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Operationism, probability and quantum mechanics

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Abstract

This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the “classical” (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, despite the fact that its philosophical back-ground strongly resembles that underlying quantum mechanics, at least according to the Copenhagen interpretation. The reasons for this are explored.

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References

  • Born, M. (1928), On the Meaning of Physical Theories, in Born (1969), pp. 13–30.

  • Born, M. (1953), Physical Reality,Philosophical Quarterly 3, pp. 139–149.

    Article  Google Scholar 

  • Born, M. (1955), Statistical Interpretation of Quantum Mechanics,Science 122, 675–679, reprinted in Born (1969), pp. 89–99.

    Article  Google Scholar 

  • Born, M. (1965a), Symbol and Reality,Universitas 7, 337–353, reprinted in Born (1969), pp. 132–146.

    Google Scholar 

  • Born, M. (1965b), In Memory of Einstein,Universitas 8, 33–44, reprinted in Born (1969), pp. 155–165.

    Google Scholar 

  • Born, M. (1969),Physics in my Generation, New York, Springer.

    Book  Google Scholar 

  • Carnap, R. (1928),Der logische Aufbau der Welt, Berlin, Weltkreis, English translationThe Logical Structure of the World, Berkeley, Univ. of California Press, 1969.

    Google Scholar 

  • Carnap, R. (1963), Intellectual Autobiography, inThe Philosophy of Rudolf Carnap, ed. by P.A.Schilpp, La Salle, Ill., Open Court, pp. 3–84.

    Google Scholar 

  • de Finetti, B. (1929), Funzione caratteristica di un fenomeno aleatorio, inAtti del Congresso Internazionale dei matematici, Bologna, Zanichelli, pp. 179–190, reprinted in de Finetti (1981), pp. 97–108.

  • de Finetti, B. (1931a), Probabilismo,Logos, 163–219, English translation inErkenntnis 31, 1989, 169–223.

  • deFinetti, B. (1931b), Sul significato soggettivo della probabilità,Fundamenta matematicae 17, 298–329, English translation in de Finetti (1993), pp. 291–321.

    Google Scholar 

  • deFinetti, B. (1931c), Le leggi differenziali e la rinunzia al determinismo,Rendiconti del Seminario Matematico della R. Università di Roma, 2nd series,7, 63–74, English translation in de Finetti (1993), pp. 323–334.

    Google Scholar 

  • deFinetti, B. (1936), Statistica e probabilità nella concezione di R. von Mises,Supplemento statistico ai Nuovi problemi di Politica, Storia ed Economia 2, 9–19, English translation in de Finetti (1993), pp. 353–364.

    Google Scholar 

  • deFinetti, B. (1937), La prévision: ses lois logiques, ses sources subjectives,Annales de l'Institut Henri Poincaré 7, 1–68, English translation in H.E. Kyburg and H.E. Smokler (eds.),Studies in Subjective Probability, New York, Wiley, 1964, pp. 95–158.

    Google Scholar 

  • deFinetti, B. (1941), Punti di vista: Hans Reichenbach,Statistica 1, 125–133, reprinted in de Finetti (1989), pp. 237–248.

    Google Scholar 

  • de Finetti, B. (1951), Recent Suggestions for the Reconciliation of Theories of Probability, inProceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, Univ. of California Press, pp. 217–225, reprinted in de Finetti (1993), pp. 375–387.

  • de Finetti, B. (1971), Probabilità di una teoria e probabilità dei fatti, inStudi di probabilitá, statistica e ricerca operaliva, ed. by G. Pompilj, Gubbio, Oderisi, pp. 86–101.

  • deFinetti, B. (1972), Subjective or Objective Probability: is the Dispute Undecidable?,Symposia Mathematica 9, 21–36.

    Google Scholar 

  • deFinetti, B. (1978), Einstein: Originality and Intuition,Scientia 72, 123–128.

    Google Scholar 

  • deFinetti, B. (1981),Scritti (1926–1930), Padova, CEDAM.

    Google Scholar 

  • deFinetti, B. (1989),La logica dell'incerto, ed. by M.Mondadori, Milano, Il Saggiatore.

    Google Scholar 

  • deFinetti, B. (1991),Scritti (1931–1936), Bologna, Pitagora.

    Google Scholar 

  • deFinetti, B. (1993),Induction and Probability, ed. by P.Monari and D.Cocchi, Bologna, CLUEB (supplement toStatistica 52, 1992, n.3).

    Google Scholar 

  • vanFraassen, B. (1991),Quantum Mechanics: An Empiricist View, Oxford, Oxford Univ. Press.

    Book  Google Scholar 

  • Galavotti, M.C. (1989), Anti-realism in the Philosophy of Probability: Bruno de Finetti's Subjectivism,Erkenntnis 31, 239–261.

    Article  Google Scholar 

  • Galavotti, M.C. (1991), The Notion of Subjective Probability in the Work of Ramsey and de Finetti,Theoria 57, 239–259.

    Article  Google Scholar 

  • Heisenberg, W. (1925), Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen,Zeitschrift für Physik 33, 879–893, English translation in van der Waerden, ed. (1967), (all page references to the English edition).

    Article  Google Scholar 

  • Heisenberg, W. (1927), Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,Zeitschrift für Physik 43, 172–198, English translation in Wheeler and Zurek, eds. (1983), (all page references to the English edition).

    Article  Google Scholar 

  • Heisenberg, W. (1930),The Physical Principles of Quantum Theory, Univ. of Chicago Press, 2nd edition New York, Dover Publ. Co., 1949 (all page references to the latter edition).

    Google Scholar 

  • Heisenberg, W. (1955),Das Naturbild der Heutigen Physik, Hamburg, Rowohlt, English translationThe Physicist's Conception of Nature, London, Hutchinson, 1958 (all page references to the latter edition).

    Google Scholar 

  • Heisenberg, W. (1958),Physics and Philosophy, reprinted London, Penguin Books, 1990 (all page references to the latter edition).

  • Laplace, P.S. (1814a),Essai philosophique sur les probabilités, Paris.

  • Laplace, P.S. (1814b),Theorie analytique des probabilités, Paris, 2nd edition.

  • Margenau, H. and Park, J.L. (1967), Objectivity in Quantum Mechanics, inDelaware Seminar in the Foundations of Physics, ed. by M.Bunge, Berlin, Springer, pp. 161–187.

    Chapter  Google Scholar 

  • vonMises, R. (1951),Positivism, Harvard, Harvard Univ. Press, reprinted New York: Dover, 1968 (all page references to the latter edition).

    Google Scholar 

  • vonMises, R. (1928),Wahrscheinlichkeit, Statistik und Wahrheit, Wien, Springer, English revised editionProbability, Statistics and Truth, New York, Dover, 1957 (all page references to the latter edition)

    Book  Google Scholar 

  • Pais, A. (1982), Max Born's Statistical Interpretation of Quantum Mechanics,Science 218, 1193–1198.

    Article  Google Scholar 

  • Ramsey, F.P. (1931),The Foundations of Mathematics and Other Logical Essays, ed. by R.B.Braithwaite, London, Routledge and Kegan Paul.

    Google Scholar 

  • Ramsey, F.P. (1991),Notes on Philosophy, Probability and Mathematics, ed. by M.C.Galavotti, Naples, Bibliopolis.

    Google Scholar 

  • Schlick, M. (1917),Raum und Zeit in der Gegenwärtigen Physik, Wien, Springer, English translation 1920, reprinted inPhilosophical Papers, vol. I, ed. by H.L. Mulder and F.B. van de Welde-Schlick, Dordrecht, Reidel, 1979, pp. 207–269.

    Book  Google Scholar 

  • van derWaerden, B.L. ed. (1967),Sources of Quantum Mechanics, Amsterdam, North-Holland.

    Google Scholar 

  • Wheeler, J.A. and Zurek, W.H. eds. (1983),Quantum Theory and Measurement, Princeton, Princeton Univ. Press.

    Google Scholar 

Download references

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Galavotti, M.C. Operationism, probability and quantum mechanics. Found Sci 1, 99–118 (1995). https://doi.org/10.1007/BF00208727

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