Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-31T23:39:12.485Z Has data issue: false hasContentIssue false
  • English
  • Français

What is the Logical Form of Probability Assignment in Quantum Mechanics?

Published online by Cambridge University Press:  01 April 2022

John F. Halpin
John F. Halpin*
Affiliation:
Department of Philosophy, Oakland University
Get access Rights & Permissions [Opens in a new window]

Abstract

The nature of quantum mechanical probability has often seemed mysterious. To shed some light on this topic, the present paper analyzes the logical form of probability assignment in quantum mechanics. To begin the paper, I set out and criticize several attempts to analyze the form. I go on to propose a new form which utilizes a novel, probabilistic conditional and argue that this proposal is, overall, the best rendering of the quantum mechanical probability assignments. Finally, quantum mechanics aside, the discussion here has consequences for counterfactual logic, conditional probability, and epistemic probability.

Type
Research Article
Information
Philosophy of Science , Volume 58 , Issue 1 , March 1991 , pp. 36 - 60
Copyright
Copyright © 1991 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 want to thank Arthur Fine, Alan Nelson, two anonymous referees for Philosophy of Science, and, especially, Paul Teller for comments on an earlier draft of this paper. These were extremely valuable. Research for this paper was supported by a Faculty Research Grant from Oakland University.

References

Bell, J. S. (1965), “On the Einstein-Podolsky-Rosen Paradox”, Physics 1: 195–200.CrossRefGoogle Scholar
Fine, A. (1982), “Some Local Models for Correlation Experiments”, Synthese 50: 279–294.CrossRefGoogle Scholar
Gibbons, P. (1987), Particles and Paradoxes: The Limits of Quantum Logic. Cambridge, England: Cambridge University Press.CrossRefGoogle Scholar
Halpin, J. F. (1986), “Stalnaker's Conditional and Bell's Problem”, Synthese 69: 325–340.CrossRefGoogle Scholar
Halpin, J. F. (1989), “Indeterminateness and the Peircean Theory of Tense”, unpublished manuscript.CrossRefGoogle Scholar
Leeds, S. (1984), “Chance, Realism, Quantum Mechanics”, The Journal of Philosophy 81: 567–578.CrossRefGoogle Scholar
Lewis, D. (1973), Counterfactuals. Cambridge, MA: Harvard University Press.Google Scholar
Lewis, D. (1979), “Counterfactual Dependence and Time's Arrow”, Nous 13: 455–476.CrossRefGoogle Scholar
Lewis, D. (1981), “A Subjectivist's Guide to Objective Chance”, in W. Harper, R. Stalnaker, and G. Pearce (eds.), Ifs; Conditionals, Belief, Decision, Chance, and Time. Dordrecht: Reidel. pp. 267–297.Google Scholar
Merzbacher, E. (1970), Quantum Mechanics. 2d ed. New York: Wiley & Sons.Google Scholar
Messiah, A. (1976), Quantum Mechanics, vol. 1. Second Reprint. Translated by G. M. Temmer. Originally published as Mécanique Quantique. (Paris: Dunod). Amsterdam: North-Holland.Google Scholar
Skyrms, B. (1980), Causal Necessity. New Haven: Yale University Press.Google Scholar
Skyrms, B. (1984), Pragmatics and Empiricism. New Haven: Yale University Press.Google Scholar
Skyrms, B. (1988), “Conditional Chance”, in J. Fetzer (ed.), Probability and Causality.: Essays in Honor of Wesley C. Salmon. Dordrecht: Reidel. pp. 161–178.CrossRefGoogle Scholar
Stalnaker, R. (1968), “A Theory of Conditionals”, in N. Rescher (ed.), Studies in Logical Theory. Oxford: Blackwell. pp. 98–112.Google Scholar
Stalnaker, R. (1981), “A Defense of Conditional Excluded Middle”, in Harper, Stalnaker, and Pearce (eds.), Ifs; Conditionals, Belief, Decision, Chance, and Time. Dordrecht: Reidel. pp. 87–104.Google Scholar
van Fraassen, B. (1982), “The Charybdis of Realism: Epistemological Implications of Bell's Inequality”, Synthese 52: 25–38.CrossRefGoogle Scholar
van Fraassen, B. (n.d.), “The End of the Stalnaker Conditional”, unpublished manuscript.Google Scholar
van Fraassen, B. and Hooker, C. (1976), “A Semantic Analysis of Niels Bohr's Philosophy of Quantum Theory”, in W. L. Harper and C. A. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, vol. 3. Dordrecht: Reidel. pp. 221–241.CrossRefGoogle Scholar
Wessels, L. (1981), “The ‘EPR’ Argument: A Post-Mortem”, Philosophical Studies 40: 3–30.CrossRefGoogle Scholar