The article deals with the reflections on determinism which appeared in the context of ancient and modern logic beginning with Aristotle’s famous Argument of the Sea Battle in the ninth chapter of his On Interpretation. The canonical interpretation of this passage is put forward according to which the unlimited validity of the Principle of Bivalence seems to imply determinism, which in turn constitutes a reason for limiting the validity of that principle while preserving the Principle of Excluded Middle. Several strategies are shown which have been used by various thinkers when coming to terms with this argument, and the argument is ultimately put into the wider context of Aristotle’s philosophy. As a reaction to the aforementioned argument the article then discusses the so-called Master Argument which originates in the Megaric school. Its reconstruction is undertaken, presenting it as an attack on Aristotle’s conception of modality, and certain objections are raised which disqualify the argument in its given form. The Stoics accepted the Argument of the Sea Battle, with its deterministic consequences, and they thus became unequivocal proponents of the unlimited validity of the Principle of Bivalence, something which showed itself in, for example, the Stoic conception of negation. The Principle of Bivalence became, with the Stoics, the foundation for the causal argument for determinism. It seems that the Epicureans, in their polemical exchanges with the Stoics, failed to consider this assumption. In the reflections of Jan Lukasiewicz on the subject of determinism, one can detect a link with the ancient problematic. Lukasiewicz, however, makes the causal argument the premise of a modified Argument of the Sea Battle and, because of a reluctance to accept determinism, infers that the Principle of Bivalence must be limited, which, in the form that he states it, leads to the rise of many-valued logic.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.