Fitch's Paradox and the Problem of Shared Content

Thorsten Sander

Abstract


According to the “paradox of knowability”, the moderate thesis
that (necessarily) all truths are knowable – ‘∀p (p ⊃ ◊Kp) ’ – implies the seemingly preposterous
claim that all truths are actually known – ‘∀p (p ⊃ Kp) ’ –, i.e. that we
are omniscient. If Fitch’s argument were successful, it would amount to a
knockdown rebuttal of anti-realism by reductio. In the paper I defend the
nowadays rather neglected strategy of intuitionistic revisionism. Employing
only intuitionistically acceptable rules of inference, the conclusion of the
argument is, firstly, not ‘∀p (p ⊃ Kp)’, but ‘∀p (p ⊃ ¬¬Kp)’. Secondly,
even if there were an intuitionistically acceptable proof of ‘∀p (p ⊃ Kp)’,
i.e. an argument based on a different set of premises, the conclusion would
have to be interpreted in accordance with Heyting semantics, and read in
this way, the apparently preposterous conclusion would be true on conceptual
grounds and acceptable even from a realist point of view. Fitch’s argument,
understood as an immanent critique of verificationism, fails because in a
debate dealing with the justification of deduction there can be no
interpreted formal language on which realists and anti-realists could agree.
Thus, the underlying problem is that a satisfactory solution to the “problem
of shared content” is not available. I conclude with some remarks on the
proposals by J. Salerno and N. Tennant to reconstruct certain arguments in
the debate on anti-realism by establishing aporias.

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