The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg

Abstract

We have earlier shown by construction that a proposition can have a well-defined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls 'solvable'. In the present reaction we investigate what Herzberg means by solvability. We discuss the advantages and disadvantages of making solvability a sine qua non, and we ventilate our misgivings about Herzberg's suggestion that the notion of solvability might help the foundationalist.We further show that the canonical series arising from an infinite chain of conditional probabilities always converges, and also that the sum is equal to the required unconditional probability if a certain infinite product of conditional probabilities vanishes.

Foundationalism with infinite regresses of probabilistic support

“…See Peijnenburg (2010) for a response to Gwiazda (2010). See Atkinson and Peijnenburg (2010b) for a response to Herzberg (2010). 7 For a recent discussion of the distinction between propositional and doxastic justification, and for references, see Silva (2015).…”

Themes from Klein

“…Peijnenburg (2007);Atkinson and Peijnenburg (2010);Peijnenburg and Atkinson (2014a, b).Atkinson and Peijnenburg (2017, Chapter 5, especially §5.3). 5 Michael Rescorla in this connection even uses the scare term "hyper-intellectualism"(Rescorla 2014).…”