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Séminaire de Logiques Non Classiques: Carlo Proietti
Séance commune avec Séminaire Inter-Universitaire de Philosophie des Mathématiques de Paris 1 et Paris 4.
Carlo Proietti (Lund Univeristy)
The knowability paradox. An approach with quantified modal logic
The knowability paradox (Fitch, 1963) consists of a derivation of (a) p -> Kp from (b) p -> MKp.
An intuitive reading of this argument is that “All truths are knowable” (weak verificationism) entails that “All truths are known” (strong verificationism). As a consequence, verificationists and anti-realists are in trouble because one of their basic claims entails a blatant absurdity. Therefore, verificationism and anti-realism are problematic on a simple logical basis.
Among other purported solutions of the paradox, so-called reformulation strategies – inaugurated by D. Edgington (1985) – deny that p -> MKp is an adequate formal rendering of weak verificationism. Supporters of these solutions claim that the problem is due to a limited expressivity of modal propositional languages. The essential core of these proposals is that “All truth are knowable” should be read as “All actual truths are possibly known by some (actual or non-actual) knower to be true of the actual situation”. Despite their intuitive plausibility these solutions face many technical problems.
I claim, in the spirit of Kvanvig (2006), that for a better understanding of the problem we need to reformulate verificationist theses in a first-order modal language which allows de re/ de dicto specifications and indexing individuals, quantifiers and properties to specific possible worlds. In one word, a first-order hybrid modal logic.
Here I will formulate my proposal for which it turns out, among other things, that:
1) There are many possible renderings of weak verificationism
2) The weak verification thesis is not expressible by a fix substitution-free schema, but rather via a translational schema
3) In the new framework the corresponding paradox is avoided without (hopefully) falling into the technical and philosophical problems affecting previous solutions of this kind.