The paradox of idealization

Analysis 69 (3):461-469 (2009)
Abstract
A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn (1976), many solutions to the paradox have been offered. In this article, we present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable.
Keywords Knowability  Anti-realism  Idealisation  Fitch's Paradox
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DOI 10.1093/analys/anp069
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References found in this work BETA
Wang's Paradox.Michael Dummett - 1975 - Synthese 30 (3-4):201--32.
Fitch's Argument and Typing Knowledge.Alexander Paseau - 2008 - Notre Dame Journal of Formal Logic 49 (2):153-176.
Intuitionism Disproved?Timothy Williamson - 1982 - Analysis 42 (4):203--7.

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