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Erkenntnis

, Volume 55, Issue 2, pp 183–215 | Cite as

Probabilities For Multiple Properties: The Models Of Hesse And Carnap And Kemeny

  • Patrick Maher
Article

Abstract

In 1959 Carnap published a probability model that was meant to allow forreasoning by analogy involving two independent properties. Maher (2000)derived a generalized version of this model axiomatically and defended themodel's adequacy. It is thus natural to now consider how the model mightbe extended to the case of more than two properties. A simple extension waspublished by Hess (1964); this paper argues that it is inadequate. Amore sophisticated one was developed jointly by Carnap and Kemeny in theearly 1950s but never published; this paper gives the first published descriptionof Carnap and Kemeny's model and argues that it too is inadequate. Since noother way of extending the two-property model is currently known, the conclusionof this paper is that a satisfactory extension to multiple properties requires somenew approach.

Keywords

Probability Model Generalize Version Multiple Property Simple Extension Independent Property 
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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REFERENCES

  1. Achinstein, P.: 1963, ‘Variety and Analogy in Confirmation Theory’, Philosophy ofScience 30, 207–221.Google Scholar
  2. Carnap, R.: 1945, ‘On Inductive Logic’, Philosophy of Science 12,72–97.Google Scholar
  3. Carnap, R.: 1952, The Continuum of Inductive Methods, University of ChicagoPress, Chicago.Google Scholar
  4. Carnap, R.: 1954, ‘m(Z) for n Families as a Combination of mλ-Functions’,Document 093–22–01 in the Rudolf Carnap Collection, University of Pittsburgh Library. The notation is explained in document 093–22-03.Google Scholar
  5. Carnap, R.: 1963, ‘Replies and Systematic Expositions’, in P. A. Schilpp(ed.), The Philosophy of Rudolf Carnap, Open Court, La Salle, IL, pp. 859–1013.Google Scholar
  6. Carnap, R.: 1975, ‘Notes on Probability and Induction’, in J. Hintikka (ed.), Rudolf Carnap, Logical Empiricist, Reidel, Dordrecht, pp. 293–324.Google Scholar
  7. Carnap, R. and W. Stegmüller: 1959, Induktive Logik undWahrscheinlichkeit, Springer, Wien.Google Scholar
  8. Copi, I. M. and C. Cohen: 1998, Introduction to Logic,Prentice Hall, Upper Saddle River, NJ, 10th edn.Google Scholar
  9. Festa, R.: 1993, Optimum Inductive Methods,Kluwer, Dordrecht.Google Scholar
  10. Fine, T. L.: 1973, Theories of Probability, Academic Press, New York.Google Scholar
  11. Hesse, M.: 1964, ‘Analogy and Confirmation Theory’, Philosophy of Science 31, 319–327.Google Scholar
  12. Hume, D.: 1748, An Enquiry Concerning Human Understanding. many reprints.Google Scholar
  13. Keynes, J. M.:1921, A Treatise on Probability, Macmillan, London.Google Scholar
  14. Kuipers, T. A. F.: 1984, ‘Two Types ofInductive Analogy by Similarity’, Erkenntnis 21, 63–87.Google Scholar
  15. Maher, P.: 2000, ‘Probabilities forTwo Properties’, Erkenntnis 52, 63–91.Google Scholar
  16. Mill, J. S.: 1874, A System of Logic,Harper, New York, 8th edition.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Patrick Maher
    • 1
  1. 1.Department of PhilosophyUniversity of IllinoisUrbanaU.S.A.

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