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Forms for probability ascriptions


I apply the distinctions between the probability of a conditional, and a conditional with a probabilistic consequent, to quantum theory. I concentrate on an application hardly studied in the literature: namely, the case where the antecedent of the conditional states which quantity is measured, and the consequent states which value the quantity has. I show how we can construe quantum theory as providing propositions of these kinds, both for intrinsic possessed values, and for measurement results. I also show that most construals satisfy a plausible constraint requiring a kind of independence between which quantity is measured and what the value or result is.

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  1. Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of ‘hidden’ variables, I and II,Physical Review,85, 166–193.

  2. Bugajski, S. (1978). Probability implication in the logics of classical and quantum mechanics,Journal of Philosophical Logic,7, 95–106.

  3. Butterfield, J. (1987). Probability and disturbing measurement,Aristotelian Society Supplementary Volume,61, 211–243.

  4. Butterfield, J. (1992). Probabilities and conditionals: Distinctions by example,Proceedings of the Aristotelian Society,91, 251–272.

  5. Dirac, P. (1958).The Principles of Quantum Mechanics, Clarendon Press, Oxford.

  6. Ghirardi, G., Rimini, A., and Weber, T. (1986). Unified dynamics for microscopic and macroscopic systems,Physical Review D,34, 470–491.

  7. Halpin, J. (1991). What is the logical form of probability assignment in quantum mechanics?Philosophy of Science,58, 36–60.

  8. Lewis, D. (1973).Counterfactuals, Blackwells, Oxford.

  9. Lewis, D. (1986).Philosophical Papers, Volume II, Oxford University Press, Oxford.

  10. Messiah, A. (1966).Quantum Mechanics, Volume I, Wiley, New York.

  11. Pearle, P. (1989). Combining stochastic dynamical state-vector reduction with spontaneous localization,Physical Review A,39, 2277–2289.

  12. Skyrms, B. (1980).Causal Necessity, Yale University Press, New Haven, Connecticut.

  13. Skyrms, B. (1984).Pragmatics and Empiricism, Yale University Press, New Haven, Connecticut.

  14. Stalnaker, R. (1968). A theory of conditionals, inCausation and Conditionals, E. Sosa, ed., Oxford University Press, Oxford.

  15. Van Fraassen, B., and Hooker, C. (1976). A semantic analysis of Niels Bohr's philosophy of quantum theory, inFoundations of Probability Theory, Statistical Inference and Statistical Theories of Science, Volume III, W. Harper and C. Hooker, eds., Reidel, Dordrecht, pp. 221–241.

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Butterfield, J. Forms for probability ascriptions. Int J Theor Phys 32, 2271–2286 (1993).

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  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Quantum Theory
  • Conditional State