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Probability and Infinity

  • Jaakko Hintikka
  • Robert S. Cohen
  • Donald Davidson
  • Gabriël Nuchelmans
  • Wesley C. Salmon
Chapter
Part of the Synthese Library book series (SYLI, volume 104)

Abstract

In the preceding chapter the relations between the epistemic concept of probability, as a logic of partial belief, and the measure-theoretic concept of probabilitywere developed for objects — sentences — of finite complexity. The account showed that there are nice relations among (i) probabilities on sets of sentences, (ii) probabilities on the Tarski-Lindenbaum Algebras associated with those sets of sentences, (iii) the transparency of partial belief, and (iv) a condition formulated there, based upon the concept of coherence, called the simple sum condition. That account seems satisfactory as far as it goes, but, leaving aside the question to what extent it can be made less relativistic, that is to say, in what ways appropriate logics T can be more precisely specified, it remains obviously incomplete in one important formal respect: The functions there defined apply only to finitely complex objects, and, in particular, are additive only over finite disjunctions of incompatible sentences, or over finite unions of disjoint sets.

Keywords

Boolean Algebra Finite Subset Chapter Versus Individual Constant Basic Sentence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1976

Authors and Affiliations

  • Jaakko Hintikka
    • 1
  • Robert S. Cohen
    • 2
  • Donald Davidson
    • 3
  • Gabriël Nuchelmans
    • 4
  • Wesley C. Salmon
    • 5
  1. 1.Academy of Finland and Stanford UniversityUSA
  2. 2.Boston UniversityUSA
  3. 3.University of ChicagoUSA
  4. 4.University of LeydenUSA
  5. 5.University of ArizonaUSA

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