# 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).

## References

- Akiba, K. (2000). Shogenji’s probabilistic measure of coherence is incoherent.
*Analysis*,*60*, 356–359.CrossRefGoogle Scholar - BonJour, L. (1985).
*The Structure of Empirical Knowledge*. Cambridge: Harvard University Press.Google Scholar - Bovens, L., & Hartmann, S. (2003).
*Bayesian epistemology*. Oxford: Oxford University Press.Google Scholar - Bovens, L., & Olsson, E. J. (2000). Coherentism, reliability and Bayesian networks.
*Mind*,*109*(436), 685–719.CrossRefGoogle Scholar - Carnap, R. (1950).
*Logical foundations of probability*. Chicago: University of Chicago Press.Google Scholar - Crupi, V., Tentori, K., & Gonzales, M. (2007). On Bayesian measures of evidential support: Theoretical and empirical issues.
*Philosophy of Science*,*74*, 229–252.CrossRefGoogle Scholar - Eells, E., & Fitelson, B. (2002). Symmetries and asymmetries in evidential support.
*Philosophical Studies*,*107*, 129–142.CrossRefGoogle Scholar - Fitelson, B. (2003). A probabilistic theory of coherence.
*Analysis*,*63*, 194–199.CrossRefGoogle Scholar - Glass, D. H. (2002). Coherence, explanation, and Bayesian networks. In M. O’Neill, R. F. E. Sutcliffe, C. Ryan, M. Eaton, & N. J. L. Griffith (Eds.),
*Artificial intelligence and cognitive science. 13th Irish conference, AICS 2002, Limerick, Ireland, September 2002*(pp. 177–182). Berlin: Springer.Google Scholar - Glass, D. H. (2005). Problems with priors in probabilistic measures of coherence.
*Erkenntnis*,*63*, 375–385.CrossRefGoogle Scholar - Hammersley, J. M., & Handscomb, D. C. (1964).
*Monte Carlo methods*. London: Methuen & Co Ltd.CrossRefGoogle Scholar - Klein, P., & Warfield, T. A. (1994). What price coherence?
*Analysis*,*54*(3), 129–132.CrossRefGoogle Scholar - Kolmogorov, A. (1956).
*Foundations of the theory of probability*. New York: AMS Chelsea Publishing.Google Scholar - Koscholke, J. (2015). Evaluating test cases for probabilistic measures of coherence.
*Forthcoming in Erkenntnis*, pp. 1–29. doi: 10.1007/s10670-015-9734-1. - Matsumoto, M., & Nishimura, T. (1998). Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator.
*ACM Transactions on Modeling and Computer Simulation*,*8*(1), 3–30.CrossRefGoogle Scholar - Meijs, W. (2005).
*Probabilistic measures of coherence*. PhD thesis, Erasmus University, Rotterdam.Google Scholar - Meijs, W., & Douven, I. (2005). Bovens and Hartmann on coherence.
*Mind*,*114*, 355–363.CrossRefGoogle Scholar - Olsson, E. J. (2002). What is the problem of coherence and truth?
*The Journal of Philosophy*,*94*, 246–272.CrossRefGoogle Scholar - Pearson, K. (1895). Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material.
*Philosophical Transactions. Royal Society of London. Series A. Mathematical and Physical Sciences*,*186*, 343–414.CrossRefGoogle Scholar - Roche, W. (2013). Coherence and probability: A probabilistic account of coherence. In M. Araszkiewicz & J. Savelka (Eds.),
*Coherence: Insights from philosophy, jurisprudence and artificial intelligence*(pp. 59–91). Dordrecht: Springer.CrossRefGoogle Scholar - Schippers, M. (2014). Probabilistic measures of coherence: From adequacy constraints towards pluralism.
*Synthese*,*191*(16), 3821–3845.CrossRefGoogle Scholar - Schippers, M., & Siebel, M. (2015). Inconsistency as a touchstone for coherence measures.
*Theoria*,*30*, 11–41.CrossRefGoogle Scholar - Schupbach, J. N. (2011). New hope for Shogenji’s coherence measure.
*British Journal for the Philosophy of Science*,*62*(1), 125–142.CrossRefGoogle Scholar - Shogenji, T. (2013). Reductio, coherence, and the myth of epistemic circularity. In F. Zenker (Ed.),
*Bayesian argumentation*(pp. 165–184). Berlin: Springer.CrossRefGoogle Scholar - Siebel, M., & Wolff, W. (2008). Equivalent testimonies as a touchstone of coherence measures.
*Synthese*,*161*, 167–182.CrossRefGoogle Scholar - Spearman, C. (1904). The proof and measurement of association between two things.
*The American Journal of Psychology*,*15*(1), 72–101.CrossRefGoogle Scholar - Tentori, K., Crupi, V., Bonini, N., & Osherson, D. (2007). Comparison of confirmation measures.
*Cognition*,*103*, 107–119.CrossRefGoogle Scholar - Wheeler, G. (2009). Focused correlation and confirmation.
*British Journal for the Philosophy of Science*,*60*(1), 79–100.CrossRefGoogle Scholar