The Logic(s) of Modal Knowledge

Abstract

This paper discusses, with the help of three examples from modal epistemology, what we can learn from formal considerations when using logic as a tool for rational reconstructions of cognitive processes. The purpose of these rational reconstructions is to explain how a certain cognitive process might eventually result in knowledge (or justi ed beliefs, etc.), if we pre-theoretically think that we have such knowledge or such justi ed beliefs. Traditionally, a rational reconstruction assumes some (more or less) unproblematic basis of knowledge and some justi cation-preserving inference pattern and then goes on to show how these two suce to generate the explicandum. In modal epistemology we try to apply the project of analytic epistemology to our knowledge of necessities and possibilities. The \method" of conceivability, as the cognitive process by which we arrive at knowledge of possibilities, is thus to be reconstructed as some sort of inference pattern by which we reason from (more or less) unproblematic knowledge to knowledge of possibilities. This paper discusses several ways how this could be done, including Carnap's modal logic C [Sch01], Diderik Batens' and Joke Meheus' Adaptive Logic of Compatibility [Meh00], and Timothy Williamson's \Modal Logic within Counterfactual Logic" [Wil07]. As we will see, there is no one logic, that captures all aspects of modal reasoning, but a plurality of di erent formal tools that help us to understand better di erent aspects of how we know what is possible and what is necessary.