Abstract

In this highly original text, Christopher Steinsvold explores an alternative semantics for logics of rational belief. Topologies, as mathematical objects, are typically interpreted in terms of space; here topologies are re-interpreted in terms of an agent with rational beliefs. The topological semantics tells us that the agent can never, in principle, know everything; that the agent's beliefs can never be complete. A number of completeness proofs are given for a variety of logics of rational belief. Beyond this, the author explores the philosophical question of why our beliefs can never be complete, and considers the possibility that a totality of truths is a dialethia. This work will be of interest to all philosophers interested in epistemology, and modal logicians as well.