Fitch's Argument and Typing Knowledge
Alexander Paseau
Source: Notre Dame J. Formal Logic Volume 49, Number 2 (2008), 153-176.
Abstract
Fitch's argument purports to show that if all truths are knowable then all truths are known. The argument exploits the fact that the knowledge predicate or operator is untyped and may thus apply to sentences containing itself. This article outlines a response to Fitch's argument based on the idea that knowledge is typed. The first part of the article outlines the philosophical motivation for the view, comparing it to the motivation behind typing truth. The second, formal part presents a logic in which knowledge is typed and demonstrates that it allows nonlogical truths to be knowable yet unknown.
Primary Subjects: 03B42
Keywords: Fitch; knowledge; type theory; knowability; epistemic paradox; epistemic logic
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1210859925
Digital Object Identifier: doi:10.1215/00294527-2008-005
Mathematical Reviews number (MathSciNet):
MR2402039
Zentralblatt MATH identifier:
1141.03003
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Notre Dame Journal of Formal Logic
