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On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues

Published online by Cambridge University Press:  01 January 2022

Abstract

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting.

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

We thank Roberto Festa, Branden Fitelson, Theo Kuipers, Daniel Osherson, and two anonymous referees for comments on previous versions of this paper. Research was supported by PRIN 2005 grant Le dinamiche della conoscenza nella società dell'informazione and by a grant from the SMC/Fondazione Cassa di Risparmio di Trento e Rovereto.

References

Carnap, R. ([1950] 1962), Logical Foundations of Probability. Chicago: University of Chicago Press.Google Scholar
Christensen, D. (1999), “Measuring Confirmation,” Journal of Philosophy 96:437461.CrossRefGoogle Scholar
Eells, E., and Fitelson, B. (2002), “Symmetries and Asymmetries in Evidential Support,” Philosophical Studies 107:129142.CrossRefGoogle Scholar
Festa, R. (1999), “Bayesian Confirmation,” in Galavotti, M. and Pagnini, A. (eds.), Experience, Reality, and Scientific Explanation. Dordrecht: Kluwer, 5587.CrossRefGoogle Scholar
Finch, H. A. (1960), “Confirming Power of Observations Metricized for Decisions among Hypotheses,” Philosophy of Science 27:293307, 391–404.CrossRefGoogle Scholar
Fitelson, B. (1999), “The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity,” Philosophy of Science 66:S362S378.CrossRefGoogle Scholar
Fitelson, B. (2001), Studies in Bayesian Confirmation Theory. PhD dissertation, University of Wisconsin, Madison.Google Scholar
Fitelson, B. (2006), “Logical Foundations of Evidential Support,” Philosophy of Science 73:500512.CrossRefGoogle Scholar
Fitelson, B. (2007), “Likelihoodism, Bayesianism, and Relational Confirmation,” Synthese 156:473489.CrossRefGoogle Scholar
Gaifman, H. (1979), “Subjective Probability, Natural Predicates and Hempel’s Ravens,” Erkenntnis 21:105147.Google Scholar
Girotto, V., and Gonzalez, M. (2001), “Solving Probabilistic and Statistical Problems: A Matter of Question Form and Information Structure,” Cognition 78:247276.CrossRefGoogle ScholarPubMed
Good, I. J. (1950), Probability and the Weighing of Evidence. London: Griffin.Google Scholar
Hawthorne, J., and Fitelson, B. (2004), “Re-solving Irrelevant Conjunction with Probabilistic Independence,” Philosophy of Science 71:505514.CrossRefGoogle Scholar
Horwich, P. (1982), Probability and Evidence. Cambridge: Cambridge University Press.Google Scholar
Joyce, J. (2004), “Bayes’s Theorem,” in Zalta, E. N. (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford University Press. http://plato.stanford.edu/archives/sum2004/entries/bayes-theorem/.Google Scholar
Kahneman, D., Slovic, P., and Tversky, A., eds. (1982), Judgment under Uncertainty: Heuristics and Biases. New York: Cambridge University Press.CrossRefGoogle Scholar
Kemeny, J., and Oppenheim, P. (1952), “Degrees of Factual Support,” Philosophy of Science 19:307324.CrossRefGoogle Scholar
Keynes, J. (1921), A Treatise on Probability. London: Macmillan.Google Scholar
Kuipers, T. (2000), From Instrumentalism to Constructive Realism. Dordrecht: Reidel.CrossRefGoogle Scholar
Marr, D. (1982), Vision: A Computational Approach. San Francisco: Freeman.Google Scholar
Mortimer, H. (1988), The Logic of Induction. Paramus, NJ: Prentice Hall.Google Scholar
Nozick, R. (1981), Philosophical Explanations. Oxford: Clarendon.Google Scholar
Osherson, D. N., Smith, E. E., Wilkie, O., Lopez, A., and Shafir, E. (1990), “Category-Based Induction,” Psychological Review 97:185200.CrossRefGoogle Scholar
Rescher, N. (1958) “A Theory of Evidence,” Philosophy of Science 25:8394.CrossRefGoogle Scholar
Rips, L. J. (2001), “Two Kinds of Reasoning,” Psychological Science 12:129134.CrossRefGoogle Scholar
Sober, E. (1994), “No Model, No Inference: A Bayesian Primer on the Grue Problem,” in Stalker, D. (ed.), Grue! The New Riddle of Induction. Chicago: Open Court, 225240.Google Scholar
Tentori, K., Crupi, V., Bonini, N., and Osherson, D. (2007), “Comparison of Confirmation Measures,” Cognition 103:107119.CrossRefGoogle ScholarPubMed