Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-23T21:40:42.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Probability, Regularity, and Cardinality

Published online by Cambridge University Press:  01 January 2022

Alexander R. Pruss
Get access Rights & Permissions [Opens in a new window]

Abstract

Regularity is the thesis that all contingent propositions should be assigned probabilities strictly between zero and one. I will prove on cardinality grounds that if the domain is large enough, a regular probability assignment is impossible, even if we expand the range of values that probabilities can take, including, for instance, hyperreal values, and significantly weaken the axioms of probability.

Type
Research Article
Information
Philosophy of Science , Volume 80 , Issue 2 , April 2013 , pp. 231 - 240
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

†

I would like to thank Trent Dougherty, Alan Hájek, Jonathan Kvanvig, and A. Paul Pedersen for discussions, comments, and encouragement and the anonymous readers for feedback that led to significant improvement of this article.

References

Appiah, Kwame Anthony. 1985. Assertion and Conditionals. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Bernstein, Allen R., and Wattenberg, Frank. 1969. “Non-standard Measure Theory.” In Applications of Model Theory of Algebra, Analysis, and Probability, ed. Luxemberg, W. A. J., 171–85. New York: Holt, Rinehart & Winston.Google Scholar
Gonzáles, Carlos G. 1995. “Dense Orderings, Partitions and Weak Forms of Choice.” Fundamenta Mathematicae 147:11–25.Google Scholar
Hájek, Alan. 2011. “Staying Regular?” Paper presented at the Australasian Association of Philosophy Conference, July.Google Scholar
Hrbacek, Karel, and Jech, Thomas. 1999. Introduction to Set Theory. 3rd ed. New York: Dekker.Google Scholar
Jeffreys, Harold. 1961. Theory of Probability. 3rd ed. Oxford: Oxford University Press.Google Scholar
Kemeny, John G. 1955. “Fair Bets and Inductive Probabilities.” Journal of Symbolic Logic 20:263–73.CrossRefGoogle Scholar
Lewis, David. 1980. “A Subjectivist’s Guide to Objective Chance.” In Studies in Inductive Logic and Probability, Vol. 2, ed. R. C. Jeffrey, 263–93. Berkeley: University of California Press.CrossRefGoogle Scholar
Lewis, David 1986. On the Plurality of Worlds. Oxford: Blackwell.Google Scholar
Pruss, Alexander R. 2001. “The Cardinality Objection to David Lewis’s Modal Realism.” Philosophical Studies 104:169–78.CrossRefGoogle Scholar
Rosinger, Elemer E. 2007. “String Theory: A Mere Prelude to Non-Archimedean Space-Time Structures?” arXiv.org, Cornell University. arXiv:physics/0703154v1.Google Scholar
Rundle, Bede. 2004. Why There Is Something Rather than Nothing. Oxford: Oxford University Press.CrossRefGoogle Scholar
Shimony, Abner. 1955. “Coherence and the Axioms of Confirmation.” Journal of Symbolic Logic 20:1–28.CrossRefGoogle Scholar
Skyrms, Brian. 1980. Causal Necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven, CT: Yale University Press.Google Scholar
Stalnaker, Robert C. 1970. “Probability and Conditionals.” Philosophy of Science 37:64–80.CrossRefGoogle Scholar
Takeuti, Gaisi, and Zaring, Wilson M. 1971. Introduction to Axiomatic Set Theory. New York: Springer.CrossRefGoogle Scholar
Weintraub, Ruth. 2008. “How Probable Is an Infinite Sequence of Heads? A Reply to Williamson.” Analysis 68:247–50.CrossRefGoogle Scholar
Williamson, Timothy. 2007. “How Probable Is an Infinite Sequence of Heads?” Analysis 67:173–80.CrossRefGoogle Scholar