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12 - Levi and the Lottery

Published online by Cambridge University Press:  05 March 2010

Erik J. Olsson
Erik J. Olsson
Affiliation:
Lunds Universitet, Sweden
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Summary

It is as rational to accept the hypothesis that ticket i will not win as it is to accept any statistical hypothesis that I can think of.

Henry E. Kyburg

It is as rational to suspend judgement regarding the outcome of a fair lottery as it is to suspend judgement in any case I can think of.

Isaac Levi

INTRODUCTION

Consider a lottery of 1,000,000 tickets where there is one and only one winner and where one ticket is as likely as any other to be the winner. In this sort of scenario it is extremely improbable that any given ticket will win. The probability that a given ticket will lose is as high as that of any statistical hypothesis one can think of. If we are ever allowed to accept a hypothesis as true, then surely we are allowed to accept, of any given ticket, that it will lose. But to accept, for each ticket, that it will lose is to commit oneself to there being no winning ticket. This contradicts our background knowledge that there is a winning ticket. It seems, then, that common sense gives us a license for holding contradictory beliefs.

The lottery paradox, first formulated by Henry Kyburg, is still a hotly disputed subject that is thought to have all sorts of radical consequences for human inquiry. Kyburg saw it as an argument for cultivating a tolerance for inconsistency and against demanding logical closure of a rational agent's beliefs.

Type
Chapter
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Knowledge and Inquiry
Essays on the Pragmatism of Isaac Levi
 , pp. 167 - 178
Publisher: Cambridge University Press
Print publication year: 2006

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References

Bovens, Luc, and Hawthorne, James. 1999. “The Preface, the Lottery, and the Logic of Belief.” Mind 108: 241–64Google Scholar
Harman, Gilbert. 1968. “Knowledge, Inference and Explanation.” American Philosophical Quarterly 5: 164–73Google Scholar
Harman, Gilbert, and Sherman, Brett. 2004. “Knowledge, Assumptions, Lotteries.” Philosophical Issues 14: 492–500CrossRefGoogle Scholar
Kyburg, Henry E. 1961. Probability and the Logic of Rational Belief. Middleton, Conn.: Wesleyan University PressGoogle Scholar
Kyburg, Henry E. 1963. “A Further Note on Rationality and Consistency.” Journal of Philosophy 60: 463–5CrossRefGoogle Scholar
Levi, Isaac. 1962. “On the Seriousness of Mistakes.” Philosophy of Science 29: 47–65CrossRefGoogle Scholar
Isaac, Levi. 1965. “Deductive Cogency in Inductive Inference.” Journal of Philosophy 62: 68–77Google Scholar
Levi, Isaac. 1967. Gambling with Truth: An Essay on Induction and the Aims of Science. Cambridge, Mass.: MIT PressGoogle Scholar
Levi, Isaac. 1980. The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance. Cambridge, Mass.: MIT PressGoogle Scholar
Levi, Isaac. 1984. Decisions and Revisions: Philosophical Essays on Knowledge and Value. Cambridge: Cambridge University PressCrossRefGoogle Scholar
Levi, Isaac. 1991. The Fixation of Belief and Its Undoing: Changing Beliefs through Inquiry. Cambridge: Cambridge University PressCrossRefGoogle Scholar
Levi, Isaac. 1996. For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inferences, and Nonmonotonic Reasoning. Cambridge: Cambridge University PressCrossRefGoogle Scholar
Levi, Isaac. 1997. The Covenant of Reason: Rationality and the Commitments of Thought. Cambridge: Cambridge University PressCrossRefGoogle Scholar
Olsson, Erik J. 2004. “F. P. Ramsey on Knowledge and Fallibilism.” Dialectica 58: 549–58CrossRefGoogle Scholar
Rabinowicz, Wlodek. 1979. “Reasonable Beliefs.” Theory and Decision 10: 61–81CrossRefGoogle Scholar
Shope, Robert, K. 2002. “Conditions and Analyses of Knowing.” In Moser, Paul K. (ed.), The Oxford Handbook of Epistemology, pp. 25–70. Oxford: Oxford University PressCrossRefGoogle Scholar
Wittgenstein, Ludwig. 1977. On Certainty, ed. Anscombe, G. E. M. and Wright, G. H., transl. Denis Paul and G. E. M. Anscombe. Oxford: Basil Blackwell, 1977Google Scholar

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  • Levi and the Lottery
  • Erik J. Olsson, Lunds Universitet, Sweden
  • Book: Knowledge and Inquiry
  • Online publication: 05 March 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511584312.014
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  • Levi and the Lottery
  • Erik J. Olsson, Lunds Universitet, Sweden
  • Book: Knowledge and Inquiry
  • Online publication: 05 March 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511584312.014
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Levi and the Lottery
  • Erik J. Olsson, Lunds Universitet, Sweden
  • Book: Knowledge and Inquiry
  • Online publication: 05 March 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511584312.014
Available formats
×