Capítulo 16. Chapter XVI.—Concerning Becoming And Perishing
[3.16.109] Both becoming and perishing are included in the refutation of addition and subtraction and physical change; for apart from these nothing would become or perish. Thus, for instance, it is as a result of the perishing of the ten, as they say, that the nine becomes by the subtraction of one, and the ten from the perishing of the nine by the addition of one; and rust becomes from the perishing of bronze by means of change. Hence, if the aforesaid motions are abolished it is likely that becoming and perishing are also necessarily abolished.
[3.16.110] Yet none the less some argue also as follows:[421] If Socrates was born, Socrates became either when Socrates existed not or when Socrates already existed; but if he shall be said to have become when he already existed, he will have become twice; and if when he did not exist, Socrates was both existent and non- existent at the same time—existent through having become, non-existent by hypothesis.
[3.16.111] And if Socrates died, he died either when he lived or when he died. Now he did not die when he lived, since he would have been at once both alive and dead; nor yet when he died, since he would have been dead twice. Therefore Socrates did not die. And by applying this argument in turn to each of the things said to become or perish it is possible to abolish becoming and perishing.
[3.16.112] Some also argue thus:[422] If a thing becomes, either the existent becomes or the non-existent. But the non-existent does not become; for to the non-existent nothing can occur; neither, therefore, can becoming occur. Nor does the existent become. For if the existent becomes, it becomes either in so far as it is existent or in so far as it is non-existent. Now in so far as it is non-existent it does not become. But if it becomes in so far as it is existent, then, since they assert that what becomes becomes other from other,[423] what becomes will be other than the existent, and that is non-existent. Therefore what becomes will be non-existent, which is nonsense.
[3.16.113] If, then, neither the non-existent becomes nor the existent, nothing becomes at all.
For the same reasons, neither does anything perish.[424] For if anything perishes, it is either the existent that perishes or the non-existent. Now the non-existent does not perish, for what perishes must be a subject of action. Nor yet does the existent perish. For it must perish either while continuing in existence or while not so continuing. And if it be while continuing in existence, it will be at one and the same time both existent and non-existent;
[3.16.114] for since it does not perish in so far as it is non-existent but in so far as it is existent, it will be other than the existent and therefore non-existent in so far as it is said to have perished, whereas in so far as it is said to perish while continuing in existence it will be existent. But it is absurd to say that the same thing is both existent and non-existent; therefore the existent does not perish while continuing in existence. And if the existent does not perish while continuing in existence but passes first into non-existence and then in this way perishes, it is no longer the existent that perishes but the non-existent; and this we have shown to be impossible. If, then, neither the existent perishes nor the non-existent, and besides these there is nothing else, nothing perishes at all.
This account of the motions[425] will suffice by way of outline, and therefrom it follows that the Physical Science of the Dogmatists is unreal and inconceivable.