Ancient Discussion on Determinism from the Perspective of a Branching Time

Abstract

The paper is devoted to the problem of the Master Argument– a historical argu ment of the Greek philosopher Diodorus Cronus. The objective of Diodorus’ argument was to evidence the correctness of the temporarily defined modalities: necessity and probability. Since the original argument was lost, many contemporary logicians have tried to reformulate it, using modern tools of logic. We present the philosophical significance of one of such reconstructions, relying on the monograph (On the Sea Battle Tomorrow That May Not Happen. A Logical and Philosophical Analysis of the Master Argument), by showing that some reconstructions of the Master Argument allowed to be interpreted in the branching time structures. This is the main argument to prove that despite the acceptance of Diodorus’ notions, the Aristotelian Sea-Battle Tomorrow may still happen or not happen. On the one hand, we focus on problems of logical tools of temporal logic and logical structures of time involved in the reconstructions of Diodorus’ argument. We mainly compare Jarmu˙ zek’s proposal with another reconstruction, also founded upon positional logic. On the other hand, we show what kind of structures must be assumed if the inferences are valid. This enables us to discuss branching and non–branching time structures that correspond to philosophical deterministic and indeterministic views on the nature of time. We conclude that logical analysis of the Master Argument raises some methodological hints for the joint use of historical and logical analysis.