the knowability paradox apr 2006

[...]... 2003), chapter 1 The Paradox 17 the attempt to find a more general paradoxicality underlying that found in the knowability paradox beyond that of truth-implying operators Moore’s paradox differs from the knowability paradox in another way Moore’s paradox implies no necessary falsehood as does the knowability paradox Self-deception or confusion of the sort required to affirm Moore’s paradoxical claim... strong verificationism as well as the claim that all truths are knowable, but it 14 Edgington, ‘ The Paradox of Knowability ’, p 558 The Paradox 21 would do so on the basis of some fact not derived from the central claim of strong verificationism as in the knowability paradox itself Furthermore, and this is the more telling point, the primary paradoxicality of the knowability paradox is not that it purports... the question reduces to whether (3) is paradoxical, and if so, whether it is of the same kind as that involved in the knowability paradox Some may try to find such a relationship indirectly, by first claiming that (3) is paradoxical in the same way as Moore’s paradox, and then attempting to link Moore’s paradox to the knowability paradox This latter identification would be a mistake, however Moore’s paradox. .. among the most far-reaching of paradoxes in terms of the variety of philosophical positions it threatens Before doing so, however, it is important to become familiar with the details of the proofs that underlie the paradox and to see more clearly exactly which elements of these proofs give rise to paradox PROOF-THEORETIC DETAILS OF THE PARADOX The theorem proved by Fitch on the way to investigating the. .. operator that generates knowability- like paradoxical results is developed by Neil Tennant.18 Tennant uses the example of the operator ‘‘wondering whether’’ together with Moore’s paradox to argue that the 18 Neil Tennant, The Taming of the True (Oxford, 1997), chapter 8 26 The Knowability Paradox knowability paradox is but an instance of a more general phenomenon Tennant advances the discussion by laying... as a commitment to the idea that a proper disarming of the paradox answers in any way to the motivations for being an anti-realist in the first place By the end of the discussion, it will become clear that the dissolution of the paradox argued for here leaves anti-realism still in jeopardy Finally, my approach to the paradox denies the working assumption of prior discussions of the paradox, which have... context &-Elimination is allowed There is in the literature a challenge to this conception of the paradox, built in the thought that there are analogues of the knowability paradox employing operators weaker than truth that can seem as puzzling as the knowability paradox itself, suggesting that there is a deeper and more general paradoxicality than is found solely by attending to the knowledge operator and... OF THE PARADOX Those who search for a more general paradoxicality here do so by focusing on alternative interpretations of the crucial operator in the knowability paradox Let a be a variable for any operator whatsoever; the two general assumptions of which those in the knowability paradox are but an instance are: p ! }ap ð1Þ The Paradox 15 p & $ ap: ð2Þ and Greater generality would be achieved, then,... knowledge of all truth The result is that restriction strategies are all red herrings when it comes to the fundamental perplexity engendered by the knowability paradox Chapter 4 examines the idea that the logical principles governing the knowledge operator are the root cause of the paradox As we will see in Chapter 1, there are two such principles The first is that knowledge implies truth, and the second is... formulate the two assumptions as Vpðp ! }KpÞ 14 The Knowability Paradox and 9pðp & $KpÞ, ignoring the unneeded complexities introduced by explicitly representing the quantifiers implicit in the K operator By now, it should be obvious how to generate the paradox from these assumptions; they are introduced only to provide alternative ways to generate the paradox for those squeamish in any way about the earlier . wish the errors that remain were their fault. 6 The Knowability Paradox 1 The Paradox The knowability paradox derives from the work of F. B. Fitch in 1963, in particular from one of several theorems. with the details of the proofs that underlie the paradox and to see more clearly exactly which elements of these proofs give rise to paradox. PROOF-THEORETIC DETAILS OF THE PARADOX The theorem. about the paradox, neither of whom had even heard of the paradox. Not yet familiar with the obscurity of the paradox, I was stunned to find philosophers whose work clearly touched on the paradox unaware