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Knowability from a Logical Point of View
, 2010
"... The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in questio ..."
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The wellknown ChurchFitch paradox shows that the verificationist knowability principle all truths are knowable, yields an unacceptable omniscience property. Our semantic analysis establishes that the knowability principle fails because it misses the stability assumption ‘the proposition in question does not change from true to false in the process of discovery, ’ hidden in the verificationist approach. Once stability is made explicit, the resulting stable knowability principle accurately represents verificationist knowability, does not yield the omniscience property, and can be offered as a resolution of the knowability paradox. Two more principles are considered: total knowability stating that it is possible to know whether a proposition holds or not, and monotonic knowability stemming from the intrinsically intuitionistic reading of knowability. The study of these four principles yields a “knowability diamond ” describing their logical strength. These results are obtained within a logical framework which opens the door to the systematic study of knowability from a logical point of view. 1
DOI 10.1007/s112290099673y Williamson’s Woes
"... defends against Williamson’s objections the antirealist’s knowability principle based on the author’s ‘local ’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson’spurportedFitchianreductio, involvingthe unknown number of books on his table, is analy ..."
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defends against Williamson’s objections the antirealist’s knowability principle based on the author’s ‘local ’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson’spurportedFitchianreductio, involvingthe unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson’s attempt to cause problems for the antirealist by means of a supposed rigid designator generates a contradiction with arithmetic right away, upon instantiating the obviously relevant theorem that every natural number is provably odd or provably even. The paper also explains and formulates a globally restricted knowability principle, which likewise blocks the attempted reductio.
(to appear in J. Salerno, ed., New Essays on the Knowability Paradox, Oxford: Oxford University Press) Tennant’s Troubles
"... First, some reminiscences. In the years 197380, when I was an undergraduate and then graduate student at Oxford, Michael Dummett’s formidable and creative philosophical presence made his arguments impossible to ignore. In consequence, one pole of discussion was always a form of antirealism. It end ..."
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First, some reminiscences. In the years 197380, when I was an undergraduate and then graduate student at Oxford, Michael Dummett’s formidable and creative philosophical presence made his arguments impossible to ignore. In consequence, one pole of discussion was always a form of antirealism. It endorsed something like the replacement of truthconditional semantics by verificationconditional semantics and of classical logic by intuitionistic logic, and the principle that all truths are knowable. It did not endorse the principle that all truths are known. Nor did it mention the now celebrated argument, first published by Frederic Fitch (1963), that if all truths are knowable then all truths are known. Even in 1970s Oxford, intuitionistic antirealism was a strictly minority view, but many others regarded it as a live theoretical option in a way that now seems very distant. As the extreme verificationist commitments of the view have combined with accumulating decades of failure to reply convincingly to criticisms of the arguments in its favour or to carry out the programme of generalizing intuitionistic semantics for 1 mathematics to empirical discourse, even in toy examples, the impression has been