Fitch's Paradox and the Problem of Shared Content

  • Thorsten Sander


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.