The Revenge of Fitch?s Knowability Paradox for Typing Approach and the Alleged Self-Refutation of Ramified Type Theory

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<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14210%2F13%3A00069409" target="_blank" >RIV/00216224:14210/13:00069409 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
The Revenge of Fitch?s Knowability Paradox for Typing Approach and the Alleged Self-Refutation of Ramified Type Theory
Original language 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. Revengeforms 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.
Czech name
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Czech description
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Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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