Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-05T11:47:58.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantum Probability in Logical Space

Published online by Cambridge University Press:  01 April 2022

John C. Bigelow
John C. Bigelow*
Affiliation:
La Trobe University
Get access Rights & Permissions [Opens in a new window]

Abstract

Probability measures can be constructed using the measure-theoretic techniques of Caratheodory and Hausdorff. Under these constructions one obtains first an outer measure over “events” or “propositions.” Then, if one restricts this outer measure to the measurable propositions, one finally obtains a classical probability theory. What I argue is that outer measures can also be used to yield the structures of probability theories in quantum mechanics, provided we permit them to range over at least some unmeasurable propositions. I thereby show that nonclassical probability theories can be seen to arise naturally within the framework of possible worlds semantics.

Type
Research Article
Information
Philosophy of Science , Volume 46 , Issue 2 , June 1979 , pp. 223 - 243
Copyright
Copyright © Philosophy of Science Association 1979

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.)

References

Bigelow, J. C. (1976), “Possible worlds foundations for probability,” Journal of Philosophical Logic, 5: pp. 299–320.Google Scholar
Bigelow, J. C. (1977), “Semantics of probability,” Synthese, 36: pp. 459–472.CrossRefGoogle Scholar
Carnap, R. (1950), Logical Foundations of Probability. London: Routledge and Kegan Paul.Google Scholar
Friedman, A. (1970), Foundations of Modern Analysis. New York: Holt, Rinehart and Winston.Google Scholar
Hooker, C. A. (1973), Contemporary Research in the Foundations and Philosophy of Quantum Theory. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Hooker, C. A. (ed.). (1975), The Logico-Algebraic Approach to Quantum Mechanics, Vol. I: Historical Evolution. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Hughes, G. E. and Cresswell, M. J. (1968), An Introduction to Modal Logic. London: Methuen.Google Scholar
Lewis, D. K. (1973), Counterfactuals. Oxford: Blackwell.Google Scholar
Munroe, M. E. (1953), Introduction to Measure and Integration. Reading, Mass.: Addison-Wesley.Google Scholar