Infinitism in epistemic justification is the thesis that the structure of justification consists in infinite, non-repeating series. Although superficially an implausible position, it is capable of presenting strong arguments in its favour, and has been growing in popularity. After briefly introducing the concept and the motivations for it, I will present a common objection (the finite minds problem) as well as a powerful reply which couches Infinitism in dispositional terms. I will then attempt to undermine this counter-objection by drawing parallels between it and the problems raised against semantic dispositionalism by Kripke’s exegesis of Wittgenstein’s private language argument.

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