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Łukasiewicz, the sea battle, and why three-valued logic was born in Lwów

In De Interpretatione 9 Aristotle considers the sentence "there will be a sea battle tomorrow". If it is already true today, isn't the battle already necessary? And if so, isn't deliberation pointless?

Around 1920 Jan Łukasiewicz, working in the Lwów–Warsaw school founded by Twardowski, introduced a third truth value, often glossed as "possible", for statements like this. His motivation was explicitly philosophical: he wanted to protect indeterminism and freedom.

Modern approaches mostly prefer supervaluationism (Thomason, 1970). "Either there will be a sea battle or there won't" comes out true, though neither disjunct is yet true, which is one way to keep classical logic for compound statements.

What I'd like to discuss: did Aristotle himself deny bivalence for future contingents, or only that their truth is necessary? The text supports both readings depending on how you translate a few lines.

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  1. Giulia Ferrante

    Fellow

    The ancient commentators already split on this. Ammonius and Boethius read Aristotle as saying future contingents are true or false, but only "indefinitely", not definitely. It's a third way that sits between your two readings.

    Helpful · 3
  2. Layla Haddad

    Fellow

    Al-Fārābī wrote a long commentary on De Interpretatione that spends a lot of time on chapter 9, partly because the theological stakes were obvious: if God knows the future, the sea battle is already settled. Zimmermann's English translation is very readable.

    1. Tomasz Wójcik

      Fellow

      Yes, divine foreknowledge sharpens the whole problem. It's the same structure Łukasiewicz saw, only with an omniscient being doing the fixing instead of truth itself.

      Helpful · 1