Adequate conditionals and Kripke's theory of truth

TL;DR

This paper introduces a new supervaluational framework called strong Kleene supervaluation to incorporate conditionals into Kripke's theory of truth, ensuring the deduction theorem holds and better handling semantic indeterminacy.

Contribution

It develops a novel supervaluational approach that allows for the integration of conditionals into Kripke's truth theory while respecting logical deduction principles.

Findings

Successful integration of conditionals respecting the deduction theorem

Development of the strong Kleene supervaluation framework

Enhanced handling of semantic indeterminacy in truth theories

Abstract

In this paper we show how to introduce a conditional to Kripke's theory of truth that respects the deduction theorem for the consequence relation associated with the theory. To this effect we develop a novel supervaluational framework, called strong Kleene supervaluation, that we take to be a promising framework for handling the truth-conditions of non-monotone notion in the presence of semantic indeterminacy more generally.