Knowability and bivalence: Intuitionistic solutions to the paradox of knowability [Book Review]

Philosophical Studies 149 (2):269 - 281 (2010)
Abstract
In this paper, I focus on some intuitionistic solutions to the Paradox of Knowability. I first consider the relatively little discussed idea that, on an intuitionistic interpretation of the conditional, there is no paradox to start with. I show that this proposal only works if proofs are thought of as tokens, and suggest that anti-realists themselves have good reasons for thinking of proofs as types. In then turn to more standard intuitionistic treatments, as proposed by Timothy Williamson and, most recently, Michael Dummett. Intuitionists can either point out the intuitionistc invalidity of the inference from the claim that all truths are knowable to the insane conclusion that all truths are known, or they can outright demur from asserting the existence of forever-unknown truths, perhaps questioning—as Dummett now suggests—the applicability of the Principle of Bivalence to a certain class of empirical statements. I argue that if intuitionists reject strict finitism—the view that all truths are knowable by beings just like us—the prospects for either proposal look bleak.
Keywords Paradox of Knowability  Semantic anti-realism  Bivalence  Idealisation  Intuitionistic conditional
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References found in this work BETA
Michael Dummett (2007). Reply to Crispin Wright. In R. E. Auxier & L. E. Hahn (eds.), The Philosophy of Michael Dummett. Open Court. 445--454.
Michael Dummett (1987). Reply to Dag Prawitz. In Barry Taylor (ed.), Michael Dummett: Contributions to Philosophy. Distributors for the United States and Canada, Kluwer Academic Publishers. 281--316.

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