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What Price Substitutivity? A Note on Probability Theory

Published online by Cambridge University Press:  01 April 2022

Hugues Leblanc
Hugues Leblanc*
Affiliation:
Department of Philosophy Temple University
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Extract

Teddy Seidenfeld recently claimed that Kolmogorov's probability theory transgresses the Substitutivity Law. Underscoring the seriousness of Seidenfeld's charge, the author shows that (Popper's version of) the law, to wit:

If (∀D)(Pr(B,D) = Pr(C,D)), then Pr(A,B) = Pr(A,C),

follows from just

five constraints on Pr of the most elementary and most basic sort.

Type
Research Article
Information
Philosophy of Science , Volume 48 , Issue 2 , June 1981 , pp. 317 - 322
Copyright
Copyright © 1981 by the Philosophy of Science Association

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Footnotes

†

The paper was sketched in July 1979 while I served as visiting Professor of Philosophy at Dalhousie University, Halifax; it was completed in the Spring of 1980 while I held a Study Leave from Temple University. Thanks are due to Teddy Seidenfeld, who read the text at each stage and on one major issue set it to rights. Thanks are also due to the referee for his criticisms and advice.

References

Harper, W. L., Leblanc, H., and van Fraassen, B. C. (1982), “On Characterizing Popper and Carnap Probability Functions”, Studies in Epistemology and Semantics, New York: Haven Publishing Corp.Google Scholar
Leblanc, H. (1960), “On Requirements for Conditional Probability Functions”, The Journal of Symbolic Logic, vol. 25: 238–242.CrossRefGoogle Scholar
Leblanc, H. (1979), “Probabilistic Semantics for First-Order Logic”, Zeitschrift für mathematische Logik und Grundlagen der Mathematik: 497–509.CrossRefGoogle Scholar
Popper, K. R. (1959), The Logic of Scientific Discovery. New York: Basic Books.Google Scholar
Seidenfeld, T. (1981), “Probability, Continuity, and Transformation of Continuous Random Variables”, Studies in Epistemology and Semantics.Google Scholar