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There Is a Reason for Everything (Probably): On the Application of Maxent to Induction

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Conditionals, Information, and Inference (WCII 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3301))

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Abstract

In this paper we show how the maxent paradigm may be used to produce an inductive method (in the sense of Carnap) applicable to a wide class of problems in inductive logic. A surprising consequence of this method is that the answers it gives are consistent with, or explicable by, the existence of underlying reasons for the given knowledge base, even when no such reasons are explicitly present. We would conjecture that the same result holds for the full class of problems of this type.

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References

  1. Bacchus, F., Grove, A.J., Halpern, J.Y., Koller, D.: From statistical knowledge bases to degrees of belief. Artificial Intelligence 87(1-2), 75–143 (1996)

    Article  MathSciNet  Google Scholar 

  2. Carnap, R.: Logical foundations of probability. University of Chicago Press, Routledge & Kegan Paul Ltd. (1950)

    Google Scholar 

  3. Carnap, R.: The continuum of inductive methods. University of Chicago Press, Chicago (1952)

    MATH  Google Scholar 

  4. Carnap, R.: Replies and systematic expositions. In: Schlipp, P.A., Salle, L. (eds.) The Philosophy of Rudolf Carnap, Illinois, Open Court(1963)

    Google Scholar 

  5. Carnap, R., Jeffrey, R.C. (eds.): Studies in inductive logic and probability. University of California Press, Berkeley (1971)

    Google Scholar 

  6. Carnap, R.: A basic system for inductive logic, part 2. In: Jeffrey, R.C. (ed.) Studies Inductive Logic and Probability (Volume II). University of California Press, Berkeley (1980)

    Google Scholar 

  7. Carnap, R., Stegmüller, W.: Induktive Logik und Wahrscheinlichkeit, pp. 243–249. Springer, Vienna (1958)

    Google Scholar 

  8. Eells, E.: On the alleged impossibility of inductive probability. British Journal for the Philosophy of Science 39, 111–116 (1988)

    Article  MathSciNet  Google Scholar 

  9. Elby, A.: Contentious contents - for inductive probability. British Journal for the Philosophy of Science 45, 193–200 (1994)

    Article  MathSciNet  Google Scholar 

  10. Fagin, R., Halpern, J.Y.: Reasoning about Knowlege and Probability. Journal of the ACM 41(2), 340–367 (1994)

    Article  MATH  Google Scholar 

  11. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  12. Gillies, D.: Discussion: In defense of the Popper-Miller argument. Philosophy of Science 53, 110–113 (1986)

    Article  MathSciNet  Google Scholar 

  13. Glaister, S.: Inductive Logic. In: Jacquette, D. (ed.) A Companion to Philosophical Logic. Blackwell Publishers, Malden (2001)

    Google Scholar 

  14. Good, I.J.: The impossibility of inductive probability. Nature 310, 434 (1984)

    Article  Google Scholar 

  15. Grove, A.J., Halpern, J.Y., Koller, D.: Asymptotic conditional probabilities: the unary case. SIAM Journal of Computing 25(1), 1–51 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  16. Grove, A.J., Halpern, J.Y., Koller, D.: Asymptotic conditional probabilities: the non-unary case. Journal of Symbolic Logic 61(1), 250–275 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Jeffrey, R.C.: The impossibility of inductive probability. Nature 310, 433 (1984)

    Article  Google Scholar 

  18. Johnson, W.E.: Probability: The deductive and inductive problems. Mind 49, 409–423 (1932)

    Article  MATH  Google Scholar 

  19. Kemeny, J.G.: A contribution to Inductive Logic. Philosophy and Phenomenological Research 13, 371–374 (1953)

    Article  MathSciNet  Google Scholar 

  20. Kemeny, J.G.: Carnap’s theory of probability and induction. In: The Philosophy of Rudolf Carnap, Open Court Publishing Company, LaSalle, Ill., pp. 711–738 (1963)

    Google Scholar 

  21. Levi, I.: The impossibility of inductive probability. Nature 310, 433 (1984)

    Article  Google Scholar 

  22. Miller, D.: Induction: a problem solved, Karl Poppers kritischer Rationalismus heute. In: Bohm, J.M., Holweg, H., Hoock, C. (eds.) Tübingen: Mohr Siebeck, pp. 81–106 (2002)

    Google Scholar 

  23. Musgrave, A.: How to do without inductive logic. Science and Education 8, 395–412 (1999)

    Article  Google Scholar 

  24. Paris, J.B.: The Uncertain Reasoner’s Companion: A Mathematical Perspective. Cambridge university Press, Cambridge (1994)

    MATH  Google Scholar 

  25. Paris, J.B.: Common sense and maximum entropy. Synthese 117, 75–93 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  26. Paris, J.B., Vencovská, A.: A note on the inevitability of maximum entropy. International Journal of Approximate Reasoning 4(3), 183–224 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  27. Paris, J.B., Vencovská, A.: Common sense and stochastic independence. In: Corfield, D., Williamson, J. (eds.) Foundations of Bayesianism, pp. 203–240. Kluwer Academic Press, Dordrecht (2002)

    Google Scholar 

  28. Paris, J.B., Vencovská, A., Wafy, M.: Some limit theorems for ME, CM ∞  and MD. Technical Report of the Manchester Centre for Pure Mathematics, University of Manchester, UK., no. 2001/9, ISSN 1472-9210 (2001)

    Google Scholar 

  29. Paris, J.B., Wafy, M.: On the emergence of reasons. Journal of the IGPL 9(2), 207–216 (2001). In: electronic form at, http://www3.oup.co.uk/igpl/Volume09/Issue02/#Paris

  30. Popper, K., Miller, D.W.: A proof of the impossibility of inductive probability. Nature 302, 687–688 (1983)

    Article  Google Scholar 

  31. Popper, K., Miller, D.W.: The impossibility of inductive probability. Nature 310, 434 (1984)

    Article  Google Scholar 

  32. Popper, K., Miller, D.W.: Has inductive probability been proved impossible? Nature 315, 461 (1985)

    Article  Google Scholar 

  33. Popper, K.: Why probabilistic support is not inductive. Philosophical Transactions of the Royal Society (Series A) 321, 569–591 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  34. Redhead, M.: On the impossibility of inductive probability. British Journal for the Philosophy of Science 36, 185–191 (1985)

    Article  MathSciNet  Google Scholar 

  35. Wafy, M.: A study of an inductive problem using inference processes, Ph.D. Thesis, Manchester University (2000)

    Google Scholar 

  36. Wise, J., Landsberg, P.T.: Has inductive probability been proved impossible? Nature 315, 461 (1985)

    Article  Google Scholar 

  37. Wise, J., Landsberg, P.T.: On the possibility of inductive probability. Nature 316, 22 (1985)

    Article  Google Scholar 

  38. Zabell, S.L.: Predicting the unpredictable. Synthese 90, 205–232 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    Jeff B. Paris & Alena Vencovská

Authors
  1. Jeff B. Paris
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  2. Alena Vencovská
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, TU Dortmund, 44221, Dortmund, Germany

    Gabriele Kern-Isberner

  2. FernUniversität in Hagen, Fachbereich Wirtschaftswissenschaft, Lehrstuhl für BWL, insb. Operations Research, 58084, Hagen, Germany

    Wilhelm Rödder

  3. FernUniversität in Hagen, Fachbereich Wirtschaftswissenschaft, Lehrstuhl BWL, insb. Operations Research, 58084, Hagen, Germany

    Friedhelm Kulmann

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Paris, J.B., Vencovská, A. (2005). There Is a Reason for Everything (Probably): On the Application of Maxent to Induction. In: Kern-Isberner, G., Rödder, W., Kulmann, F. (eds) Conditionals, Information, and Inference. WCII 2002. Lecture Notes in Computer Science(), vol 3301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408017_11

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  • DOI: https://doi.org/10.1007/11408017_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25332-7

  • Online ISBN: 978-3-540-32235-1

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