Abstract
Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some probabilistic measure of coherence, and a probability distribution such that all the probabilities on which A’s degree of coherence depends (according to the measure in question) are defined. Then, the argument goes, the degree to which A is coherent depends solely on the details of the distribution in question and not at all on the explanatory relations, if any, standing between the propositions in A. This is problematic, the argument continues, because, first, explanation matters for coherence, and, second, explanation cannot be adequately captured solely in terms of probability. We argue that Siebel’s argument falls short.
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Notes
See Douven and Meijs (2007) for details on how to generalize from the case where A consists of two propositions to the case where A consists of n propositions.
Swain’s complaint (about BonJour 1985) in the following passage is typical:
One of the most disappointing features of BonJour’s book is the lack of detail provided in connection with the central notion of coherence. No effort is made at defining this concept. Instead, we are given several rather vaguely formulated conditions which loosely characterize coherence. (1989, p. 116)
BonJour himself later notes that “the precise nature of coherence remains a largely unsolved problem” (1999, p. 124).
See the references given in note 1. See also Koscholke (2013).
Strictly speaking, Siebel appeals to a slightly different thesis: If H 1 explains D 1 and D 2, whereas H 2 explains only D 1, then, ceteris paribus, \( \left\{ {H_{1} ,D_{1} ,D_{2} } \right\} \) is more coherent than \( \left\{ {H_{2} ,D_{1} ,D_{2} } \right\} \). But Siebel (personal communication) does accept (1) and does hold that probabilistic measures of coherence run afoul of (1). What we say about (1) can be said mutatis mutandis about the slightly different thesis just mentioned. We focus on (1), and not on the slightly different thesis, in part because (1) is the simpler of the two theses.
The same is true in cases where H 1 and H 2 confer on D a probability less than 1 (assuming there can be cases of this sort).
It should also be noted that the Screening-Off Thesis is distinct from the considerably stronger thesis that explanatoriness is evidentially irrelevant; see Roche and Sober (2013) for discussion.
BonJour (1985, pp. 99–100) goes on to consider and reject the view that only explanatory relations are coherence-increasing.
It might be countered that by definition a probabilistic coherence measure implies that any two sets having the same probability profile also have the same coherence value. Fine. The important point is that even if extant probabilistic coherence measures are false because they run counter to theses such as (1) and (2), there are coherence measures very much in the spirit of extant probabilistic coherence measures and on which two sets can have the same probability profile and yet differ in coherence because of differences concerning explanation. Such measures, as with extant probabilistic coherence measures, are quantitative and render formally precise the notion of coherence.
References
BonJour, L. (1985). The structure of empirical knowledge. Cambridge, MA: Harvard University Press.
BonJour, L. (1999). The dialectic of foundationalism and coherentism. In J. Greco & E. Sosa (Eds.), The Blackwell guide to epistemology (pp. 117–142). Malden: Blackwell.
Crupi, V., & Tentori, K. (2012). A second look at the logic of explanatory power (with two novel representation theorems). Philosophy of Science, 79, 365–385.
Crupi, V., Tentori, K., & Gonzalez, M. (2007). On Bayesian measures of evidential support: Theoretical and empirical issues. Philosophy of Science, 74, 229–252.
Douven, I., & Meijs, W. (2007). Measuring coherence. Synthese, 156, 405–425.
Eells, E., & Fitelson, B. (2002). Symmetries and asymmetries in evidential support. Philosophical Studies, 107, 129–142.
Festa, R. (1999). Bayesian confirmation. In M. Galavotti & A. Pagnini (Eds.), Experience, reality, and scientific explanation (pp. 55–87). Dordrecht: Kluwer.
Fitelson, B. (2003). A probabilistic theory of coherence. Analysis, 63, 194–199.
Harman, G. (1986). Change in view: Principles of reasoning. Cambridge, MA: MIT Press.
Hempel, C. G. (1965). Aspects of scientific explanation. In his Aspects of scientific explanation and other essays in the philosophy of science (pp. 331–496). New York: Free Press.
Koscholke, J. (2013). Last measure standing: Evaluating test cases for probabilistic coherence measures, unpublished manuscript.
Lycan, W. (1988). Judgement and justification. Cambridge: Cambridge University Press.
Meijs, W. (2006). Coherence as generalized logical equivalence. Erkenntnis, 64, 231–252.
Olsson, E. J. (2002). What is the problem of coherence and truth? Journal of Philosophy, 99, 246–272.
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.
Roche, W., & Sober, E. (2013). Explanatoriness is evidentially irrelevant, or inference to the best explanation meets Bayesian confirmation theory. Analysis, 73, 659–668.
Schupbach, J. N. (2011). New hope for Shogenji’s coherence measure. British Journal for the Philosophy of Science, 62, 125–142.
Schupbach, J. N., & Sprenger, J. (2011). The logic of explanatory power. Philosophy of Science, 78, 105–127.
Shogenji, T. (1999). Is coherence truth conducive? Analysis, 59, 338–345.
Siebel, M. (2005). Against probabilistic measures of coherence. Erkenntnis, 63, 335–360.
Siebel, M. (2011). Why explanation and thus coherence cannot be reduced to probability. Analysis, 71, 264–266.
Swain, M. (1989). BonJour’s coherence theory of justification. In J. Bender (Ed.), The current state of the coherence theory: Critical essays on the epistemic theories of Keith Lehrer and Laurence BonJour, with replies (pp. 115–124). Dordrecht: Kluwer.
Thagard, P. (1992). Conceptual revolutions. Princeton: Princeton University Press.
Acknowledgments
We thank Jakob Koscholke, Michael Roche, Mark Siebel, and two anonymous reviewers for helpful comments or discussion. This work was partly supported by Grant SI 173/1-1 to Mark Siebel from the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program “New Frameworks of Rationality” (SPP 1516).
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Roche, W., Schippers, M. Coherence, Probability and Explanation. Erkenn 79, 821–828 (2014). https://doi.org/10.1007/s10670-013-9566-9
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DOI: https://doi.org/10.1007/s10670-013-9566-9