Fitch's Paradox and Level-Bridging Principles

Journal of Philosophy 117 (1):5-29 (2020)
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Abstract

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result is in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig.

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Weng Kin San
New York University

References found in this work

Knowledge and its limits.Timothy Williamson - 2000 - New York: Oxford University Press.
Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.
Constructing the World.David Chalmers (ed.) - 2012 - Oxford: Oxford University Press.
Knowledge and Its Limits.Timothy Williamson - 2005 - Philosophy and Phenomenological Research 70 (2):452-458.
Blindspots.Roy A. Sorensen - 1988 - New York: Oxford University Press.

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