Abstract
Can the axioms of probability theory and the classical patterns of statistical inference ever be falsified by observation? Various possible answers to this question are examined in a set theoretical context and in relation to the findings of microphysics.
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References
Bell, J. S.: 1966, ‘On the Einstein-Podolsky-Rosen Paradox’, Physics 1, 195–200.
Birkhoff, G. and von Neumann, J.: 1936, ‘The Logic of Quantum Mechanics’, Annals of Mathematics 37, 823–843.
Bub, J.: 1977, ‘Von Neumann's Projection Postulate as a Probability Conditionalization in Quantum Mechanics’, Journal of Philosophical Logic 6, 381–390.
Carnap, R.: 1950, Logical Foundations of Probability, The University of Chicago Press, Chicago.
Chow, Y. S. and Teicher, H.: 1978, Probability Theory, Independence Interchangeability, Martingales, Springer Verlag, Berlin.
Feynman, R.: 1951, ‘The Concept of Probability in Quantum Mechanics’, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley.
Friedman, M. and Putnam, H.: 1978, ‘Quantum Logic, Conditional Probability and Interference’, Dialectica 32, 305–315.
Fraassen, B. C. van: 1982, ‘The Charybdis of Realism: Epistemological Implication of Bell's Inequality’, Synthese 52, 25–38.
Gleason, A. M.: 1957, ‘Measures on Closed Subspaces of a Hilbert Space’, Journal of Mathematics and Mechanics 6, 885–893.
Hume, D.: 1948, An Inquiry Concerning Human Understanding (1955 edition, edited by C. W. Hendel) Bobbs-Merrill, Indianapolis.
Mermin, N. D.: 1981, ‘Quantum Mysteries for Anyone’, The Journal of Philosophy 78, 397–408.
Mises, R. Von: 1957, Probability Statistics and Truth, Dover, New York (First German Edition 1928).
Popper, K. R.: 1974, The Logic of Scientific Discovery, Hutchinson, London (First German Edition 1934).
Popper, K. R.: 1983, Realism and the Aim of Science (Postscript) Rowman and Littlefield, Totowa, N.J.
Putnam, H.: 1968, ‘Is Logic Empirical?’, in R. S. Cohen and M. W. Wartofsky (eds.), Boston Studies in the Philosophy of Science, Vol. V, 216–241.
Quine, W. V. O.: 1953, From a Logical Point of View, Harper & Row, New York.
Reichenbach, H.: 1949, The Theory of Probability, The University of California Press, Berkeley.
Schlick, M.: 1918, General Theory of Knowledge, Springer Verlag, New York (English Edition 1974).
Solovey, R. M.: 1970, ‘A Model of Set Theory in Which Every Set of Reals is Lebesgue Measurable’, Annals of Mathematics 92, 1–56.
Weinberg, S.: 1972, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York.
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Pitowsky, I. On the status of statistical inferences. Synthese 63, 233–247 (1985). https://doi.org/10.1007/BF00485368
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DOI: https://doi.org/10.1007/BF00485368