Truth and Subjunctive Theories of Knowledge: No Luck?

TL;DR

This paper investigates applying Kripke's theory of truth to subjunctive theories of knowledge, demonstrating fixed points exist despite non-monotonic semantics, thus supporting the use of Kripke's framework in anti-luck epistemology.

Contribution

It shows that Kripke's theory of truth can be effectively applied to non-monotone, subjunctive theories of knowledge using quasi-inductive definitions, overcoming previous limitations.

Findings

Kripke's jump has fixed points in non-monotone semantics.

Kripke's truth theory is compatible with subjunctive knowledge conditions.

Fixed point results are established for non-classical, non-monotone semantics.

Abstract

The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by mere luck as to be found in Gettier-style counterexamples to the analysis of knowledge as justified true belief. Because of the subjunctive nature of these conditions the resulting semantics turns out to be non-monotone, even if it is based on non-classical evaluation schemes such as strong Kleene or FDE. This blocks the usual road to fixed-point results for Kripke's theory of truth within these semantics and consequently the paper is predominantly an exploration of fixed point results for Kripke's theory of truth within non-monotone semantics. Using the theory of quasi-inductive definitions we show that in case of the subjunctive theories of knowledge the so-called Kripke jump will have fixed points despite the non-monotonicity of the semantics: Kripke's theory of truth can be successfully applied in the framework of subjunctive theories of knowledge.