Probabilistic Justification and the Regress Problem

Peijnenburg, Jeanne; Atkinson, Doug

doi:10.1007/s11225-008-9132-7

Cited by 7 publications

(23 citation statements)

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“…In earlier papers we have discussed the four most intriguing ones -involving chains and loops of infinite size. 3 We showed there that infinite chains and infinite loops can converge, yielding a unique and well-defined probability value for the target proposition E 0 .…”

Section: Introductionmentioning

confidence: 88%

Pluralism in Probabilistic Justification

Atkinson

Peijnenburg

2012

Probabilities, Laws, and Structures

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Section: Introductionmentioning

confidence: 88%

Pluralism in Probabilistic Justification

Atkinson

Peijnenburg

2012

Probabilities, Laws, and Structures

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“…In several papers we have given counterexamples to this claim. That is, we have demonstrated that a proposition can have a well-defined nonzero probability, even though its probabilistic justification is forever postponed [1], [2], [3], [4].…”

mentioning

confidence: 89%

“…(for the meaning of the symbols β and γ see Herzberg's [5] and our [2]). Following Herzberg, we shall say that Eq.…”

mentioning

confidence: 99%

The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg

Atkinson

Peijnenburg

2010

Stud Logica

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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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“…The paper is organised as follows: We begin, in Section 2, with a review of the Probabilistic Regress Problem, largely based on the recent paper by Peijnenburg and Atkinson [7]. In Section 3 and Section 4, we formalise the notions of a probabilistic regress and its closed-form solvability; then, we briefly summarise Peijnenburg and Atkinson's [7] example of a probabilistic regress which allows for a closed-form solution (Section 5).…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3 and Section 4, we formalise the notions of a probabilistic regress and its closed-form solvability; then, we briefly summarise Peijnenburg and Atkinson's [7] example of a probabilistic regress which allows for a closed-form solution (Section 5). In Section 6, we state and prove the main result of this paper: Every probabilistic regress whose forward-iteration solution avoids obvious contradictions already has a mathematical model (in terms of a probability space and a sequence of events on that probability space which carry the conditional probability assignments prescribed by the regress).…”

Section: Introductionmentioning

confidence: 99%

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

Herzberg

2010

Stud Logica

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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.

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Probabilistic Justification and the Regress Problem

Abstract: We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.

Cited by 7 publications

References 10 publications

Pluralism in Probabilistic Justification

Pluralism in Probabilistic Justification

The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg

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

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