The Revenge of Fitch’s Knowability Paradox for Typing Approach and the Alleged Self-Refutation of Ramified Type Theory
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| Year of publication | 2013 |
| Type | Conference abstract |
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| Description | Russellian typing knowledge is capable to resolve the famous Fitch's knowability paradox and it is immune to the recently raised criticism. But there is a special form of the criticism proposing a revenge problem, which is addressed in this talk. Revenge forms of Fitch's paradox were proposed by Williamson, Hart and also Carrara with Fassio. The basic idea employs quantification over type levels, as suggested already by Gödel in his criticism of ramified theory of types. From the viewpoint of a type theorist, however, the formalism used by the critics is ambivalent. I recover altogether six possible readings of the revenge form of the paradox. It is then evident that the revenge arguments go through only when they directly violate typing rules. In other words, the approach is immune to the criticism. |
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