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Probability functions and their assumption sets. The singulary case. (English) Zbl 0539.60007
Probability is a relative concept. Philosophers tend to make binary probability functions their main concern. On the other hand, mathematicians treat probability as an absolute function. However, following Rényi some mathematicians have started to study binary probability functions. The author, aware of the relativity of probability assessments, finds the use of binary probability functions an ineffective and wrong-headed response. The paper is an attempt to find a new response to this problem.
Reviewer: D.Costantini

60A99 Foundations of probability theory
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[1] Carnap, R., 1950: Logical Foundations of Probability, The University of Chicago Press, Chicago. · Zbl 0040.07001
[2] Field, H. H., 1977: ?Logic, Meaning, and Conceptual Role?, The Journal of Philosphy 74, 379-409.
[3] Keynes, J. M., 1921: A Treatise on Probability, Macmillan, London.
[4] Kolmogorov, A. N., 1933: Grundbegriffe der Wahrscheinlichkeitsrechnung, Berlin. · JFM 59.1154.01
[5] Leblanc, H., 1979. ?Probabilistic Semantics for First-Order Logic?, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 25, 497-509. · Zbl 0424.03006
[6] Leblanc, H., 1982. ?Popper’s 1955 Axiomatization of Absolute Probability?, Pacific Philosophical Quarterly 69, 133-145.
[7] Leblanc, H., 1983. ?Alternatives to Standard First-Order Semantics?, Handbook of Philosphical Logic, Vol. I, D. M. Gabbay and F. Guenthner (eds.), D. Reidel, Dordrecht, pp. 189-274. · Zbl 0875.03077
[8] Leblanc, H. and Morgan, C. G., 1984: ?Probability Functions and their Assumption Sets: The Binary Case?, to appear in Synthèse.
[9] Leblanc, H. and Van Fraassen, B. C., 1979. ?On Carnap and Popper Probability Functions?, The Journal of Symbolic Logic 44, 369-373. · Zbl 0419.03018
[10] Morgan, C. G. and Leblanc, H., 1983: ?Probability Theory, Intuitionism, Semantics, and the Dutch Book Argument?, Notre Dame Journal of Formal Logic 24, 289-304. · Zbl 0531.03037
[11] Popper, K. R., 1955: ?Two Autonomous Axiom Systems for the Calculus of Probabilities?, The British Journal for the Philosophy of Science 6, 51-57, 176, 351.
[12] Quine, W. V., 1940: Mathematical Logic, Norton, New York. · JFM 66.0027.03
[13] Rényi, A., 1955: ?On a New Axiomatic Theory of Probability?, Acta Mathematica Acad. Scient. Hungaricae 6, 285-335. · Zbl 0067.10401
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