Foundationalism with infinite regresses of probabilistic support

Abstract

There is a long-standing debate in epistemology on the structure of justification. Some recent work in formal epistemology promises to shed some new light on that debate. I have in mind here some recent work by David Atkinson and Jeanne Peijnenburg, hereafter "A&P", on infinite regresses of probabilistic support. A&P show that there are probability distributions defined over an infinite set of propositions {p 1 , p 2 , p 3 , …, p n , …} such that (i) p i is probabilistically supported by p i+1 for all i and (ii) p 1 has a high probability. Let this result be "APR" (short for "A&P's Result"). A&P oftentimes write as though they believe that APR runs counter to foundationalism. This makes sense, since there is some prima facie plausibility in the idea that APR runs counter to foundationalism, and since some prominent foundationalists argue for theses inconsistent with APR. I argue, though, that in fact APR does not run counter to foundationalism. I further argue that there is a place in foundationalism for infinite regresses of probabilistic support.

Fading Foundations

“… Cling 2004, 111; see alsoMoser 1985, who makes a point similar to that ofCling. 28 William Roche doubts whether a probabilistic regress can take away Cling's worry(Roche 2016). We think that it can indeed, for the reasons explained here and in Sections 4.4 and 8.5.…”

“… Fumerton 1995, 57. 3 Thus we do not have many quibbles with William Roche when he argues that foundationalism, if suitably generalized, can be reconciled with infinite regresses of probabilistic support(Roche 2016). Much depends on what is meant by foundationalism: as we indicated in Section 4.4, we do not want to become embroiled in a verbal dispute.…”