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Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of nonequivalent 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 (...) 



Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “countersupport” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H. 

Confirmation of a hypothesis by evidence can be measured by one of the so far known incremental measures of confirmation. As we show, incremental measures can be formally defined as the measures of confirmation satisfying a certain small set of basic conditions. Moreover, several kinds of incremental measure may be characterized on the basis of appropriate structural properties. In particular, we focus on the socalled Matthew properties: we introduce a family of six Matthew properties including the reverse Matthew effect; we (...) 

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure (...) 

So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; in (...) 

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that (...) 



