Skip to main content
Log in

A Note on Binary Inductive Logic

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

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

    Google Scholar 

  3. Carnap, R.: A basic system of inductive logic, in R. C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II, University of California Press, Chicago, IL, pp. 7–155, 1980.

    Google Scholar 

  4. Carnap, R.: On the application of inductive logic, Philosophy and Phenomenological Research 8, (1947), 133–147.

    Article  Google Scholar 

  5. Carnap, R.: Reply to Nelson Goodman, Philosophy and Phenomenological Research 8, (1947), 461–462.

    Article  Google Scholar 

  6. Coletti, G. and Scozzafava, R.: Probabilistic logic in a coherent setting, Trends in Logic, 15, Kluwer, London, Dordrecht, 2002.

    Google Scholar 

  7. de Finetti, B.: On the condition of partial exchangeability, in R.C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II, University of California Press, Berkley, CA, 1980.

    Google Scholar 

  8. de Finetti, B.: Theory of Probability, Vol. 1, Wiley, New York, 1974.

    Google Scholar 

  9. Fitelson, B.: Inductive Logic: http://fitelson.org/il.pdf

  10. Gaifman, H.: Concerning measures on first order calculi, Israel Journal of Mathematics 2 (1964), 1–18.

    Google Scholar 

  11. Gaifman, H. and Snir, M.: Probabilities over rich languages, Journal of Symbolic Logic 47(3) (1982), 495–548.

    Article  Google Scholar 

  12. Glaister, S.: Inductive logic, in D. Jacquette (ed.), A Companion to Philosophical Logic, Blackwell, London, 2001, pp. 565–581.

    Google Scholar 

  13. Goodman, N.: Fact, Fiction and Forecast, 4th edition, Harvard UP, Cambridge MA, 1983.

    Google Scholar 

  14. Goodman, N.: A query on confirmation, Journal of Philosophy 43 (1946), 383–385.

    Article  Google Scholar 

  15. Goodman, N.: On infirmities in confirmation-theory, Philosophy and Phenomenological Research 8 (1947), 149–151.

    Article  Google Scholar 

  16. Hill, M.J., Paris, J.B., and Wilmers, G.M.: Some observations on induction in predicate probabilistic reasoning, Journal of Philosophical Logic 31(1) (2002), 43–75.

    Article  Google Scholar 

  17. Hoover, D.N.: Relations on probability spaces and arrays of random variables. Preprint, Institute of Advanced Study, Princeton, 1979.

  18. Jeffrey, R.C.: Goodman’s query, Journal of Philosophy 63(11) (1966), 281–288.

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Kallenberg, O.: Probabilistic Symmetries and Invariance Principles, Springer, New York, ISBN-10: 0-387-25115-4, 2005.

    Google Scholar 

  21. Kallenberg, O., The Ottawa Workshop, http://www.mathstat.uottawa.ca/~givanoff/wskallenberg.pdf

  22. Kawalec, P., Back to green as perspectives on confirmation, Justification, Truth and Belief, http://www.jtb-forum.pl, January, 2002.

  23. Kemeny, J.G.: Carnap’s theory of probability and induction, in P.A. Schilpp (ed.), The Philosophy of Rudolf Carnap, Open Court, La Salle, IL, 1963, pp. 711–738.

    Google Scholar 

  24. Krauss, P.H.: Representation of symmetric probability models, Journal of Symbolic Logic 34(2) (1969), 183–193.

    Article  Google Scholar 

  25. Landes, J.: Doctorial Thesis, Manchester University, UK, to appear.

  26. Maher, P.: Probabilities for two properties, Erkenntnis 52 (2000), 63–91.

    Article  Google Scholar 

  27. Maher, P.: Probabilities for multiple properties: The models of Hesse, Carnap and Kemeny, Erkenntnis 55 (2001), 183–216.

    Article  Google Scholar 

  28. Matúš, F.: Block-factor fields of Bernoulli shifts, Proceedings of Prague Stochastics’98, Vol.II, 1998, pp. 383–389.

  29. Miller, D.: Popper’s qualitative theory of versimilitude, British Journal for the Philosophy of Science 25 (1974), 166–177.

    Article  Google Scholar 

  30. Nix, C.J., Probabilistic Induction in the Predicate Calculus Doctorial Thesis, Manchester University, Manchester, UK, 2005. See http://www.maths.man.ac.uk/~jeff/#students.

  31. Nix, C.J. and Paris, J.B.: A Continuum of inductive methods arising from a generalized principle of instantial relevance, Journal of Philosophical Logic, Online First Issue, DOI 10,1007/s 10992-005-9003x, ISSN 0022-3611 (Paper) 1573–0433, 2005.

  32. Paris, J.B.: The Uncertain Reasoner’s Companion, Cambridge University Press, Cambridge, UK, 1994.

    Google Scholar 

  33. Russell, B., Principles of Mathematics 2nd edition, Allen, London, UK, 1937.

    Google Scholar 

  34. Scott, D. and Krauss, P.: Assigning probabilities to logical formulas, in J. Hintikka and P. Suppes (eds.), Aspects of Inductive Logic, North-Holland, Amsterdam, 1966, pp. 219–264.

    Google Scholar 

  35. Stalker, D. (ed.), Grue! The New Riddle of Induction, Open Court, La Salle, IL, 1994.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. B. Paris.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nix, C.J., Paris, J.B. A Note on Binary Inductive Logic. J Philos Logic 36, 735–771 (2007). https://doi.org/10.1007/s10992-007-9066-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-007-9066-y

Key words

Navigation