The Consistency of Probabilistic Regresses. A Reply to Jeanne Peijnenburg and David Atkinson

摘要

In a recent paper, Jeanne Peijnenburg and David Atkinson [Studia Logica, 89(3):333-341 (2008)] have challenged the foundationalist rejection of infinitism by giving an example of an infinite, yet explicitly solvable regress of probabilistic justification. So far, however, there has been no criterion for the consistency of infinite probabilistic regresses, and in particular, foundationalists might still question the consistency of the solvable regress proposed by Peijnenburg and Atkinson. In this paper, we employ Robinsonian nonstandard analysis to prove that a probabilistic regress is already consistent if it is admissible in the sense that its forward-iteration solution does not lead to obvious contradictions; naturally, the converse also holds true. As a consequence, it turns out that there is a rich class of probabilistic regresses, which generically will fail to be solvable. We therefore propose a weaker version of the Probabilistic Regress Problem which concedes the existence of solvable regresses, but denies their genericity.