To be Cancelled or Not Cancelled?

Aristotle, On Interpretation 19a

“What is exists whenever it does; what does not exist does not exist when it does not. Still, there’s no necessity to everything in existing or not existing. For it is not the same thing to say that everything that exists does exist and that everything exists by necessity when it occurs. Clearly, it is the same with things that do not exist.

The same argument obtains here as with contrary statements. Everything necessarily exists or does not exist and will be or will not be. But it it not possible for us to say which thing will necessarily happen. For example, I say that there will be a sea-battle tomorrow or maybe there won’t be. There’s certainly nothing to make it necessary that a sea-battle will happen tomorrow or not. But it is certainly necessary that it either happens or it doesn’t.”

Τὸ μὲν οὖν εἶναι τὸ ὂν ὅταν ᾖ, καὶ τὸ μὴ ὂν μὴ εἶναι ὅταν μὴ ᾖ, ἀνάγκη· οὐ μὴν οὔτε τὸ ὂν ἅπαν ἀνάγκη εἶναι οὔτε τὸ μὴ ὂν μὴ εἶναι. οὐ γὰρ ταὐτόν ἐστι τὸ ὂν ἅπαν εἶναι ἐξ ἀνάγκης ὅτε ἔστι, καὶ τὸ ἁπλῶς εἶναι ἐξ ἀνάγκης. ὁμοίως δὲ καὶ ἐπὶ τοῦ μὴ ὄντος. καὶ ἐπὶ τῆς ἀντιφάσεως ὁ αὐτὸς λόγος. εἶναι μὲν ἢ μὴ εἶναι ἅπαν ἀνάγκη, καὶ ἔσεσθαί γε ἢ μή· οὐ μέντοι διελόντα γε εἰπεῖν θάτερον ἀναγκαῖον. λέγω δὲ οἷον ἀνάγκη μὲν ἔσεσθαι ναυμαχίαν αὔριον ἢ μὴ ἔσεσθαι, οὐ μέντοι ἔσεσθαί γε αὔριον ναυμαχίαν ἀναγκαῖον οὐδὲ μὴ γενέσθαι· γενέσθαι μέντοι ἢ μὴ γενέσθαι ἀναγκαῖον.

File:Gent, Justus van - Aristotle - c. 1476.jpg
Justus van Gent, Aristotle 1476

Zeno (Aristotle, Metaphysics, Β 4.1001 b7)



[Zeno said that] “That which does not make something bigger or smaller when it is added or taken away is not real.”


ὃ γὰρ  µήτε προστιθέµενον µήτε ἀφαιρούµενον ποιεῖ µεῖζον

µηδὲ ἔλαττον, οὔ φησιν εἶναι τοῦτο τῶν ὄντων


From Zeno of Elea, a student of Parmenides.  Famous for paradoxes (he even appears as an interlocutor for Socrates in Plato’s Parmenides).

(Not the Zeno who founded Stoicism)