The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity

Abstract

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity.

How Bayesian Confirmation Theory Handles the Paradox of the Ravens

“…There are many Bayesian relevance measures c that have been proposed and defended in the contemporary literature on Bayesian confirmation. The four most popular of these measures are the following (see Fitelson 1999Fitelson , 2001 for historical surveys). 10 The Difference:…”

Hempel’s logic of confirmation

“…This seems to me a clear refutation of [3.1]. ... What may be the reasons that have led Hempel to the consistency conditions [3.1] and [3]? He regards it as a great advantage of any explicatum satisfying [3] "that is sets a limit, so to speak, to the strength of the hypotheses which can be confirmed by given evidence" ...…”

Experimental Philosophy Meets Formal Epistemology

“…Importantly, which of these explicata one adopts can make a crucial difference to philosophical conclusions about confirmation we draw from them; e.g., Fitelson (1999) shows that various Bayesian "resolutions" of well--known paradoxes hinge sensitively on one's choice of measure. …”