Review of Symbolic Logic 13 (4):748-775 (2020)

Authors
Adam Bjorndahl
Carnegie Mellon University
Abstract
In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge 35. Building on Stalnaker’s core insights, and using frameworks developed in 11 and 3, we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and what is knowable; we argue that the foundational axioms of Stalnaker’s system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an “evidence-in-hand” conception of knowledge and a weaker “evidence-out-there” notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker’s postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics.
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DOI 10.1017/s1755020319000509
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References found in this work BETA

Knowledge and its Limits.Timothy Williamson - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.
Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
Dynamic Logic for Belief Revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.
Knowledge: Undefeated Justified True Belief.Keith Lehrer & Thomas Paxson - 1969 - Journal of Philosophy 66 (8):225-237.
A Logical Analysis of Some Value Concepts.Frederic Fitch - 1963 - Journal of Symbolic Logic 28 (2):135-142.

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Citations of this work BETA

Formal Representations of Belief.Franz Huber - 2008 - Stanford Encyclopedia of Philosophy.

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