Philosophical Studies

, Volume 149, Issue 2, pp 269–281 | Cite as

Knowability and bivalence: intuitionistic solutions to the Paradox of Knowability

  • Julien MurziEmail author


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.


Paradox of Knowability Semantic anti-realism Bivalence Idealisation Intuitionistic conditional 



This is the sequel of a paper I wrote with my colleague and friend Salvatore Florio, to whom I am very much indebted. Many thanks to Dominic Gregory, Bob Hale, Stephen Read, Joe Salerno, Fredrik Stjernberg, Gabriele Usberti, Tim Williamson, and an anonymous referee for valuable comments and discussion on some of the topics discussed herein. An earlier version of this material was presented at the University of Cambridge and at the Eastern Division of the American Philosophical Association in Baltimore. I am grateful to the members of these audiences, especially to Luca Incurvati, for their valuable feedback. I wish to thank the University of Sheffield and the Royal Institute of Philosophy for their generous financial support.


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.University of SheffieldSheffieldUK

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