Against relative overlap measures of coherence
Coherence is the property of propositions hanging or fitting together. Intuitively, adding a proposition to a set of propositions should be compatible with either increasing or decreasing the set’s degree of coherence. In this paper we show that probabilistic coherence measures based on relative overlap are in conflict with this intuitive verdict. More precisely, we prove that (i) according to the naive overlap measure it is impossible to increase a set’s degree of coherence by adding propositions and that (ii) according to the refined overlap measure no set’s degree of coherence exceeds the degree of coherence of its maximally coherent subset. We also show that this result carries over to all other subset-sensitive refinements of the naive overlap measure. As both results stand in sharp contrast to elementary coherence intuitions, we conclude that extant relative overlap measures of coherence are inadequate.
KeywordsBayesian coherentism Probabilistic coherence measures Relative overlap
We would like to thank two anonymous reviewers whose comments helped us to improve this paper. This work was supported by Grant SI 1731/1-1 to Mark Siebel from the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program “New Frameworks of Rationality” (SPP 1516).
- 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
- 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
- Koscholke, J. (2015). Evaluating test cases for probabilistic measures of coherence. Forthcoming in Erkenntnis. doi: 10.1007/s10670-015-9734-1.
- Olsson, E. J., & Schubert, S. (2007). Reliability conducive measures of coherence. Synthese, 157(3), 297–308.Google Scholar
- Rescher, N. (1973). The coherence theory of truth. Oxford: Oxford University Press.Google 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.Google Scholar
- Schippers, M. (2015). The grammar of Bayesian coherentism. Studia Logica, 103:955–984.Google Scholar