Epistemic logic with evidence and relevant alternatives

Zhaoqing Xu

Bo Chen

Peking University

pp. 535-555

in: Hans van Ditmarsch, Paul-Gabriel Sandu (eds), Jaakko Hintikka on knowledge and game-theoretical semantics, Berlin, Springer, 2018

Abstract

Starting with Jaakko Hintikka's seminal work, epistemic logic has now grown up to a huge academic industry. When we look back to its history, however, there is a practical paradox. While Hintikka's original purpose was to facilitate epistemological discussion, most subsequent work of epistemic logic has been done outside of philosophy, and has been ignored by most mainstream epistemologists. At the current point, one might naturally wonder, does epistemic logic still have something to do with epistemology? Along with Hintikka and a growing number of formal epistemologists, we believe the answer is "yes". Contemporary epistemology has largely focused on the goal of providing an analysis of knowledge and an answer to skepticism. To avoid skepticism, many epistemologists prefer to define knowledge in terms of evidence and relevant alternatives. A typical saying is that "in order to know that p, one only needs evidence to eliminate all relevant alternatives, rather than all alternatives". We see such a project as perfectly congenial to the spirit of Hintikka's epistemic logic. In this paper, we propose an epistemic logic (EREL) to deal with evidence and relevant alternatives explicitly, and extend EREL to its dynamic version (PARL) to investigate how different notions of knowledge behavior with the decrease and increase of relevant alternatives. To illustrate its philosophical application, we provide a new formalization of the so called factivity problem of epistemic contextualism. We conclude with some remarks on further developments of our framework.

Cited authors

Hintikka Jaakko