Carnap’s Relevance Measure as a Probabilistic Measure of Coherence

A Remark on Probabilistic Measures of Coherence

“…First, it is interesting to note that basically the same argument as in Section 2 would show that A cannot be consistent, by taking Γ as a consistency theory and WWSP as a principle concerning consistency theories. 13 This suggests that the notion of coherence could have a structure similar to that of the notion of consistency and hence it would share some of the limitative results in Gödel [11] that affect the latter. Thus, mirroring the first incompleteness theorem, which, very roughly, says that if a theory is consistent, then it is incomplete, we can claim that PMC theories are incomplete-in the sense that they cannot decide on the coherence of certain sets-unless they are incoherent.…”

“…Thanks to an anonymous reviewer for pressing this question. 13 Thanks to Elia Zardini for suggesting this line of thought.…”

“…Thus, 1 is a neutral point with respect to the degree of coherence. A value of the function which is greater than 1 indicates that the set of propositions is coherent, 1 See also Glass [10], Meijs [17], Schupbach [23], Roche [21], Schippers [22] and Koscholke [13]. and a value of the function between 0 (included) and 1 (not included) indicates that the set is incoherent.…”

The sufficiency of the evidence, the relevancy of the evidence, and quantifying both with a single number

“…The degree of that relevance is known as the relevancy of the evidence to whether some hypothesis is true (Koehler, 2002). The many other proposed measures of the relevancy of the evidence include the relative belief ratio, which is the posterior probability of a hypothesis divided by its prior probability (Evans, 2015), and the relevance measure of Carnap (1962, §67); see Koscholke (2017).…”

Tracking the eye of the beholder: is explanation subjective?

“…Over the past two decades, mathematicians and mathematically inclined philosophers have done much to show that the main theoretical virtues can be given rigorous formal definitions, making it hard to maintain that these virtues are empty. See, for instance, Li and Vitányi (1997) and Sober (2015) for promising formalizations of simplicity, and see Bovens and Hartmann (2003), Douven and Meijs (2007), Schippers (2015), and Koscholke (2016) for mathematically precise accounts of coherence. Schupbach and Sprenger (2011) even present a formal measure of explanatory strength directly in probabilistic terms, without invoking the notions of coherence or simplicity at all.…”