Synthese 194 (10):3955-3977 (2017)

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Abstract
Some propositions are structurally unknowable for certain agents. Let me call them ‘Moorean propositions’. The structural unknowability of Moorean propositions is normally taken to pave the way towards proving a familiar paradox from epistemic logic—the so-called ‘Knowability Paradox’, or ‘Fitch’s Paradox’—which purports to show that if all truths are knowable, then all truths are in fact known. The present paper explores how to translate Moorean statements into a probabilistic language. A successful translation should enable us to derive a version of Fitch’s Paradox in a probabilistic setting. I offer a suitable schematic form for probabilistic Moorean propositions, as well as a concomitant proof of a probabilistic Knowability Paradox. Moreover, I argue that traditional candidates to play the role of probabilistic Moorean propositions will not do. In particular, we can show that violations of the so-called ‘Reflection Principle’ in probability need not yield structurally unknowable propositions. Among other things, this should lead us to question whether violating the Reflection Principle actually amounts to a clear case of epistemic irrationality, as it is often assumed. This result challenges the importance of the principle as a tool to assess both synchronic and diachronic rationality—a topic which is largely independent of Fitch’s Paradox—from a somewhat unexpected source.
Keywords Knowability  Fitch’s Paradox  Moore  Reflection Principle
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DOI 10.1007/s11229-015-0884-0
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References found in this work BETA

The Taming of the True.Neil Tennant - 1997 - Oxford, England: Oxford University Press.
Very Improbable Knowing.Timothy Williamson - 2014 - Erkenntnis 79 (5):971-999.
Ulysses and the Sirens: Studies in Rationality and Irrationality.Jon Elster (ed.) - 1979 - Editions De La Maison des Sciences De L'Homme.
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

Abominable KK Failures.Kevin Dorst - 2019 - Mind 128 (512):1227-1259.
A Tale of Two Epistemologies?Alan Hájek & Hanti Lin - 2017 - Res Philosophica 94 (2):207-232.
Fitch's Paradox and Level-Bridging Principles.Weng Kin San - 2020 - Journal of Philosophy 117 (1):5-29.

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Fitch's Paradox of Knowability.Berit Brogaard & Joe Salerno - 2010 - The Stanford Encyclopedia of Philosophy.
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