1 · First we must settle what a name is and what a verb is, and then what a [16a1] negation, an affirmation, a statement and a sentence1 are.
Now spoken sounds are symbols of affections in the soul, and written marks symbols of spoken sounds. And just as written marks are not the same for all men, [5] neither are spoken sounds. But what these are in the first place signs of—affections of the soul—are the same for all; and what these affections are likenesses of—actual things—are also the same. These matters have been discussed in the work on the soul2 and do not belong to the present subject.
Just as some thoughts in the soul are neither true nor false while some are [10] necessarily one or the other, so also with spoken sounds. For falsity and truth have to do with combination and separation. Thus names and verbs by themselves—for instance ‘man’ or ‘white’ when nothing further is added—are like the thoughts that [15] are without combination and separation; for so far they are neither true nor false. A sign of this is that even ‘goat-stag’ signifies something but not, as yet, anything true or false—unless ‘is’ or ‘is not’ is added (either simply or with reference to time).
2 · A name is a spoken sound significant by convention, without time, none of whose parts is significant in separation. For in ‘Whitfield’ the ‘field’ does not [20] signify anything in its own right, as it does in the phrase ‘white field’. Not that it is the same with complex names as with simple ones: in the latter the part is in no way significant, in the former it has some force but is not significant of anything in [25] separation, for example the ‘boat’ in ‘pirate-boat’.
I say ‘by convention’ because no name is a name naturally but only when it has become a symbol. Even inarticulate noises (of beasts, for instance) do indeed reveal something, yet none of them is a name.
‘Not man’ is not a name, nor is there any correct name for it. It is neither a [30] phrase nor a negation. Let us call it an indefinite name.
‘Philo’s’, ‘to-Philo’, and the like are not names but inflexions of names. The [16b1] same account holds for them as for names except that an inflexion when combined with ‘is’, ‘was’, or ‘will be’ is not true or false whereas a name always is. Take, for example, ‘Philo’s is’ or ‘Philo’s is not’; so far there is nothing either true or false. [5]
3 · A verb is what additionally signifies time, no part of it being significant separately; and it is a sign of things said of something else.
It additionally signifies time: ‘recovery’ is a name, but ‘recovers’ is a verb, because it additionally signifies something’s holding now. And it is always a sign of [10] what holds, that is, holds of a subject.
‘Does not recover’ and ‘does not ail’ I do not call verbs. For though they additionally signify time and always hold of something, yet there is a difference—for which there is no name. Let us call them indefinite verbs, because they hold [15] indifferently of anything whether existent or non-existent. Similarly, ‘recovered’ and ‘will-recover’ are not verbs but inflexions of verbs. They differ from the verb in that it additionally signifies the present time, they the time outside the present.
When uttered just by itself a verb is a name and signifies something—the [20] speaker arrests his thought and the hearer pauses—but it does not yet signify whether it is or not. For not even3 ‘to be’ or ‘not to be’ is a sign of the actual thing (nor if you say simply ‘that which is’); for by itself it is nothing, but it additionally [25] signifies some combination, which cannot be thought of without the components.
4 · A sentence is a significant spoken sound some part of which is significant in separation—as an expression, not as an affirmation.
I mean that animal, for instance, signifies something, but not that it is or is not [30] (though it will be an affirmation or negation if something is added); the single syllables of ‘animal’, on the other hand, signify nothing. Nor is the ‘ice’ in ‘mice’ significant; here it is simply a spoken sound. In double words, as we said, a part does signify, but not in its own right.
[17a1] Every sentence is significant (not as a tool but, as we said, by convention), but not every sentence is a statement-making sentence, but only those in which there is truth or falsity. There is not truth or falsity in all sentences: a prayer is a sentence but is neither true or false. The present investigation deals with the statement [5] making sentence; the others we can dismiss, since consideration of them belongs rather to the study of rhetoric or poetry.
5 · The first single statement-making sentence is the affirmation, next is the negation. The others are single in virtue of a connective.
[10] Every statement-making sentence must contain a verb or an inflexion of a verb. For even the definition of man is not yet a statement-making sentence—unless ‘is’ or ‘will be’ or ‘was’ or something of this sort is added. (To explain why ‘two-footed land animal’ is one thing and not many belongs to a different inquiry; [15] certainly it will not be one simply through being said all together.)
A single statement-making sentence is either one that reveals a single thing or one that is single in virtue of a connective. There are more than one if more things than one are revealed or if connectives are lacking.
(Let us call a name or a verb simply an expression, since by saying it one cannot reveal anything by one’s utterance in such a way as to be making a statement, whether one is answering a question or speaking spontaneously.)
Of these the one is a simple statement, affirming or denying something of [20] something, the other is compounded of simple statements and is a kind of composite sentence. The simple statement is a significant spoken sound about whether something does or does not hold (in one of the divisions of time).
6 · An affirmation is a statement affirming something of something, a [25] negation is a statement denying something of something.
Now it is possible to state of what does hold that it does not hold, of what does not hold that it does hold, of what does hold that it does hold, and of what does not hold that it does not hold. Similarly for times outside the present. So it must be [30] possible to deny whatever anyone has affirmed, and to affirm whatever anyone has denied. Thus it is clear that for every affirmation there is an opposite negation, and for every negation an opposite affirmation. Let us call an affirmation and a negation which are opposite a contradiction. I speak of statements as opposite when they affirm and deny the same thing of the same thing—not homonymously, [35] together with all other such conditions that we add to counter the troublesome objections of sophists.
7 · Now of actual things some are universal, others particular (I call universal that which is by its nature predicated of a number of things, and particular that which is not; man, for instance, is a universal, Callias a particular). [17b1] So it must sometimes be of a universal that one states that something holds or does not, sometimes of a particular. Now if one states universally of a universal that something holds or does not, there will be contrary statements (examples of what I mean by ‘stating universally of a universal’ are: every man is white—no man is [5] white). But when one states something of a universal but not universally, the statements are not contrary (though what is being revealed may be contrary). Examples of what I mean by ‘stating of a universal not universally’ are: a man is white—a man is not white; man is a universal but it is not used universally in the [10] statement (for ‘every’ does not signify the universal but that it is taken universally). It is not true to predicate a universal universally of a subject, for there cannot be an affirmation in which a universal is predicated universally of a subject, for instance: [15] every man is every animal.
I call an affirmation and a negation contradictory opposites when what one signifies universally the other signifies not universally, e.g. every man is white—not every man is white, no man is white—some man is white. But I call the universal affirmation and the universal negation contrary opposites, e.g. every man is [20] just—no man is just. So these cannot be true together, but their opposites may both be true with respect to the same thing, e.g. not every man is white—some man is [25] white.
Of contradictory statements about a universal taken universally it is necessary for one or the other to be true or false; similarly if they are about particulars, e.g. Socrates is white—Socrates is not white. But if they are about a universal not taken [30] universally it is not always the case that one is true and the other false. For it is true to say at the same time that a man is white and that a man is not white, or that a man is noble and a man is not noble (for if base, then not noble; and if something is becoming something, then it is not that thing). This might seem absurd at first [35] sight, because ‘a man is not white’ looks as if it signifies also at the same time that no man is white; this, however, does not signify the same, nor does it necessarily hold at the same time.
It is evident that a single affirmation has a single negation. For the negation must deny the same thing as the affirmation affirmed, and of the same thing, [18a1] whether a particular or a universal (taken either universally or not universally). I mean, for example, Socrates is white—Socrates is not white. But if something else is denied, or the same thing is denied of something else, that will not be the opposite statement, but a different one. The opposite of ‘every man is white’ is ‘not every man [5] is white’; of ‘some man is white’, ‘no man is white’; of ‘a man is white’, ‘a man is not white’.
We have explained, then: that a single affirmation has a single negation as its contradictory opposite, and which these are; that contrary statements are different, [10] and which these are; and that not all contradictory pairs are true or false, why this is, and when they are true or false.
8 · A single affirmation or negation is one which signifies one thing about one thing (whether about a universal taken universally or not), e.g. every man is [15] white—not every man is white, a man is white—a man is not white, no man is white—some man is white—assuming that ‘white’ signifies one thing.
But if one name is given to two things which do not make up one thing, there is not a single affirmation. Suppose, for example, that one gave the name cloak to [20] horse and man; ‘a cloak is white’ would not be a single affirmation. For to say this is no different from saying a horse and a man is white, and this is no different from saying a horse is white and a man is white. So if this last signifies more than one [25] thing and is more than one affirmation, clearly the first also signifies either more than one thing or nothing (because no man is a horse). Consequently it is not necessary, with these statements either, for one contradictory to be true and the other false.
9 · With regard to what is and what has been it is necessary for the affirmation or the negation to be true or false. And with universals taken universally [30] it is always necessary for one to be true and the other false, and with particulars too, as we have said; but with universals not spoken of universally it is not necessary. But with particulars that are going to be it is different.
For if every affirmation or negation is true or false it is necessary for [35] everything either to be the case or not to be the case. For if one person says that something will be and another denies this same thing, it is clearly necessary for one of them to be saying what is true—if every affirmation is true or false; for both will not be the case together under such circumstances. For if it is true to say that it is white or is not white, it is necessary for it to be white or not white; and if it is white or [18b1] is not white, then it was true to say or deny this. If it is not the case it is false, if it is false it is not the case. So it is necessary for the affirmation or the negation to be true. It follows that nothing either is or is happening, or will be or will not be, by [5] chance or as chance has it, but everything of necessity and not as chance has it (since either he who says or he who denies is saying what is true). For otherwise it might equally well happen or not happen, since what is as chance has it is no more thus than not thus, nor will it be.
Again, it if is white now it was true to say earlier that it would be white; so that [10] it was always true to say of anything that has happened that it would be so. But if it was always true to say that it was so, or would be so, it could not not be so, or not be going to be so. But if something cannot not happen it is impossible for it not to happen; and if it is impossible for something not to happen it is necessary for it to happen. Everything that will be, therefore, happens necessarily. So nothing will [15] come about as chance has it or by chance; for if by chance, not of necessity.
Nor, however, can we say that neither is true—that it neither will be nor will not be so. For, firstly, though the affirmation is false the negation is not true, and though the negation is false the affirmation, on this view, is not true. Moreover, if it [20] is true to say that something is white and large,4 both have to hold of it, and if true that they will hold tomorrow, they will have to hold tomorrow;5 and if it neither will be nor will not be the case tomorrow, then there is no ‘as chance has it’. Take a sea-battle: it would have neither to happen nor not to happen. [25]
These and others like them are the absurdities that follow if it is necessary for every affirmation and negation either about universals spoken of universally or about particulars, that one of the opposites be true and the other false, and that nothing of what happens is as chance has it, but everything is and happens of [30] necessity. So there would be no need to deliberate or to take trouble (thinking that if we do this, this will happen, but if we do not, it will not). For there is nothing to prevent someone’s having said ten thousand years beforehand that this would be the case, and another’s having denied it; so that whichever of the two was true to say [35] then, will be the case of necessity. Nor, of course, does it make any difference whether any people made the contradictory statements or not. For clearly this is how the actual things are even if someone did not affirm it and another deny it. For it is not because of the affirming or denying that it will be or will not be the case, nor is it a question of ten thousand years beforehand rather than any other time. Hence, [19a1] if in the whole of time the state of things was such that one or the other was true, it was necessary for this to happen, and for the state of things always to be such that everything that happens happens of necessity. For what anyone has truly said would [5] be the case cannot not happen; and of what happens it was always true to say that it would be the case.
But what if this is impossible? For we see that what will be has an origin both in deliberation and in action, and that, in general, in things that are not always [10] actual there is the possibility of being and of not being; here both possibilities are open, both being and not being, and consequently, both coming to be and not coming to be. Many things are obviously like this. For example, it is possible for this cloak to be cut up, and yet it will not be cut up but will wear out first. But equally, its [15] not being cut up is also possible, for it would not be the case that it wore out first unless its not being cut up were possible. So it is the same with all other events that are spoken of in terms of this kind of possibility. Clearly, therefore, not everything is or happens of necessity: some things happen as chance has it, and of the affirmation [20] and the negation neither is true rather than the other; with other things it is one rather than the other and as a rule, but still it is possible for the other to happen instead.
What is, necessarily is, when it is; and what is not, necessarily is not, when it is not. But not everything that is, necessarily is; and not everything that is not, [25] necessarily is not. For to say that everything that is, is of necessity, when it is, is not the same as saying unconditionally that it is of necessity. Similarly with what is not. And the same account holds for contradictories: everything necessarily is or is not, and will be or will not be; but one cannot divide and say that one or the other is [30] necessary. I mean, for example: it is necessary for there to be or not to be a sea-battle tomorrow; but it is not necessary for a sea-battle to take place tomorrow, nor for one not to take place—though it is necessary for one to take place or not to take place. So, since statements are true according to how the actual things are, it is clear that wherever these are such as to allow of contraries as chance has it, the [35] same necessarily holds for the contradictories also. This happens with things that are not always so or are not always not so. With these it is necessary for one or the other of the contradictories to be true or false—not, however, this one or that one, but as chance has it; or for one to be true rather than the other, yet not already true or false.
[19b1] Clearly, then, it is not necessary that of every affirmation and opposite negation one should be true and the other false. For what holds for things that are does not hold for things that are not but may possibly be or not be; with these it is as we have said.
[5] 10 · Now an affirmation signifies something about something, this last being either a name or a ‘non-name’; and what is affirmed must be one thing about one thing. (Names and ‘non-names’ have already been discussed. For I do not call ‘not-man’ a name but an indefinite name—for what it signifies is in a way one thing, [10] but indefinite—just as I do not call ‘does not recover’ a verb). So every affirmation will contain either a name and a verb or an indefinite name and a verb. Without a verb there will be no affirmation or negation. ‘Is’, ‘will be’, ‘was’, ‘becomes’, and the like are verbs according to what we laid down, since they additionally signify time. So a first affirmation and negation are: ‘a man is’, ‘a man is not’; then, ‘a not-man [15] is’, ‘a not-man is not’; and again, ‘every man is’, ‘every man is not’, ‘every not-man is’, ‘every not-man is not’. For times other than the present the same account holds.
But when ‘is’ is predicated additionally as a third thing, there are two ways of expressing opposition. (I mean, for example, a man is just; here I say that the ‘is’ is a [20] third component—whether name or verb—in the affirmation.) Because of this there will here be four cases (two of which will be related, as to order of sequence, to the affirmation and negation in the way the privations are, while two will not). I mean that ‘is’ will be added either to ‘just’ or to ‘not-just’, and so, too, will the [25] negation. Thus there will be four cases. What is meant should be clear from the following diagram:
(a) ‘a man is just’ |
(b) ‘a man is not just’ |
|---|---|
(d) ‘a man is not not-just’ |
(c) ‘a man is not-just’ |
‘Is’ and ‘is not’ are here added to ‘just’ and to ‘not-just’. [30]
This then is how these are arranged (as is said in the Analytics).6 Similarly, too, if the affirmation is about the name taken universally, e.g.:
(a) ‘every man is just’ |
(b) ‘not every man is just’ |
|---|---|
(d) ‘not every man is not-just’ |
(c) ‘every man is not-just’ |
Here, however, it is not in the same way possible for diagonal statements to be true [35] together, though it is possible sometimes.
These, then, are two pairs of opposites. There are others if something is added to ‘not-man’ as a sort of subject, thus:
(a) ‘a not-man is just’ |
(b) ‘a not-man is not just’ |
|---|---|
(d) ‘a not-man is not not-just’ |
(c) ‘a not-man is not-just’ |
There will not be any more oppositions than these. These last are a group on their [20a1] own separate from the others, in that they use ‘not-man’ as a name.
In cases where ‘is’ does not fit (e.g. with ‘recovers’ or ‘walks’) the verbs have the same effect when so placed as if ‘is’ were joined on, e.g.: [5]
(a) ‘every man recovers’ |
(b) ‘every man does not recover’ |
|---|---|
(d) ‘every not-man does not recover’ |
(c) ‘every not-man recovers’ |
Here one must not say ‘not every man’ but must add the ‘not’, the negation, to ‘man’. For ‘every’ does not signify a universal, but that it is taken universally. This is clear from the following. [10]
(b) ‘a man does not recover’ |
|
|---|---|
(d) ‘a not-man does not recover’ |
(c) ‘a not-man recovers’ |
For these differ from the previous ones in not being universal. So ‘every’ or ‘no’ additionally signify nothing other than that the affirmation or negation is about the [15] name taken universally. Everything else, therefore, must be added unchanged.
Since the contrary negation of ‘every animal is just’ is that which signifies that no animal is just, obviously these will never be true together or of the same thing, but their opposites sometimes will (e.g. not every animal is just, and some animal is [20] just). ‘No man is just’ follows from ‘every man is not-just’, while the opposite of this, ‘not every man is not-just’, follows from ‘some man is just’ (for there must be one). It is clear too that, with regard to particulars, if it is true, when asked something, to [25] deny it, it is true also to affirm something. For instance: Is Socrates wise? No. Then Socrates is not-wise. With universals, on the other hand, the corresponding affirmation is not true, but the negation is true. For instance: Is every man wise? No. Then every man is not-wise. This is false, but ‘then not every man is wise’ is [30] true; this is the opposite statement, the other is the contrary.
Names and verbs that are indefinite (and thereby opposite), such as ‘not-man’ and ‘not-just’, might be thought to be negations without a name and a verb. But they are not. For a negation must always be true or false; but one who says [35] not-man—without adding anything else—has no more said something true or false (indeed rather less so) than one who says man.
‘Every not-man is just’ does not signify the same as any of the above, nor does its opposite, ‘not every not-man is just’. But ‘every not-man is not-just’ signifies the same as ‘no not-man is just’.
[20b1] If names and verbs are transposed they still signify the same thing, e.g. a man is white—white is a man. For otherwise the same statement will have more than one negation, whereas we have shown that one has only one. For ‘a man is white’ has for [5] negation ‘a man is not white’, while ‘white is a man’—if it is not the same as ‘a man is white’—will have for negation either ‘white is not a not-man’ or ‘white is not a man’. But one of these is a negation of ‘white is a not-man’, the other of ‘a man is [10] white’. Thus there will be two negations of one statement. Clearly, then, if the name and the verb are transposed the same affirmation and negation are produced.
11 · To affirm or deny one thing of many, or many of one, is not one [15] affirmation or negation unless the many things together make up some one thing. I do not call them one if there exists one name but there is not some one thing they make up. For example, man is perhaps an animal and two-footed and tame, yet these do make up some one thing; whereas white and man and walking do not make up one thing. So if someone affirms some one thing of these it is not one affirmation; [20] it is one spoken sound, but more than one affirmation. Similarly, if these are affirmed of one thing, that is more than one affirmation. So if a dialectical question demands as answer either the statement proposed or one side of a contradiction (the statement in fact being a side of one contradiction), there could not be one answer in these cases. For the question itself would not be one question, even if true. These [25] matters have been discussed in the Topics.7 (It is also clear that ‘What is it?’ is not a dialectical question either; for the question must give one the choice of stating whichever side of the contradiction one wishes. The questioner must specify further and ask whether man is this or not this.) [30]
Of things predicated separately some can be predicated in combination, the whole predicate as one, others cannot. What then is the difference? For of a man it is true to say two-footed separately and animal separately, and also to say them as one; similarly, white and man separately, and also as one. But if someone is good [35] and a cobbler it does not follow that he is a good cobbler. For if because each of two holds both together also hold, there will be many absurdities. For since of a man both ‘white’ and ‘a man’ are true, so also is the whole compound; again, if ‘white’ then the whole compound—so that he will be a white white man, and so on indefinitely. Or, again, we shall have ‘walking white musician’, and then these [21a1] compounded many times over. Further, if Socrates is a man and is Socrates he will be a man Socrates; and if two-footed and a man then a two-footed man. Clearly, then, one is led into many absurdities if one lays down without restriction that the [5] compounds come about. How the matter should be put we will now explain.
Of things predicated, and things they get predicated of, those which are said accidentally, either of the same thing or of one another, will not be one. For example, a man is white and musical, but ‘white’ and ‘musical’ are not one, because [10] they are both accidental to the same thing. And even if it is true to say that the white is musical, ‘musical white’ will still not be one thing; for it is accidentally that the musical is white, and so ‘white musical’ will not be one.8 Nor, consequently, will the cobbler who is (without qualification) good, though an animal which is two-footed [15] will (since this is not accidental). Further, where one of the things is contained in the other, they will not be one. This is why ‘white’ is not repeated and why a man is not an animal man or a two-footed man; for two-footed and animal are contained in man.
It is true to speak of the particular case even without qualification; e.g. to say that some particular man is a man or some particular white man white. Not always, [20] though. When in what is added some opposite is contained from which a contradiction follows, it is not true but false (e.g. to call a dead man a man); but when no such opposite is contained, it is true. Or rather, when it is contained it is always not true, but when it is not, it is not always true. For example, Homer is [25] something (say, a poet). Does it follow that he is? No, for the ‘is’ is predicated accidentally of Homer; for it is because he is a poet, not in its own right, that the ‘is’ is predicated of Homer. Thus, where predicates both contain no contrariety if definitions are put instead of names and are predicated in their own right and not [30] accidentally, in these cases it will be true to speak of the particular thing even without qualification. It is not true to say that what is not, since it is thought about, is something that is; for what is thought about it is not that it is, but that it is not.
12 · Having cleared up these points, we must consider how negations and [35] affirmations of the possible to be and the not possible are related to one another, and of the admissible and not admissible, and about the impossible and the necessary. For there are some puzzles here.
Suppose we say that of combined expressions those are the contradictory opposites of one another which are ordered by reference to ‘to be’ and ‘not to be’. [21b1] For example, the negation of ‘to be a man’ is ‘not to be a man’, not ‘to be a not-man’, and the negation of ‘to be a white man’ is ‘not to be a white man’, not ‘to be a not-white man’ (otherwise, since of everything the affirmation or the negation [5] holds, the log will be truly said to be a not-white man). And if this is so, in cases where ‘to be’ is not added what is said instead of ‘to be’ will have the same effect. For example, the negation of ‘a man walks’ is not ‘a not-man walks’ but ‘a man does not walk’; for there is no difference between saying that a man walks and saying that a man is walking.
[10] So then, if this holds good everywhere, the negation of ‘possible to be’ is ‘possible not to be’, and not ‘not possible to be’. Yet it seems that for the same thing it is possible both to be and not to be. For everything capable of being cut or of walking is capable also of not walking or of not being cut. The reason is that [15] whatever is capable in this way is not always actual, so that the negation too will hold of it: what can walk is capable also of not walking, and what can be seen of not being seen. But it is impossible for opposite expressions to be true of the same thing. [20] This then is not the negation. For it follows from the above that either the same thing is said and denied of the same thing at the same time, or it is not by ‘to be’ and ‘not to be’ being added that affirmations and negations are produced. So if the former is impossible we must choose the latter. The negation of ‘possible to be’, therefore, is ‘not possible to be’.
[25] The same account holds for ‘admissible to be’: its negation is ‘not admissible to be’. Similarly with the others, ‘necessary’ and ‘impossible’. For as in the previous examples ‘to be’ and ‘not to be’ are additions, while the actual things that are subjects are white and man, so here ‘to be’ serves as subject, while ‘to be possible’ [30] and ‘to be admissible’ are additions—these determining the possible and not possible in the case of ‘to be’, just as in the previous cases ‘to be’ and ‘not to be’ determine the true.
The negation of ‘possible not to be’ is ‘not possible not to be’. This is why [35] ‘possible to be’ and ‘possible not to be’ may be thought actually to follow from one another. For it is possible for the same thing to be and not to be: such statements are not contradictories of one another. But ‘possible to be’ and ‘not possible to be’ never [22a1] hold together, because they are opposites. Nor do ‘possible not to be’ and ‘not possible not to be’ ever hold together.
Similarly, the negation of ‘necessary to be’ is not ‘necessary not to be’ but ‘not [5] necessary to be’; and of ‘necessary not to be’, ‘not necessary not to be’. And of ‘impossible to be’ it is not ‘impossible not to be’ but ‘not impossible to be’; and of ‘impossible not to be’, ‘not impossible not to be’. Universally, indeed, as has been said, one must treat ‘to be’ and ‘not to be’ as the subjects, and these others must be joined on to ‘to be’ and ‘not to be’ to make affirmations and negations. We must take [10] the opposite expressions to be these: possible—not possible; admissible—not admissible; impossible—not impossible; necessary—not necessary; true—not true.
13 · With this treatment the implications work out in a reasonable way. From ‘possible to be’ follow ‘admissible to be’ (and, reciprocally, the former from [15] the latter) and ‘not impossible to be’ and ‘not necessary to be’. From ‘possible not to be’ and ‘admissible not to be’ follow both ‘not necessary not to be’ and ‘not impossible not to be’. From ‘not possible to be’ and ‘not admissible to be’ follow ‘necessary not to be’ and ‘impossible to be’. From ‘not possible not to be’ and ‘not [20] admissible not to be’ follow ‘necessary to be’ and ‘impossible not to be’. What we are saying can be seen from the following table.
I |
II |
|---|---|
possible to be |
not possible to be |
III |
IV |
possible not to be |
not possible not to be |
‘Impossible’ and ‘not impossible’ follow from ‘admissible’ and ‘possible’ and ‘not possible’ and ‘not admissible’ contradictorily but conversely; for the negation of ‘impossible’ follows from ‘possible to be’, and the affirmation from the negation, [35] ‘impossible to be’ from ‘not possible to be’ (for ‘impossible to be’ is an affirmation, ‘not impossible’ a negation).
But what about the necessary? Evidently things are different here: it is contraries which follow, and the contradictories are separated. For the negation of ‘necessary not to be’ is not ‘not necessary to be’. For both may be true of the same [22b1] thing, since the necessary not to be is not necessary to be. The reason why these do not follow in the same way as the others is that it is when applied in a contrary way that ‘impossible’ and ‘necessary’ have the same force. For if it is impossible to be it is [5] necessary for this (not, to be, but) not to be; and if it is impossible not to be it is necessary for this to be. Thus if those follow from ‘possible’ and ‘not possible’ in the same way, these follow in a contrary way, since ‘necessary’ and ‘impossible’ do signify the same but (as we said) when applied conversely.
But perhaps it is impossible for the contradictories in the case of the necessary [10] to be placed thus? For the necessary to be is possible to be. (Otherwise the negation will follow, since it is necessary either to affirm or to deny it; and then, if it is not possible to be, it is impossible to be; so the necessary to be is impossible to [15] be—which is absurd.) However, from ‘possible to be’ follows ‘not impossible to be’, and from this follows ‘not necessary to be’; with the result that the necessary to be is not necessary to be—which is absurd.
However, it is not ‘necessary to be’ nor yet ‘necessary not to be’ that follows from ‘possible to be’. For with this both may happen, but whichever of the others is [20] true these will no longer be true; for it is at the same time possible to be and not to be, but if it is necessary to be or not to be it will not be possible for both. It remains, therefore, for ‘not necessary not to be’ to follow from ‘possible to be’; for this is true of ‘necessary to be’ also. Moreover, this proves to be contradictory to what follows [25] from ‘not possible to be’, since from that follow ‘impossible to be’ and ‘necessary not to be’, whose negation is ‘not necessary not to be’. So these contradictories, too, follow in the way stated, and nothing impossible results when they are so placed.
One might raise the question whether ‘possible to be’ follows from ‘necessary [30] to be’. For if it does not follow the contradictory will follow, ‘not possible to be’—or if one were to deny that this is the contradictory one must say that ‘possible not to be’ is; both of which are false of ‘necessary to be’. On the other hand, the same thing seems to be capable of being cut and of not being cut, of being and of not being, so [35] that the necessary to be will be admissible not to be; but this is false.
Well now, it is evident that not everything capable either of being or of walking is capable of the opposites also. There are cases of which this is not true. Firstly, with things capable non-rationally; fire, for example, can heat and has an irrational [23a1] capability. While the same rational capabilities are capabilities for more than one thing, for contraries, not all irrational capabilities are like this. Fire, as has been said, is not capable of heating and of not heating, and similarly with everything else that is actualized all the time. Some, indeed, even of the things with irrational [5] capabilities are at the same time capable of opposites. But the point of our remarks is that not every capability is for opposites—not even all those which are capabilities of the same kind.
Again, some capabilities are homonymous. For the capable is spoken of in more than one way: either because it is true as being actualized (e.g. it is capable of walking because it walks, and in general capable of being because what is called [10] capable already is in actuality), or because it might be actualized (e.g. it is capable of walking because it might walk). This latter capability applies to changeable things only, the former to unchangeable things also. (Of both it is true to say that it is not impossible for them to walk, or to be—both what is already walking and [15] actualized and what can walk.) Thus it is not true to assert the second kind of capability of that which is without qualification necessary, but it is true to assert the other. So, since the universal follows from the particular, from being of necessity there follows capability of being—though not every sort.
Perhaps, indeed, the necessary and not necessary are first principles of [20] everything’s either being or not being, and one should look at the others as following from these. It is evident from what has been said that what is of necessity is in actuality; so that, if the things which are eternal are prior, then also actuality is prior to capability. Some things are actualities without capability (like the primary substances), others with capability (and these are prior by nature but posterior in [25] time to the capability); and others are never actualities but only capabilities.
14 · Is the affirmation contrary to the negation, or the affirmation to the affirmation—the statement that every man is just contrary to the statement ‘no man is just’, or ‘every man is just’ contrary to ‘every man is unjust’? Take, for [30] example, Callias is just, Callias is not just, Callias is unjust; which of these are contraries?
Now if spoken sounds follow things in the mind, and there it is the belief of the contrary which is contrary (e.g. the belief that every man is just is contrary to the belief ‘every man is unjust’), the same must hold also of spoken affirmations. But if [35] it is not the case there that the belief of the contrary is contrary, neither will the affirmation be contrary to the affirmation, but rather the above-mentioned negation. So we must inquire what sort of true belief is contrary to a false belief, the belief of the negation or the belief that the contrary holds. What I mean is this: there is a true belief about the good, that it is good, another (false) one, that it is not [23b1] good, and yet another, that it is bad; now which of these is contrary to the true one? And if they are one belief, by reason of which is it contrary? (It is false to suppose that contrary beliefs are distinguished by being of contraries. For the belief about the good, that it is good, and the one about the bad, that it is bad, are perhaps the [5] same—and true, whether one belief or more than one. Yet these are contrary things. It is not, then, through being of contraries that beliefs are contrary, but rather through being to the contrary effect.)
Now about the good there is the belief that it is good, the belief that it is not good, and the belief that it is something else, something which does not and cannot hold of it. (We must not take any of the other beliefs, either to the effect that what does not hold holds or to the effect that what holds does not hold—for there is an [10] indefinite number of both kinds, both of those to the effect that what does not hold holds and of those to the effect that what holds does not hold—but only those in which there is deception. And these are from things from which comings-into-being arise. But comings-into-being are from opposites. So also, then, are cases of deceit.) Now the good is both good and not bad, the one in itself, the other accidentally (for [15] it is accidental to it to be not bad); but the more true belief about anything is the one about what it is in itself; and if this holds for the true it holds also for the false. Therefore the belief that the good is not good is a false belief about what holds in itself, while the belief that it is bad is a false belief about what holds accidentally, so [20] that the more false belief about the good would be that of the negation rather than that of the contrary. But it is he who holds the contrary belief who is most deceived with regard to anything, since contraries are among things which differ most with regard to the same thing. If, therefore, one of these is contrary, and the belief of the contradiction is more contrary, clearly this must be the contrary. The belief that the [25] good is bad is complex; for the same person must perhaps suppose also that it is not good.
Further, if in other cases also the same must hold, it would seem that we have given the correct account of this one as well. For either everywhere that of the contradiction is the contrary, or nowhere. But in cases where there are no contraries [30] there is still a false belief, the one opposite to the true one; e.g. he who thinks that the man is not a man is deceived. If, therefore, these are contraries, so too elsewhere are the beliefs of the contradiction.
Further, the belief about the good that it is good and that about the not good that it is not good are alike; and so, too, are the belief about the good that it is not [35] good and that about the not good that it is good. What belief then is contrary to the true belief about the not good that it is not good? Certainly not the one which says that it is bad, for this might sometimes be true at the same time, while a true belief is never contrary to a true one. (There is something not good which is bad, so that it is possible for both to be true at the same time.) Nor again is it the belief that it is not bad, for these also might hold at the same time. There remains, then, as [24a1] contrary to the belief about the not good that it is not good, the belief about the not good that it is good. Hence, too, the belief about the good that it is not good is contrary to that about the good that it is good.
Evidently it will make no difference even if we make the affirmation [5] universally. For the universal negation will be contrary; e.g. the belief that none of the goods is good will be contrary to the belief to the effect that every good is good. For if in the belief about the good that it is good ‘the good’ is taken universally, it is the same as the belief that whatever is good is good. And this is no different from the belief that everything which is good is good. And similarly also in the case of the not [24b1] good.
If then this is how it is with beliefs, and spoken affirmations and negations are symbols of things in the soul, clearly it is the universal negation about the same thing that is contrary to an affirmation; e.g. the contrary of ‘every good is good’ or ‘every man is good’ is ‘no good is good’ or ‘no man is good’, while ‘not every good is [5] good’ or ‘not every man is good’ are opposed contradictorily. Evidently also it is not possible for either a true belief or a true contradictory statement to be contrary to a true one. For contraries are those which enclose their opposites; and while these latter may possibly be said truly by the same person, it is not possible for contraries to hold of the same thing at the same time.