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v. 1. Nominalism and realism.--v. 2. A theory of universals. |
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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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