Chapter 9 derives determinism from a single premise: every affirmation and negation is either true or false (excluded middle plus bivalence).
One person now says “there will be a sea battle tomorrow,” another says “there will not.” Their sentences are a contradictory pair, so one of them must be true. In that case, that truth already holds — now. And if it has been true all along, then the thing cannot but happen. So every event of “tomorrow” becomes necessary.
Οὐδὲν ἄρα οὔτε ἔστιν οὔτε γίνεται οὔτε ἀπὸ τύχης οὔθ᾿ ὁπότερ᾿ ἔτυχεν … ἀλλ᾿ ἐξ ἀνάγκης ἅπαντα.
Nothing, then, either is or comes to be by chance or as things chance to fall … but everything by necessity. (ch. 9, 18b; Greek quotations throughout, Japanese and English are L/LAB working translations.)
Aristotle rejects this conclusion as “absurd (ἄτοπον).” It would make deliberation and preparation useless — yet we plainly see that acting is a starting point of what will be.
Aristotle’s cut
His counter-example is an everyday one.
τουτὶ τὸ ἱμάτιον δυνατόν ἐστι διατμηθῆναι καὶ οὐ διατμηθήσεται, ἀλλ᾿ ἔμπροσθεν κατατριβήσεται.
This cloak is capable of being cut up, and it will not be cut up, but will wear out first. (ch. 9, 19a)
“Can be cut up” and “can end up uncut” — both are real possibilities. The future holds things that fall “either way (ὁπότερ᾿ ἔτυχεν).” And so Aristotle concludes:
ἀνάγκη μὲν ἔσεσθαι ναυμαχίαν αὔριον ἢ μὴ ἔσεσθαι, οὐ μέντοι ἔσεσθαί γε αὔριον ναυμαχίαν ἀναγκαῖον οὐδὲ μὴ γενέσθαι· γενέσθαι μέντοι ἢ μὴ γενέσθαι ἀναγκαῖον.
It is necessary that a sea battle either will or will not take place tomorrow — but it is not necessary that a sea battle take place tomorrow, nor that it not take place; that it either take place or not, however, is necessary. (ch. 9, 19a)
The whole disjunction “A ∨ ¬A” is necessary. But neither disjunct is fixed as true now. That is Aristotle’s solution.
Two readings, and the afterlife
The reading of this one chapter has been split since antiquity.
- The traditional reading: for future contingent events, Aristotle restricts bivalence. “There will be a sea battle” is now neither true nor false (a truth-value gap, or a third value).
- Another reading: true-or-false still holds now, but not definitely (not in a settled way). Only necessity is denied; bivalence is kept.
Either way, the influence is vast. The Stoic Diodorus Cronus went the other way and chose determinism (the “Master Argument”); the Middle Ages laboured over reconciling divine foreknowledge with future contingency. And in 1920, motivated by exactly this chapter, Łukasiewicz built three-valued logic (true, false, undetermined). The single word “tomorrow” has kept logic moving for more than two thousand years.