Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality
This paper addresses Ludwig Wittgenstein’s claim that “there can never be surprises in logic” (TLP 6.1251) from a perspective of the distinction between substantial and dynamic models of formality. It attempts to provide an interpretation of this claim as stressing the dynamic formality of logic. Focusing on interactive interpretation
of compositionality as dynamic formality, it argues for the advantages of dynamic, i.e., game-theoretical approach to some binary semantical phenomena. Firstly, model-theoretical and game-theoretical interpretations of binary quantifiers are compared. Secondly, the paper offers an analysis ofWittgenstein’s idea that mixed colours (e.g., bluish green, reddish yellow, etc.) possess logical structures. To answer some experimental challenges, it provides a game-theoretical interpretation of the colours opponency in Payoff Independence (PI) logic. Comparing Nikolay Vasiliev’s logical principles and Wittgenstein’s internal properties and relations, Wittgenstein’s approach is argued for as an attempt of modelling a balance between logic and the empirical.