Fitch’s Paradox and Probabilistic Antirealism

Abstract

Fitch's paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch's result while still offering all that antirealists should care for.

On Bradley’s preservation condition for conditionals

“…It would thus seem that any modal-epistemic logic on which (3) comes out as being inconsistent must be unacceptable. So we can safely assume that, 2 In fact, given some widely accepted assumptions about agents' introspective capacities (see, e.g., Sobel, 1987 andMilne, 1991; but see also Douven 2007b), it is reasonable to think that the logic of epistemic possibility and certainty is KD45. One easily verifies that the properties of this logic displayed by Propositions 2.6.1 and 2.6.2 in Meyer and van der Hoek (1995, p. 73 f) are all desirable ones given our interpretation of the diamond (which corresponds to Meyer and van der Hoek's operator M).…”