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Fitch's paradox of knowability is one of the fundamental puzzles of epistemic logic. It provides a challenge to the ''knowability thesis'', which states that every truth is, in principle, knowable. The paradox is that this assumption implies the ''omniscience principle'', which asserts that every truth is known. Essentially, Fitch's paradox asserts that the existence of an unknown truth is unknowable. So if all truths were knowable, it would follow that all truths are in fact known. The paradox is of concern for verificationist or anti-realist accounts of truth, for which the ''knowability thesis'' is very plausible, but the omniscience principle is very implausible. The paradox appeared as a minor theorem in a 1963 paper by Frederic Fitch, "A Logical Analysis of Some Value Concepts". Other than the knowability thesis, his proof makes only modest assumptions on the modal nature of knowledge and of possibility. He also generalised the proof to different modalities. It resurfaced in 1979 when W. D. Hart wrote that Fitch's proof was an "unjustly neglected logical gem". == Proof == Suppose ''p'' is a sentence which is an ''unknown truth''; that is, the sentence ''p'' is true, but it is not ''known'' that ''p'' is true. In such a case, the sentence "the sentence ''p'' is an unknown truth" is true; and, if all truths are knowable, it should be possible to know that "''p'' is an unknown truth". But this isn't possible, because as soon as we know "''p'' is an unknown truth", we know that ''p'' is true, rendering ''p'' no longer an ''unknown'' truth, so the statement "''p'' is an unknown truth" becomes a falsity. Hence, the statement "''p'' is an unknown truth" cannot be both known and true at the same time. Therefore, if all truths are knowable, the set of "all truths" must not include any of the form "''something'' is an unknown truth"; thus there must be no unknown truths, and thus all truths must be known. This can be formalised with modal logic. K and L will stand for ''known'' and ''possible'', respectively. Thus LK means ''possibly known'', in other words, ''knowable''. The modality rules used are: The proof proceeds: The last line states that if ''p'' is true then it is known. Since nothing else about ''p'' was assumed, it means that every truth is known. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fitch's paradox of knowability」の詳細全文を読む スポンサード リンク
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