Return to Aristotle, On Interpretation
1. Since, however, affirmation signifies something of something, and this is either a noun, or anonymous; but it is necessary that what is in affirmation should be one thing, and of one thing; all affirmation and negation, will be either from a noun and a verb, or from an indefinite noun and verb. But what a noun is, and what the anonymous, has been shown by us before. For I do not call not-man a noun, but an indefinite noun; since an indefinite noun in a certain respect signifies one thing; just as is not well, is not a verb, but an indefinite verb.
2. But without a verb there is no affirmation nor negation. For it is, or it will be, or it was, or it is becoming to be, and other things of the like kind are verbs, [as is evident] from what has been before asserted; since in addition to something else they signify time.
3. Hence the first affirmation and negation will be, man is, man is not; and afterwards, non-man is, non-man is not. Again, every man is, every man is not, every non-man is, every non-man is not; and there is the same reasoning in external times.
4. But when [the verb] is is additionally predicated as the third thing, then the oppositions are said to subsist doubly.
5. I say, for instance, a man is just: for here the word is, is, I say, composed as the third thing in this affirmation, whether it be [called] a noun or a verb. Hence, on this account, these will be four, of which two, indeed, will subsist with reference to affirmation and negation, according to the order of consecution, as privations, but two will not. But I say that [the verb] is either is added to the just, or to the non-just; and, therefore negation also is added. Hence there will be four. We shall understand, however, what is said from the underwritten [examples]: a man is just; the negation of this is, a man is not just. He is not a just man; of this the negation is, he is not not a just man. For here the [verb] is and is not are added to the just, and the not just. These, therefore, as we have shown in our Analytics are thus arranged.
6. The like also will take place if the affirmation is of a noun universally considered. For instance, every man is just: of this the negation is, not every man is just. Every man is not just, not every man is not just; except that it does not similarly happen that those which are diametrically opposed are co-verified. Sometimes, however, this happens to be the case.
7. These two, therefore, are opposed to each other.
8. But the other two [are similarly opposed to each other], with respect to non-man, as to a certain added subject. Thus, for instance, non-man is just, non-man is not just. That is not just which is not man, that is not not just which is not man.
9. There are not, however, more oppositions than these.
10. But these separate from those, will be themselves by themselves, as using the noun not-man.
11. But in those in which [the verb] is is not adapted, as in [the verbs] to be well and to walk, in these it effects the same when thus posited, as if [the verb] is were added. Thus, for instance, every man is well, every man is not well, every non-man is well, every non-man is not well.
12. For it must not be said, not every man, but the negation not must be added to man. For every does not signify the universal, but that [a thing is assumed universally]. But this is evident from what follows: a man is well, a man is not well; non-man is well, non-man is not well. For these differ from those, because they are not universally [assumed]. Hence every, or no one signifies nothing else than that affirmation or negation is of a noun universally [assumed]. It is necessary, therefore, to add other things in the same manner.
13. But because to this [affirmation] every animal is just, the negation is contrary, signifying that no animal is just, it is evident that these will never be at the same time true, nor in the same; but the opposites to these will be sometime or other [at one and the same time] true. Thus, for instance, not every animal is just, and some animal is just. But these follow: This indeed, no man is just follows that every man is not just; but the opposite, viz. Some man is just, follows this, not every man is not just; for it is necessary that some man should be just.
14. It is evident, however in particulars, that if any one being interrogated truly denies, [that which he denies] is also truly affirmed. For instance, is Socrates a wise man? No. Socrates, therefore, is not a wise man. But in universals [the affirmation] is not true, which similarly asserted; but the negation is true. For instance, is every man wise? No. Every man, therefore, is not wise. For this is false. But this, not every man, therefore, is wise, is true. And this is opposite, but that contrary.
15. But the opposites according to indefinite nouns and verbs, such as non-man, and non-just, may appear to be as it were negations without a noun and verb. They are not, however. For it is always necessary that negation should be either true or false. But he who says non-man does not speak more truly or falsely, but less so, unless something is added.
16. This assertion, however, every non-man is just, does not signify the same thing as some one of those [former enunciations]; nor the opposite to this, viz. not every non-man is just. But this assertion, every one not just is not a man, is the same with this, no one is just who is not a man.
17. Nouns and verbs, however, when transposed signify the same thing. For instance, he is a white man, he is a man white. For unless it is so, there will be many negations of the same thing. It has been shown, however, that there is one negation of one thing. For the negation of this assertion, he is a white man, is, he is not a white man. But of this assertion, he is a man white, unless it is the same with the enunciation he is a white man, the negation will either be, he is not not a man white, or he is not a man white. But the one is a negation of this, he is not a man white, and the other of this, he is a white man. It is evident, therefore, that a noun and verb being transposed, there will be the same affirmation and negation.
Return to Aristotle, On Interpretation
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