The Problem of Measure Sensitivity Redux

Abstract

for their invaluable feedback on various versions of this paper. I also want to emphasize my gratitude to James M. Joyce for the permission to cite and quote his unpublished manuscript "On the Plurality of Probabilist Measures of Evidential Relevance." Finally, I also would like to thank Robert Lehnert and Ben Young for proofreading the manuscript.

Two Impossibility Results for Measures of Corroboration

“…Some of the above adequacy conditions have been proposed for measures of evidential support or explanatory power; others could be potentially interesting in these contexts. For instance, Brössel (2013) has recently discussed the condition Logicality, which resembles our Strong/Weak Informativity. Hence, our results also make sense in the framework of Bayesian Confirmation Theory, as indicating the impossibility of probabilistic measures that caputre informativity and statistical relevance at the same time.…”

Acceptance, values, and probability

“…Despite their strongly anti-acceptance stances, Howson and Urbach also speak of accepting evidence (1993, 406e 407), while Earman includes accepted background knowledge as a term in Bayes' theorem (see 1992, 33;cf. Fitelson, 1999;Brössel, 2013). Thus, voluntary decisions about what to accept can influence personal probabilities even within conventional Bayesian approaches.…”

“…A large number of non-equivalent Bayesian measures of confirmation exist, including P(HjE) À P(H), P(HjE)/P(H), and P(EjH)/P(Ej:H). And there is no general agreement about which measure is correct, or even that there is one universally correct measure of confirmation (Brössel, 2013;Fitelson, 1999). Choices about which confirmation measure to adopt, therefore, are another arena in which acceptance 3 See Harsanyi (1985) and Steel (2013) for critiques of such theories of acceptance.…”

Bayesian Confirmation: A Means with No End

“…5), and there are other quantities the distance between which can be measured (Joyce [2003]). The way distance is measured, and the quantities between which it is measured, affect the validity of various arguments in Bayesian confirmation theory (Brössel [2013]; Fitelson [1999]). However, these differences do not matter for present purposes.…”