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A Continuum of Inductive Methods Arising from a Generalized Principle of Instantial Relevance

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Abstract

In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∈ [0, 1).

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References

  1. Carnap, R. (1950): Logical Foundations of Probability, University of Chicago Press, Chicago, and Routledge & Kegan Paul Ltd.

    Google Scholar 

  2. Carnap, R. (1952): The Continuum of Inductive Methods, University of Chicago Press.

  3. Carnap, R. (1953): On the comparative concept of confirmation, Br. J. Philos. Sci. 3, 311–318.

    Article  Google Scholar 

  4. Carnap, R. (1950): Induktive Logik und Wahrscheinlichkeit. (Bearbeitet von Wolfgang Stegmuller), Springer, Wein. (Anhang B: Ein neues Axiomensystem).

    Google Scholar 

  5. Feller, W. (1966): An Introductions to Probability Theory and its Applications, Volume II, John Wiley & Sons, New York.

    Google Scholar 

  6. Gaifman, H. (1971): Applications of de Finetti's Theorem to inductive logic, in R. Carnap, R. C. Jeffrey (eds.), Studies in Inductive Logic and Probability (Volume I), University of California Press, Berkeley and Los Angeles.

    Google Scholar 

  7. Gaifman, H. (1964): Concerning measures on first order calculi, Isr. J. Math. 2 1–18.

    Article  Google Scholar 

  8. Hill, M. J. (1999): Aspects of Induction and the Principle of Duality, Ph.D.Thesis, Manchester University.

  9. Humburg, J. (1971): The principle of instantial relevance, in R. Carnap, R. C. Jeffrey (eds.), Studies in Inductive Logic and Probability (Volume I), University of California Press, Berkeley and Los Angeles.

    Google Scholar 

  10. Johnson, W. E. (1932): Probability: The deductive and inductive problems, Mind, 41(164), 409–423.

    Article  Google Scholar 

  11. Miller, D. (1974): Popper's qualitative theory of versimilitude, Br. J. Philos. Sci. 25, 565–575.

    Google Scholar 

  12. Nix, C. J. (2005): Probabilistic Induction in the Predicate Calculus, Ph.D. Thesis, Manchester University.

  13. Paris, J. B. (1994): The Uncertain Reasoner's Companion, Cambridge University Press.

  14. Hill, M. J., Paris, J. B., Wilmers, G. M. (2002): Some observations on induction in predicate probabilistic reasonin, J. Philos. Logic 31(1), 43–75.

    Article  Google Scholar 

  15. Quine, W. V. (1977): Ontological Relativity and Other Essays, Columbia University Press.

  16. Schervish, M. (1995): Theory of Statistics, Springer.

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Authors and Affiliations

  1. Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    C. J. Nix & J. B. Paris

Authors
  1. C. J. Nix
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  2. J. B. Paris
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Correspondence to C. J. Nix.

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*Supported by a UK Engineering and Physical Sciences Research Council (EPSRC) Research Studentship

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Nix, C.J., Paris, J.B. A Continuum of Inductive Methods Arising from a Generalized Principle of Instantial Relevance. J Philos Logic 35, 83–115 (2006). https://doi.org/10.1007/s10992-005-9003-x

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  • DOI: https://doi.org/10.1007/s10992-005-9003-x

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