LESSON XV

It Is Concluded that Propositions Are True as They Correspond to

the Way in Which Things Are in Reality

             19a 23 Now that which is, when it is, necessarily is, and that which is not, when it is not, necessarily is not. But it is not necessary for everything that is, to be, nor is it necessary for that which is not, not to be. For these are not the same: that everything be necessarily when it is and to be simply from necessity. And the case is similar with respect to that which is not.

             19a 27 And this is also the case with respect to contradiction. It is necessary that everything be or not be; and that it will be or will not be; however, taking them separately, it is not possible to say one of the two is necessary. For example, it is necessary that there will or will not be a naval battle tomorrow; however, it is not necessary that a naval battle take place tomorrow, nor is it necessary that it not take place. Yet it is necessary that it either take place or not take place.

             19a 32 And so, since speech is true as it corresponds to things, it is clear that when things are such that they are indeterminate to either of two, and opposites are possible, the corresponding contradiction must be similar. This is the case in those things that do not always exist or always not exist. Of these it is necessary that one part of the contradiction be true or false, not however this or that part, but either of the two indeterminately. One may be more likely to be true, but it is not yet actually true or false.

             19a 39 Therefore it is clear that it is not necessary that of every affirmation and negation of opposites, one is true and one false. For the case is not the same in regard to those things that are and those that are not but could be or not be. It is as we have just stated.

             1. Now that the Philosopher has shown the impossibilities that follow from the foresaid arguments, he concludes what the truth is on this point. In arguing to the impossibility of the position, he proceeded from enunciations to things, and has already rejected the unlikely consequences in respect to things. Now, in the converse order, he first shows the way in which there is truth about things; secondly, the way in which there is truth in enunciations, where he says, And so, since speech is true as it corresponds to things, etc. With respect to truth about things he first shows the way in which there is truth and necessity about things absolutely considered; secondly, the way in which there is truth and necessity about things through a comparing of their opposites, where he says, And this is also the case with respect to contradiction, etc.

             2. He begins, then, as though concluding from premises: if the foresaid things are unlikely (namely, that all things take place of necessity), then the case with respect to things must be this: everything that is must be when it is, and everything that is not, necessarily not be when it is not. This necessity is founded on the principle that it is impossible at once to be and not be; for if something is, it is impossible that it at the same time not be; therefore it is necessary that it be at that time. For "impossible not to be" signifies the same thing as "necessary to be," as Aristotle says in the second book.

             Similarly, if something is not, it is impossible that it at the same time be. Therefore it is necessary that it not be, for they also signify the same thing. Clearly it is true, then, that everything that is must be when it is, and everything that is not must not be when it is not.

             This is not absolute necessity, but necessity by supposition. Consequently, it cannot be said absolutely and simply that everything that is must be, and that everything that is not must not be. For "every being, when it is, necessarily is" does not signify the same thing as "every being necessarily is, simply." The first signifies necessity by supposition, the second, absolute necessity.

             What has been said about to be must be understood to apply also to not to be, for "necessarily not to be simply" and "necessarily not to be when it is not" are also different.

             By this Aristotle seems to exclude what was said above, namely, that if in those things that are, one of the two is determinately true, then even before it takes place one of the two would determinately be going to be.

             3. He shows how truth and necessity is had about things through the comparing of their opposites where he says, This is also the case with respect to contradiction, etc. The reasoning is the same, he says, in respect to contradiction and in respect to supposition. For just as that which is not absolutely necessary becomes necessary by supposition of the same (for it must be when it is), so also what in itself is not necessary absolutely, becomes necessary through the disjunction of the opposite, for of each thing it is necessary that it is or is not, and that it will or will not be in the future, and this under disjunction. This necessity is founded upon the principle that it is impossible for contradictories to be at once true and false. Accordingly, it is impossible that a thing neither be nor not be; therefore it is necessary that it either be or not be. However if one of these is taken separately [i.e., divisively], it is not necessary that that one be absolutely. This he manifests by example: it is necessary that there will be or will not be a naval battle tomorrow; but it is not necessary that a naval battle will take place tomorrow, nor is it necessary that it will not take place, for this pertains to absolute necessity. It is necessary, however, that it will take place or will not take place tomorrow. This pertains to the necessity which is under disjunction.

             4. Then when he says, And so, since speech is true as it corresponds to things, etc., he shows how truth in speech corresponds to the way things are. First he shows in what way truth of speech conforms to the being and nonbeing of things; secondly, and finally, he arrives at the truth of the whole question, where he says, Therefore it is clear that it is not necessary that of every affirmation and negation of opposites, one is true and one false, etc.

             He says, then, that enunciative speech is related to truth in the way the thing is to being or nonbeing (for from the fact that a thing is or is not, speech is true or false). It follows, therefore, that when things are such as to be indeterminate to either of two, and when they are such that their contradictories could happen in whichever way, whether equally or one for the most part, the contradiction of enunciations must also be such.

             He explains next what the things are in which contradictories can happen. They are those that neither always are (i.e., the necessary), nor always are not (i.e., the impossible), but sometimes are and sometimes are not. He shows further how this is maintained in contradictory enunciations. In those enunciations that are about contingent things, one part of the contradiction must be true or false under disjunction; but it is related to either, not to this or that determinately. If it should turn out that one part of the contradiction is more true, as happens in contingents that are for the most part, it is nevertheless not necessary on this account that one of them is determinately true or false.

             5. Then he says, Therefore, it is clear that it is not necessary that of every affirmation and negation of opposites, one is true and one false, etc. This is the conclusion he principally intended. It is evident from what has been said that it is not necessary in every genus of affirmation and negation of opposites that one is determinately true and the other false, for truth and falsity is not had in the same way in regard to things that are already in the present and those that are not but which could be or not be. The position in regard to each has been explained. In those that are, it is necessary that one of them be determinately true and the other false; in things that are future, which could be or not be, the case is not the same. The first book ends with this.