Fitch’s paradox in light of hybrid logic

Fitch’s paradox shows that the concept of knowability is as problematic as the concept of knowledge. This is so because of the fact that the most natural logical representation of knowability as OK (in terms of bimodal logic containing alethic and epistemic modalities), taken together with some natural principles and assumptions, leads to contradiction. This paper is aimed at elaborating a formalization of the concept of knowability de re that should allow us to accept the principle of knowability de re without facing Fitch’s paradox. (In my view, the concept of knowability de re and the concept of knowability de dicto should have different logical representations, and I leave the concept of knowability de dicto out of the scope of the paper.) I suggest a system of hybrid logic in terms of which knowability de re can be accurately represented; I call it HLK - hybrid logic of knowability de re. HLK is a modification of a system suggested by Kocurek in order to represent cross-world predication. Changes made by me affect definitions of term, model, and truth; I also add to Kocurek’s logic the epistemic machinery. HLK includes two modalities - the alethic and epistemic ones - and its vocabulary contains hybrid items: possible world variables, two hybrid sentential operators, and a hybrid term operator. Thanks to the hybrid part of vocabulary together with relevant parts of syntax and semantics, HLK has a substantial advantage over standard bimodal systems in terms of expressive power. This makes it apt to express knowledge and knowability de re in a way that allows adopting the principle of knowability de re without facing Fitch’s paradox. I describe the syntax and semantics of HLK, demonstrate its expressive power, define the HLK representation of epistemic concepts under consideration, and demonstrate on examples that the suggested representation meets their intuitive meaning. The author declares no conflicts of interests.

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