## Notre Dame Journal of Formal Logic

### Fitch's Argument and Typing Knowledge

Alexander Paseau

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 15 May 2008

https://projecteuclid.org/euclid.ndjfl/1210859925

Digital Object Identifier
doi:10.1215/00294527-2008-005

Mathematical Reviews number (MathSciNet)
MR2402039

Zentralblatt MATH identifier
1141.03003

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

#### Citation

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. https://projecteuclid.org/euclid.ndjfl/1210859925.

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