Abstract
The thesis of this article is that the nature of probability is centered on its formal properties, not on any of its standard interpretations. Section 2 is a survey of Bayesian applications. Section 3 focuses on two examples from physics that seem as completely objective as other physical concepts. Section 4 compares the conflict between subjective Bayesians and objectivists about probability to the earlier strident conflict in physics about the nature of force. Section 5 outlines a pragmatic approach to the various interpretations of probability. Finally, Sect. 6 argues that the essential formal nature of probability is expressed in the standard axioms, but more explicit attention should be given to the concept of randomness.
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References
Alekseev, V. M. (1968–1969a). Quasirandom dynamical systems I, II, III. Mathematicheskii USSR Sbornik 5–7, 505–560 (and 1–43).
Alekseev, V. M. (1969b). Quasirandom dynamical systems (Russian). Mathematicheskii Zametki 6(4):489–498. (English translation in Mathematical Notes 6 (1969), 749–753.)
Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society 53:370–418. (Reprinted in Facsimiles of two papers by Bayes with a commentary by W. Edwards Deming, Ed., 1940, New York: Hafner Pub. Co.)
Birkhoff, G. D. (1927/1966). Dynamical systems, Vol. 9. New York: AMS College Publications.
Birkhoff, G. D. (1935). Nouvelles Recherches sur les systèmes dynamiques. Memoriae Pontificiae Academiae Scientiarum Novi Lyncaei, 1, 85–216.
Boullier, F. (1868). Histoire de la Philosophie Cartesienne (3rd ed.). Paris: Delagrave.
Carnap, R. (1950). The logical foundations of probability. Chicago, IL: University of Chicago Press.
Dawid, A. P. (1986). Probability forecasting. In S. Kotz, N. L. Johnson, & C. B. Read (Eds.), Encyclopedia of statistical sciences (pp. 210–218). New York: Wiley.
Descartes, R. (1644/1983). Principia philosophiae. Amsterdam: Ludovicum Elzevirium. (V. R. Miller & R. P. Miller (Ed.), Trans., Principles of philosophy. Dordrecht: Reidel, 1983.)
Descartes, R. (1897). Meditationes De Prima Philosophia. In C. Adam & P. Tannery (Eds.), Oeuvres des Descartes. Paris: L. Cerf.
Downey, R., Hirschfeldt, D. R., Nies, A., & Terwijn, S. A. (2006). Calibrating randomness. The Bulletin of Symbolic Logic, 12, 411–491.
Epicurus. (1940). Epicurus to Herodotus. In W. J. Oates (Ed.), The Stoic and Epicurean philosophers: The complete extant writings of Epicurus, Epictetus, Lucretius. New York: Random House. (by arrangement with Oxford University Press).
Jaynes, E. T. (1978). Where do we stand on maximum entropy? In R. D. Rosenkrantz (Ed.), Papers on probability, statistics and statistical physics (pp. 211–314). Dordrecht: Reidel.
Jeffreys, H. (1948). Theory of probability (2nd ed.). Oxford: Clarendon Press. (First published in 1939).
Kant, I. (1786/1970). Metaphysical foundations of natural science. New York: Bobbs-Merrill Company, Inc. (First published in 1786. J. Ellington, Trans., with introduction and essay.)
Laplace, P. S. (1799/1966). Mécanique céleste. Bronx, NY: Chelsea Publishing Co. (Vols. 1–4 is a Reprint of the English translation by Nathaniel Bowditch of the edition published in Boston, 1829–1839.)
Makridakis, S., Andersen, A., Carbone, R., Fildes, R., Hilbon, M., Lewandowski, R., et al. (1984). The forecasting accuracy of major time series methods. Chichester, UK: Wiley.
Miller, J. S., & Nies, A. (2006). Randomness and computability: open questions. The Bulletin of Symbolic Logic, 12, 390–410.
Moser, J. (1973). Stable and random motions in dynamical systems with special emphasis on celestial mechanics. Herman Weyl Lectures, the Institute for Advanced Study. Princeton, NJ: Princeton University Press.
Mosteller, F., & Wallace, D. L (1964/1984). Applied Bayesian and classical inference: The case of the federalist papers. Springer Series in Statistics. New York: Springer.
Mouy, P. (1934). Le Developpement de la Physique Cartesienne 1646–1712. Paris: J. Vrin.
Newton, I. (1686/1946). Philosophiae Naturalis Principia Mathematica. Berkeley, CA: University of California Press. (First published in 1687. F. Cajori, Trans.)
Ornstein, D. S., & Weiss, B. (1991). Statistical properties of chaotic systems. Bulletin of the American Mathematical Society (New Series), 24, 11–116.
Sitnikov, K. (1960). Existence of oscillating motions for the three-body problem. Doklady Akademii Nauk, USSR, 133(2), 303–306.
Skyrms, B. (1990). The dynamics of rational deliberation. Cambridge, MA: Harvard University Press.
Suppes, P. (1954). Descartes and the problem of action at a distance. Journal of the History of Ideas, 15, 146–152.
Suppes, P. (1967). Some extensions of Randall’s Interpretation of Kant’s philosophy of science. In J. P. Anton (Ed.), Naturalism and historical understanding: Essays on the philosophy of John Herman Randall, Jr (pp. 108–120). New York: State University of New York Press.
Suppes, P. (1983). Arguments for randomizing. In P. D. Asquith & T. Nickles (Eds.), PSA 1982. Lansing, MI: Philosophy of Science Association.
Suppes, P. (2002). Representation and invariance of scientific structures. Stanford University: CSLI Publications.
Suppes, P. (2007). Where do Bayesian priors come from? Synthese, 156, 441–471.
Whewell, W. (1857). History of the inductive sciences (3rd ed.). London: John W. Parker and Son.
Whittaker, E. T. (1910). A history of the theories of aether and electricity. London: Longmans, Green & Co. (Dublin University Press).
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It is a pleasure to dedicate this article to Brian Skyrms on the occasion of his 70th birthday. We have been talking about philosophical matters for more than 30 years, and I have learned much from these talks as well as his books.
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Suppes, P. The nature of probability. Philos Stud 147, 89–102 (2010). https://doi.org/10.1007/s11098-009-9453-z
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DOI: https://doi.org/10.1007/s11098-009-9453-z