According to the "paradox of knowability", the moderate thesis that (necessarily) all truths areknowable - [...] - implies the seemingly preposterous claim that all truths areactually known - [...] -, i.e. that we are omniscient. If Fitch's argument weresuccessful, 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 argumentis, firstly, not [...], but [...]. Secondly, even if there were anintuitionistically acceptable proof of [...], i.e. an argument based on a different set ofpremises, 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 conceptualgrounds and acceptable even from a realist point of view.Fitch's argument, understood as an immanent critique of verificationism, fails because in adebate dealing with the justification of deduction there can be no interpreted formal language onwhich realists and anti-realists could agree. Thus, the underlying problem is that a satisfactorysolution to the "problem of shared content" is not available.I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstructcertain arguments in the debate on anti-realism by establishing aporias.