by Aristotle
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
admissible to be
not impossible to be
not necessary to be
not possible to be
not admissible to be [25]
impossible to be
necessary not to be
III
IV
possible not to be
admissible not to be
not impossible not to be
not necessary not to be
not possible not to be
not admissible not to be
impossible not to be [30]
necessary 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. (Othe
rwise 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.
**TEXT: L. Minio-Paluello, OCT, Oxford, 1956, 2nd ed.
1‘Sentence’ here and hereafter translates λόγoς.
2See de Anima III 3–8.
3Read oὐδὲ γάρ.
4Read λευκòν καὶ μέγα.
5Read εἰ δὲ ύπάρξει …, ύπάρξειν …
6See Prior Analytics I 46.
7See esp. Topics VIII.
8Read μoυσικòν ὲν.
PRIOR ANALYTICS**
A. J. Jenkinson
BOOK I
1 · First we must state the subject of the enquiry and what it is about: the [24a10] subject is demonstration, and it is about demonstrative understanding.1 Next we must determine what a proposition2 is, what a term is, and what a deduction3 is (and what sort of deduction is perfect and what imperfect); and after that, what it is for one thing to be or not be in another as a whole, and what we mean by being predicated of every or of no. [15]