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The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg

Atkinson, David and Peijnenburg, Jeanne (2010) The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg. Studia Logica, 94.


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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.

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Item Type: Published Article or Volume
Atkinson, David
Peijnenburg, Jeanne
Keywords: Probabilistic justification, regress problem, foundationalism, infinitism.
Subjects: General Issues > Confirmation/Induction
Depositing User: David Atkinson
Date Deposited: 14 Dec 2011 13:17
Last Modified: 14 Dec 2011 13:17
Item ID: 8949
Journal or Publication Title: Studia Logica
Subjects: General Issues > Confirmation/Induction
Date: 2010
Volume: 94

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