the propositions which deal with a condition of

privation; the other two do not correspond with these.

  I mean that the verb 'is' is added either to the term 'just' or to

the term 'not-just', and two negative propositions are formed in the

same way. Thus we have the four propositions. Reference to the

subjoined table will make matters clear: