Abstract
In a recent paper Ronald Meester and Timber Kerkvliet argue by example that infinite epistemic regresses have different solutions depending on whether they are analyzed with probability functions or with belief functions. Meester and Kerkvliet give two examples, each of which aims to show that an analysis based on belief functions yields a different numerical outcome for the agent’s degree of rational belief than one based on probability functions. In the present paper we however show that the outcomes are the same. The only way in which probability functions and belief functions can yield different solutions for the agent’s degree of belief is if they are applied to different examples, i.e. to different situations in which the agent finds himself.
Highlights
It is a truth widely acknowledged that a belief which is justified must be based on a reason
Probabilistic regresses turn out to be consistent in both analyses, Meester and Kerkvliet argue that an analysis with belief functions may yield a different numerical outcome than one using probability functions
Given a particular infinite epistemic regress, the value of Bel(E0) may differ from that of P(E0). This would mean that our degree of rational belief in E0 could vary, dependent on whether we analyze the regress with probability functions or with belief functions
Summary
It is a truth widely acknowledged that a belief which is justified must be based on a reason. Ronald Meester and Timber Kerkvliet have made a welcome and original attempt to analyze such regresses in terms of Shafer belief functions.7 Their findings reinforce the view that epistemic regresses are consistent once they have been given a probabilistic interpretation rather than an interpretation in terms of entailment. Probabilistic regresses turn out to be consistent in both analyses, Meester and Kerkvliet argue that an analysis with belief functions may yield a different numerical outcome than one using probability functions. Given a particular infinite epistemic regress, the value of Bel(E0) may differ from that of P(E0) This would mean that our degree of rational belief in E0 could vary, dependent on whether we analyze the regress with probability functions or with belief functions. Can there exist other examples which do the job? In Sect. 5 we explain that this is impossible: probability functions and belief functions always yield the same numerical outcome when applied to a particular probabilistic regress in a particular situation
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