Notre Dame Journal of Formal Logic

A Remark on Probabilistic Measures of Coherence

Sergi Oms

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In recent years, some authors have proposed quantitative measures of the coherence of sets of propositions. Such probabilistic measures of coherence (PMCs) are, in general terms, functions that take as their argument a set of propositions (along with some probability distribution) and yield as their value a number that is supposed to represent the degree of coherence of the set. In this paper, I introduce a minimal constraint on PMC theories, the weak stability principle, and show that any correct, coherent, and complete PMC cannot satisfy it. As a matter of fact, the argument offered in this paper can be applied to any coherence theory that uses a priori procedures. I briefly explore some consequences of this fact.

Article information

Notre Dame J. Formal Logic, Volume 61, Number 1 (2020), 129-140.

Received: 19 August 2018
Accepted: 11 February 2019
First available in Project Euclid: 29 November 2019

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Digital Object Identifier

Primary: 81P05: General and philosophical
Secondary: 03A10: Logic in the philosophy of science

probabilistic measures of coherence completeness liar-like entities


Oms, Sergi. A Remark on Probabilistic Measures of Coherence. Notre Dame J. Formal Logic 61 (2020), no. 1, 129--140. doi:10.1215/00294527-2019-0035.

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  • [1] Aczel, P., Non-Well-Founded Sets, vol. 14 of CSLI Lecture Notes, Stanford University Center for the Study of Language and Information Publications, Stanford, 1988.
  • [2] Akiba, K., “Shogenji’s probabilistic measure of coherence is incoherent,” Analysis (Oxford), vol. 60 (2000), pp. 356–59.
  • [3] Barwise, J., and J. Etchemendy, The Liar: An Essay on Truth and Circularity, Oxford University Press, New York, 1987.
  • [4] BonJour, L., Epistemology, Rowman and Littlefield, Lanham, 2002.
  • [5] Bovens, L., and S. Hartmann, Bayesian Epistemology, Oxford University Press, Oxford, 2003.
  • [6] Carnap, R., Logical Foundations of Probability, 2nd edition, University of Chicago Press, Chicago, 1962.
  • [7] Douven, I., and W. Meijs, “Measuring coherence,” Synthese, vol. 156 (2007), pp. 405–25.
  • [8] Dummett, M., Truth and Other Enigmas, Harvard University Press, Cambridge, MA, 1978.
  • [9] Fitelson, B., “A probabilistic theory of coherence,” Analysis (Oxford), vol. 63 (2003), pp. 194–99.
  • [10] Glass, D. H., “Coherence, explanation, and Bayesian networks,” pp. 177–82 in Artificial Intelligence and Cognitive Science, 13th Irish Conference, AICS 2002, edited by M. O’Neill, R. F. E. Sutcliffe, C. Ryan, and M. Eaton, Springer, Berlin, 2002.
  • [11] Gödel, K., “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I,” Monatshefte für Mathematik, vol. 38 (1931), pp. 173–98.
  • [12] Horwich, P., Truth, 2nd edition, Oxford University Press, Oxford, 1998.
  • [13] Koscholke, J., “Carnap’s relevance measure as a probabilistic measure of coherence,” Erkenntnis, vol. 82 (2017), pp. 339–50.
  • [14] Koscholke, J., and M. Schippers, “Against relative overlap measures of coherence,” Synthese, vol. 193 (2016), pp. 2805–14.
  • [15] Kripke, S., “Outline of a theory of truth,” Journal of Philosophy, vol. 72 (1975), pp. 690–716.
  • [16] Lewis, C. I., An Analysis of Knowledge and Valuation, Open Court, La Salle, 1946.
  • [17] Meijs, W., “Coherence as generalized logical equivalence,” Erkenntnis, vol. 64 (2006), pp. 231–52.
  • [18] Moretti, L., and K. Akiba, “Probabilistic measures of coherence and the problem of belief individuation,” Synthese, vol. 154 (2007), pp. 73–95.
  • [19] Olsson, E. J., “What is the problem of coherence and truth?” Journal of Philosophy, vol. 99 (2002), pp. 246–72.
  • [20] Olsson, E. J., Against Coherence: Truth, Probability and Justification, Oxford University Press, Oxford, 2005.
  • [21] Roche, W., “Coherence and probability: A probabilistic account of coherence,” pp. 59–91 in Coherence: Insights from Philosophy, Jurisprudence and Artificial Intelligence, edited by M. Araszkiewicz and J. Šavelka, Springer, Dordrecht, 2013.
  • [22] Schippers, M., “Probabilistic measures of coherence: From adequacy constraints towards pluralism,” Synthese, vol. 191 (2014), pp. 3821–45.
  • [23] Schupbach, J. N., “New hope for Shogenji’s coherence measure,” British Journal for the Philosophy of Science, vol. 62 (2011), pp. 125–42.
  • [24] Shogenji, T., “Is coherence truth conducive?” Analysis, vol. 59 (1999), pp. 338–45.
  • [25] Shogenji, T., “The role of coherence in epistemic justification,” Australasian Journal of Philosophy, vol. 79 (2001), pp. 90–106.
  • [26] Siebel, M., “Against probabilistic measures of coherence,” Erkenntnis, vol. 63 (2005), pp. 335–60.
  • [27] Siebel, M., “Why explanation and thus coherence cannot be reduced to probability,” Analysis (Oxford), vol. 71 (2011), pp. 264–66.
  • [28] Suppe, P., The Structure of Scientific Theories, University of Illinois Press, Urbana, 1974.
  • [29] Tarski, A., “The concept of truth in formalized languages,” pp. 152–278 in Logic, Semantics, Metamathematics, edited by J. Corcoran, Hackett, Indianapolis, 1983.
  • [30] Uchii, S., “Higher order probabilities and coherence,” Philosophy of Science, vol. 40 (1973), pp. 373–81.
  • [31] van Fraassen, B. C., Laws and Symmetry, Oxford University Press, New York, 1989.