Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T00:23:57.345Z Has data issue: false hasContentIssue false
  • English
  • Français

How to Confirm the Conjunction of Disconfirmed Hypotheses

Published online by Cambridge University Press:  01 January 2022

David Atkinson ,
Jeanne Peijnenburg  and
Theo Kuipers
Get access Rights & Permissions [Opens in a new window]

Abstract

Could some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it might, moreover under conditions that are the same for ten different measures of confirmation. Further, we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

Type
Research Article
Information
Philosophy of Science , Volume 76 , Issue 1 , January 2009 , pp. 1 - 21
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

We would like to thank Igor Douven for having made most useful comments. He brought our attention to the fact that a particular class of examples of what we in Appendix B shall call the Alan Author Effect has been recently published by him (Douven 2007, 155–156). We acknowledge also the lively and helpful comments of the members of the Groningen research group PCCP (Promotion Club Cognitive Patterns).

References

Bovens, L., and Hartmann, S. (2003a), Bayesian Epistemology. Oxford: Oxford University Press.Google Scholar
Bovens, L., and Hartmann, S. (2003b), “Solving the Riddle of Coherence”, Solving the Riddle of Coherence 112:601–633.Google Scholar
Bovens, L., and Hartmann, S. (2005), “Coherence and the Role of Specificity: A Response to Meijs and Douven”, Coherence and the Role of Specificity: A Response to Meijs and Douven 114:365–369.Google Scholar
Carnap, R. (1950), Logical Foundations of Probability. Chicago: University of Chicago Press.Google Scholar
Carnap, R. (1962), Logical Foundations of Probability, 2nd ed. Chicago: University of Chicago Press.Google Scholar
Christensen, D. (1999), “Measuring Confirmation”, Measuring Confirmation 96:437–461.Google Scholar
Crupi, V., Fitelson, B., and Tentori, K. (2008), “Probability, Confirmation, and the Conjunction Fallacy”, Probability, Confirmation, and the Conjunction Fallacy 14:182–199.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
Douven, I. (2007), “Fitch's Paradox and Probabilistic Antirealism”, Fitch's Paradox and Probabilistic Antirealism 86:149–182.Google Scholar
Douven, I., and Meijs, W. (2006), “Bootstrap Confirmation Made Quantitative”, Bootstrap Confirmation Made Quantitative 149:97–132.Google Scholar
Douven, I., and Meijs, W. (2007), “Measuring Coherence”, Measuring Coherence 156:405–425.Google Scholar
Eells, E. (1982), Rational Decision and Causality. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Fisk, J. E. (2004), “Conjunction Fallacy”, in Pohl, R. F. (ed.), Cognitive Illusions. New York: Psychology Press, 23–42.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): S363–S378.Google Scholar
Fitelson, B. (2001), “A Bayesian Account of Independent Evidence with Applications”, A Bayesian Account of Independent Evidence with Applications 68:123–140.Google Scholar
Fitelson, B. (2003), “A Probabilistic Theory of Coherence”, A Probabilistic Theory of Coherence 63:194–199.Google Scholar
Good, I. J. (1950), Probability and the Weighing of Evidence. London: Griffin.Google Scholar
Joyce, J. (1999), The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kahneman, D., and Tversky, A. (1972), “Subjective Probability: A Judgment of Representativeness”, Subjective Probability: A Judgment of Representativeness 3:430–454.Google Scholar
Kahneman, D., and Tversky, A. (1973), “On the Psychology of Prediction”, On the Psychology of Prediction 80:237–251.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
Meijs, W., and Douven, I. (2005), “Bovens and Hartmann on Coherence”, Bovens and Hartmann on Coherence 114:355–363.Google Scholar
Milne, P. (1996), “Log$[ p( h/ eb) / p( h/ b) ] $ is the One True Measure of Confirmation”, Philosophy of Science 63:21–26.CrossRefGoogle Scholar
Nozick, R. (1981), Philosophical Explanations. Oxford: Clarendon.Google Scholar
Shogenji, T. (1999), “Is Coherence Truth-Conducive?”, Is Coherence Truth-Conducive? 59:338–345.Google Scholar
Sides, A., Osherson, D., Bonini, N., and Viale, R. (2002), “On the Reality of the Conjunction Fallacy”, On the Reality of the Conjunction Fallacy 30:191–198.Google ScholarPubMed
Tentori, K., Crupi, V., Bonini, N., Osherson, D. (2007), “Comparison of Confirmation Measures”, Comparison of Confirmation Measures 103:107–119.Google ScholarPubMed
Tversky, A., and Kahneman, D. (1983), “Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment”, Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment 90:293–315.Google Scholar