Abstract
Carnap and Reichenbach made extraordinary contributions to our understanding of the foundations of probability.1 Each of them provided a precise logical and mathematical analysis of probability that satisfied the formal calculus of probability. Reichenbach’s theory of probability analysed probability as the limit of relative frequency, while Carnap’s theory of probability explicated probability as a degree of logical connection. Carnap articulated his account of the foundations of probability by insisting that there were two concepts of probability, his own, probability one, and the other, including Reichenbach’s, probability two. Probability one is a logical conception, and the truth of the probability statements is a consequence of the definition of a measure function. Probability two is a factual conception, and the truth of the probability statements is a consequence of the existence of limits of relative frequencies. Explained in this way, the two accounts are not competitive. In fact, there is no inconsistency between the two accounts. They offer us two different interpretations of the calculus of probability.
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Notes
The major works of Carnap and Reichenbach pertaining to the foundations of probability, are H. Reichenbach, Wahrscheinlichkeitslehre, (Leiden, 1935), translated into English as The Theory of Probability, Berkeley, 1949, and R. Carnap, Logical Foundations of Probability, Chicago, 1950, The Continuum of Inductive Methods, Chicago, 1952, and chapters 1 and 2 of Studies in Inductive Logic and Probability, R. Carnap and R.C. Jeffrey, eds., Berkeley and Los Angeles, 1971.
J. Hintikka, “A Two-dimensional Continuum of Inductive Methods”, in: Aspects of Inductive Logic, J. Hintikka and P. Suppes, eds., Amsterdam, 1966.
I. Hacking, “Linguistically Invariant Inductive Logic”, Synthese 20, 1969, pp.25–47 contains a reply to W.C. Salmon, “Carnap’s Inductive Logic”, Journal of Philosophy 21, 1967.
O. Neurath, “Soziologie im Physikalismus” (1931), in: Otto Neurath, Gesammelte philosophische und methodologische Schriften,R. Haller and H. Rutte, eds., Vienna, 1981. “Unified Science as Encyclopedic Integration”, in International Encyclopedia of Unified Science,vol.1, part 1, R. Carnap and C.W. Morris, eds. Chicago, 1938 is a fundamental statement of Neurath’s views. I am much indebted to the essays by R. Haller for my interpretation of Neurath, especially those in: Rediscovering the Forgotten Vienna Circle,T.E. Uebel, ed., Dordrecht and Boston, 1991, in particular, “History and the System of Science of Otto Neurath”, pp.33–40.
H. Reichenbach, Theory of Probability op.cit.n.1. My exposition is based on this work passim, and further citations are omitted.
R. Carnap, Logical Foundations of Probability. op.cit.n.1.
Cf. Chapters 1 and 2 in Studies in Inductive Logic and Probability.
R.C. Jeffrey, The Logic of Decision, New York and London, 1965.
J. Hintikka, “A Two-dimensional Continuum of Inductive Methods” op.cit.n.2.
Cf. R. Haller, “History and System of Science in Otto Neurath” op.cit.n.4, esp. pp.38–39.
K. Lehrer and C. Wagner, Rational Consensus in Science and Society: A Philosophical and Mathematical Study, Dordrecht, 1981.
T.S. Kuhn, The Structure of Scientific Revolutions, Chicago, 1962.
Ibid.
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Lehrer, K. (1993). Carnap and Reichenbach on Probability with Neurath the Winner. In: Stadler, F. (eds) Scientific Philosophy: Origins and Developments. Vienna Circle Institute Yearbook [1993], vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2964-2_10
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