How to Lewis a Kripke–Hintikka

Alessandro Torza

pp. 743-779

in: Johan van Benthem, Vincent F. Hendricks, John Symons (eds), Between logic and intuition, Synthese 190 (4), 2013.

Abstract

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics.

Cited authors

Lewis David

Kripke Saul

Hintikka Jaakko