# Carnap’s Relevance Measure as a Probabilistic Measure of Coherence

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## Abstract

Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his *Logical Foundations of Probability* discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to investigate Carnap’s measure regarding its plausibility as a candidate for a probabilistic measure of coherence by comparing it to Shogenji’s. It turns out that both measures (i) satisfy and violate the same adequacy constraints, (ii) despite not being ordinally equivalent exhibit a strong correlation with each other in a Monte Carlo simulation and (iii) perform similarly in a series of test cases for probabilistic coherence measures.

## Keywords

Probabilistic Measure Alternative Version Coherence Measure Maximal Coherence Probabilistic Independence## Notes

### Acknowledgments

I would like to thank (in alphabetical order) Michael Schippers, Jonah Schupbach, Mark Siebel and Elia Zardini for helpful comments or discussion. This work was funded by the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program SPP 1516 New Frameworks of Rationality (grant SI 1731/1-1 to Mark Siebel).

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