Notre Dame Journal of Formal Logic

Fitch's Argument and Typing Knowledge

Alexander Paseau


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.

Article information

Notre Dame J. Formal Logic Volume 49, Number 2 (2008), 153-176.

First available in Project Euclid: 15 May 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B42: Logics of knowledge and belief (including belief change)

Fitch knowledge type theory knowability epistemic paradox epistemic logic


Paseau, Alexander. Fitch's Argument and Typing Knowledge. Notre Dame J. Formal Logic 49 (2008), no. 2, 153--176. doi:10.1215/00294527-2008-005.

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