What price substitutivity? A note on probability theory

Philosophy of Science 48 (2):317-322 (1981)
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Abstract

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 C1. 0≤ Pr(A,B)≤ 1 C2. Pr(A,A)=1 C3. Pr(A & B,C)=Pr(A,B & C)× Pr(B,C) C4. Pr(A & B,C)=Pr(B & A,C) C5. Pr(A,B & C)=Pr(A,C & B), five constraints on Pr of the most elementary and most basic sort

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10.1086/289000

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Citations of this work

The autonomy of probability theory (notes on Kolmogorov, rényi, and popper).Hugues Leblanc - 1989 - British Journal for the Philosophy of Science 40 (2):167-181.
Physical probabilities.Peter Milne - 1987 - Synthese 73 (2):329 - 359.
Probabilistic Substitutivity at a Reduced Price.David Miller - 2011 - Principia: An International Journal of Epistemology 15 (2):271-.

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References found in this work

The Logic of Scientific Discovery.Karl Popper - 1959 - Studia Logica 9:262-265.
Probabilistic Semantics for First‐Order Logic.Hugues Leblanc - 1979 - Mathematical Logic Quarterly 25 (32):497-509.
Probabilistic Semantics for First-Order Logic.Hugues Leblanc - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (32):497-509.
On requirements for conditional probability functions.Hugues Leblanc - 1960 - Journal of Symbolic Logic 25 (3):238-242.

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