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Irrelevant Conjunction: Statement and Solution of a New Paradox

Published online by Cambridge University Press:  01 January 2022

Vincenzo Crupi  and
Katya Tentori
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Abstract

The so-called problem of irrelevant conjunction has been seen as a serious challenge for theories of confirmation. It involves the consequences of conjoining irrelevant statements to a hypothesis that is confirmed by some piece of evidence. Following Hawthorne and Fitelson, we reconstruct the problem with reference to Bayesian confirmation theory. Then we extend it to the case of conjoining irrelevant statements to a hypothesis that is disconfirmed by some piece of evidence. As a consequence, we obtain and formally present a novel and more troublesome problem of irrelevant conjunction. We conclude by indicating a possible solution based on a measure-sensitive approach and by critically discussing a major alternative way to address the problem.

Type
Research Article
Information
Philosophy of Science , Volume 77 , Issue 1 , January 2010 , pp. 1 - 13
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

Research was supported by a grant from the Spanish Department of Science and Innovation (FFI2008–01169/FISO). We would like to thank Branden Fitelson and Roberto Festa for very useful exchanges and Valeriano Iranzo and an anonymous reviewer for helpful comments.

References

Carnap, R. ([1950] 1962), Logical Foundations of Probability. Chicago: University of Chicago Press.Google Scholar
Chandler, J. (2007), “Solving the Tacking Problem with Contrast Classes”, Solving the Tacking Problem with Contrast Classes 58:489–502.Google Scholar
Christensen, D. (1999), “Measuring Confirmation”, Measuring Confirmation 96:437–461.Google Scholar
Cooke, R. M. (1991), Experts in Uncertainty: Opinion and Subjective Probability in Science. Oxford: Oxford University Press.Google Scholar
Crupi, V., Festa, R., and Buttasi, C. (2010), “Towards a Grammar of Confirmation”, in Suárez, M., Dorato, M., and Rèdei, M. (eds.), Epistemology and Methodology of Science. Berlin: Springer, 73–93.Google Scholar
Crupi, V., Tentori, K., and Gonzalez, M. (2007), “On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues”, On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues 74:229–252.Google Scholar
Earman, J. (1992), Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT Press.Google Scholar
Festa, R. (1999), “Bayesian Confirmation”, in Galavotti, M. and Pagnini, A. (eds.), Experience, Reality, and Scientific Explanation. Dordrecht: Kluwer, 55–87.CrossRefGoogle Scholar
Finch, H. A. (1960), “Confirming Power of Observations Metricized for Decisions among Hypotheses”, Confirming Power of Observations Metricized for Decisions among Hypotheses 27:293–307, 391–404.Google Scholar
Fitelson, B. (1999), “The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity”, The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity 66 (Proceedings): S362–S378.Google Scholar
Fitelson, B. (2002), “Putting the Irrelevance Back into the Problem of Irrelevant Conjunction”, Putting the Irrelevance Back into the Problem of Irrelevant Conjunction 69:611–622.Google Scholar
Fitelson, B. (2006), “Logical Foundations of Evidential Support”, Logical Foundations of Evidential Support 73:500–512.Google Scholar
Fitelson, B. (2007), “Likelihoodism, Bayesianism, and Relational Confirmation”, Likelihoodism, Bayesianism, and Relational Confirmation 156:473–489.Google Scholar
Gaifman, H. (1979), “Subjective Probability, Natural Predicates and Hempel's Ravens”, Subjective Probability, Natural Predicates and Hempel's Ravens 21:105–147.Google Scholar
Good, I. J. (1950), Probability and the Weighing of Evidence. London: Griffin.Google Scholar
Good, I. J. (1984), “The Best Explicatum for Weight of Evidence”, The Best Explicatum for Weight of Evidence 19:294–299.Google Scholar
Hawthorne, J., and Fitelson, B. (2004), “Re-solving Irrelevant Conjunction with Probabilistic Independence”, Re-solving Irrelevant Conjunction with Probabilistic Independence 71:505–514.Google Scholar
Horwich, P. (1982), Probability and Evidence. Cambridge: Cambridge University Press.Google Scholar
Huber, F. (2008), “Milne's Argument for the Log-Ratio Measure”, Milne's Argument for the Log-Ratio Measure 75:413–420.Google Scholar
Joyce, J. (2004), “Bayes's Theorem”, in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Summer 2004 ed. http://plato.stanford.edu/archives/sum2004/entries/bayes-theorem/.Google Scholar
Kemeny, J., and Oppenheim, P. (1952), “Degrees of Factual Support”, Degrees of Factual Support 19:307–324.Google Scholar
Keynes, J. (1921), A Treatise on Probability. London: Macmillan.Google Scholar
Kuipers, T. (2000), From Instrumentalism to Constructive Realism. Dordrecht: Reidel.CrossRefGoogle Scholar
Maher, P. (2004), “Bayesianism and Irrelevant Conjunction”, Bayesianism and Irrelevant Conjunction 71:515–520.Google Scholar
Milne, P. (1996), “Log[p(h/eb)/p(h/b)] Is the One True Measure of Confirmation”, Log[p(h/eb)/p(h/b)] Is the One True Measure of Confirmation 63:21–26.Google Scholar
Mortimer, H. (1988), The Logic of Induction. Paramus, NJ: Prentice Hall.Google Scholar
Mura, A. (2006), “Deductive Probability, Physical Probability and Partial Entailment”, in Alai, M. and Tarozzi, G. (eds.), Karl Popper Philosopher of Science. Soveria Mannelli, Italy: Rubbettino, 181–202.Google Scholar
Mura, A. (2008), “Can Logical Probability Be Viewed as a Measure of Degrees of Partial Entailment?”, Can Logical Probability Be Viewed as a Measure of Degrees of Partial Entailment? 6:25–33.Google Scholar
Nozick, R. (1981), Philosophical Explanations. Oxford: Clarendon.Google Scholar
Rescher, N. (1958), “A Theory of Evidence”, A Theory of Evidence 25:83–94.Google Scholar
Rips, L. J. (2001), “Two Kinds of Reasoning”, Two Kinds of Reasoning 12:129–134.Google Scholar
Rosenkrantz, R. (1994), “Bayesian Confirmation: Paradise Regained”, Bayesian Confirmation: Paradise Regained 45:467–476.Google Scholar
Shortliffe, E. H., and Buchanan, B. G. (1975), “A Model of Inexact Reasoning in Medicine”, A Model of Inexact Reasoning in Medicine 23:351–379.Google 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, 225–240.Google Scholar
Tentori, K., Crupi, V., Bonini, N., and Osherson, D. (2007), “Comparison of Confirmation Measures”, Comparison of Confirmation Measures 103:107–119.Google ScholarPubMed