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Unfolding the Grammar of Bayesian Confirmation: Likelihood and Antilikelihood Principles

Published online by Cambridge University Press:  01 January 2022

Roberto Festa  and
Gustavo Cevolani
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Abstract

We explore the grammar of Bayesian confirmation by focusing on some likelihood principles, including the Weak Law of Likelihood. We show that none of the likelihood principles proposed so far is satisfied by all incremental measures of confirmation, and we argue that some of these measures indeed obey new, prima facie strange, antilikelihood principles. To prove this, we introduce a new measure that violates the Weak Law of Likelihood while satisfying a strong antilikelihood condition. We conclude by hinting at some relevant links between the likelihood principles considered here and other properties of Bayesian confirmation recently explored in the literature.

Type
Research Article
Information
Philosophy of Science , Volume 84 , Issue 1 , January 2017 , pp. 56 - 81
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

We would like to thank Vincenzo Crupi, Theo Kuipers, and Luca Tambolo for helpful comments on a previous draft of this article. Financial support from the PRIN grant Models and Inferences in Science (20122T3PTZ), from the FIRB project Structures and Dynamics of Knowledge and Cognition (Turin unit: D11J12000470001), and from the University of Turin and the Compagnia San Paolo project Assessing Information Models: Exploring Theories and Applications of Optimal Information Search (D16D15000190005) is gratefully acknowledged.

References

Bar-Hillel, Yehoshua, and Carnap, Rudolf. 1953. “Semantic Information.” British Journal for the Philosophy of Science 4:147–57.CrossRefGoogle Scholar
Brössel, Peter. 2013. “The Problem of Measure Sensitivity Redux.” Philosophy of Science 80:378–97.CrossRefGoogle Scholar
Carnap, Rudolf. 1950/1950. Logical Foundations of Probability. Chicago: University of Chicago Press.Google Scholar
Crupi, Vincenzo. 2015. “Confirmation.” In Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N.. Stanford, CA: Stanford University. http://plato.stanford.edu/archives/sum2015/entries/confirmation/.Google Scholar
Crupi, Vincenzo, Chater, Nick, and Tentori, Katya. 2013. “New Axioms for Probability and Likelihood Ratio Measures.” British Journal for the Philosophy of Science 64:189–204.CrossRefGoogle Scholar
Crupi, Vincenzo, Festa, Roberto, and Buttasi, Carlo. 2010. “Towards a Grammar of Bayesian Confirmation.” In Epistemology and Methodology of Science, ed. Suárez, M., Dorato, M., and Rédei, M., 73–93. Dordrecht: Springer.Google Scholar
Crupi, Vincenzo, and Tentori, Katya. 2014. “State of the Field: Measuring Information and Confirmation.” Studies in History and Philosophy of Science A 47:81–90.CrossRefGoogle Scholar
Edwards, Anthony W. F. 1972. Likelihood. Cambridge: Cambridge University Press.Google Scholar
Festa, Roberto. 1999. “Bayesian Confirmation.” In Experience, Reality, and Scientific Explanation, ed. Galavotti, Maria Carla and Pagnini, Alessandro, 55–87. Dordrecht: Springer.CrossRefGoogle Scholar
Pagnini, Alessandro 2012. “‘For Unto Every One That Hath Shall Be Given’: Matthew Properties for Incremental Confirmation.” Synthese 184:89–100.Google Scholar
Festa, Roberto, and Cevolani, Gustavo. 2015. “Matthew Properties for Incremental Confirmation and the Weak Law of Likelihood.” Unpublished manuscript, University of Trieste and University of Turin.Google Scholar
Fitelson, Branden. 1999. “The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity.” Philosophy of Science 66:378.CrossRefGoogle Scholar
Fitelson, Branden 2007. “Likelihoodism, Bayesianism, and Relational Confirmation.” Synthese 156:473–89.CrossRefGoogle Scholar
Gaifman, Haim. 1979. “Subjective Probability, Natural Predicates and Hempel’s Ravens.” Erkenntnis 14:105–47.Google Scholar
Glass, David H., and McCartney, Mark. 2014. “A New Argument for the Likelihood Ratio Measure of Confirmation.” Acta Analytica 30:59–65.CrossRefGoogle Scholar
Good, I. J. 1950. Probability and the Weighing of Evidence. London: Griffin.Google Scholar
Hacking, Ian. 1965. Logic of Statistical Inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hájek, Alan, and Joyce, James. 2013. “Confirmation.” In Routledge Companion to the Philosophy of Science, ed. Psillos, S. and Curd, M., 115–29. New York: Routledge.Google Scholar
Hildebrand, David K., Laing, James D., and Rosenthal, Howard. 1977. Analysis of Ordinal Data. Beverly Hills, CA: Sage.CrossRefGoogle Scholar
Iranzo, Valeriano, and de Lejarza, Ignacio Martínez. 2012. “On Ratio Measures of Confirmation.” Journal for General Philosophy of Science 44:193–200.CrossRefGoogle Scholar
Joyce, James. 2008. “Bayes’ Theorem.” In Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N.. Stanford, CA: Stanford University. http://plato.stanford.edu/archives/fall2008/entries/bayes-theorem/.Google Scholar
Keynes, John M. 1921. A Treatise on Probability. London: Macmillan.Google Scholar
Kuipers, Theo A. F. 2000. From Instrumentalism to Constructive Realism. Dordrecht: Kluwer.CrossRefGoogle Scholar
Mortimer, Halina. 1988. The Logic of Induction. Chichester: Halsted.Google Scholar
Nozick, Robert. 1981. Philosophical Explanations. Cambridge, MA: Harvard University Press.Google Scholar
Popper, Karl R. 1959. The Logic of Scientific Discovery. London: Routledge.Google Scholar
Roche, William. 2014. “A Note on Confirmation and Matthew Properties.” Logic and Philosophy of Science 12:91–101.Google Scholar
Roche, William 2015a. “Confirmation, Increase in Probability, and Partial Discrimination: A Reply to Zalabardo.” European Journal for Philosophy of Science 6:1–7.CrossRefGoogle Scholar
Roche, William 2015b. “Evidential Support, Transitivity, and Screening-Off.” Review of Symbolic Logic 8:785–806.CrossRefGoogle Scholar
Roche, William, and Shogenji, Tomoji. 2014. “Dwindling Confirmation.” Philosophy of Science 81:114–37.CrossRefGoogle Scholar
Royall, Richard. 1997. Statistical Evidence: A Likelihood Paradigm. London: Chapman & Hall.Google Scholar
Salmon, Wesley C. 1975. “Confirmation and Relevance.” Minnesota Studies in the Philosophy of Science 6:3–36.Google Scholar
Sober, Elliott. 1990. “Contrastive Empiricism.” In Scientific Theories, ed. Savage, C. Wade, 392–410. Minneapolis: University of Minnesota Press.Google Scholar
Savage, C. Wade 2008. Evidence and Evolution: The Logic Behind the Science. Cambridge: Cambridge University Press.Google Scholar
Zalabardo, José. 2009. “An Argument for the Likelihood-Ratio Measure of Confirmation.” Analysis 69:630–35.CrossRefGoogle Scholar