Carnap’s Relevance Measure as a Probabilistic Measure of Coherence
- 329 Downloads
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.
KeywordsProbabilistic Measure Alternative Version Coherence Measure Maximal Coherence Probabilistic Independence
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).
- 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
- Carnap, R. (1950). Logical foundations of probability. Chicago: University of Chicago Press.Google 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
- 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.
- Meijs, W. (2005). Probabilistic measures of coherence. PhD thesis, Erasmus University, Rotterdam.Google Scholar