Topological Models of Belief Logics

Dissertation, Cuny Graduate Center (2007)
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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.



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Citations of this work

A Computational Learning Semantics for Inductive Empirical Knowledge.Kevin T. Kelly - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Springer International Publishing. pp. 289-337.
Johan van Benthem on Logic and Information Dynamics.Alexandru Baltag & Sonja Smets (eds.) - 2014 - Cham, Switzerland: Springer International Publishing.
Some Formal Semantics for Epistemic Modesty.Christopher Steinsvold - 2020 - Logic and Logical Philosophy 29 (3):381-413.

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