Aristotle's "Sea Battle" Scenario: a matter of Strict versus Lazy Evaluation

Abstract

From Aristotle's "de Interpretatione IX" we are familiar with the famous scenario: "tomorrow there will be a sea battle, OR tomorrow there will be NO sea battle". From a purely syntactic-formal point of view, Aristotle's example sentence has the form S = (B v ~B) which ought to be tautologically true in Aristotle's own classical bi-valent logic which was based on the principle of "tertium non datur" (TND). For this specific example S, however, Aristotle abandoned his own TND principle as he was (unnecessarily) worried that a logical tautology of sentences with future contingencies in their material semantics would imply an ontological determinism in history. As an opponent of ontological-historic determinism, Aristotle thus decided to forbid the application of the TND principle in all sentences that materially express future contingencies. Formally, this corresponds to a strict interpretation of the trivalent Kleene Logic with its third truth value U, in which (B v ~B) with I(B)=U is no tautology. Philosophically, however, the questions arise: Are we anyhow "forced" to "follow" Aristotle in his decision to abandon the TND principle for future contingencies? Or do we have an alternative option to "rescue" the TND principle also for future contingency sentences - and, if yes, how? In this PSSA'24 talk it is argued that the TND principle can indeed be "reconciled" with future contingencies and Kleene's U if we admit as a valid method of formal reasoning the so-called "Lazy Evaluation" strategy for which we can find application examples both in classical Mathematics as well as modern Informatics (Computer Science). A full paper, in which the main argument of this talk shall be elaborated in further details, shall be forthcoming in due course.