Explication of Inductive Probability


Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap’s inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

This is a preview of subscription content, access via your institution.


  1. 1.

    Carnap, R. (1936). Testability and meaning, parts I–III. Philosophy of Science, 3, 419–471. Reprinted by the Graduate Philosophy Club, Yale University, 1950.

  2. 2.

    Carnap, R. (1937). The logical syntax of language. Routledge and Kegan Paul. Translated by Amethe Smeaton.

  3. 3.

    Carnap, R. (1945). On inductive logic. Philosophy of Science, 12, 72–97.

    Google Scholar 

  4. 4.

    Carnap, R. (1950). Logical foundations of probability (2nd ed., 1962). University of Chicago Press.

  5. 5.

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

  6. 6.

    Carnap, R. (1956). Meaning and necessity (2nd ed.). University of Chicago Press.

  7. 7.

    Carnap, R. (1963). Intellectual autobiography. In P. A. Schilpp (Ed.), The philosophy of Rudolf Carnap (pp. 1–84). Open Court.

  8. 8.

    Carnap, R. (1971). A basic system of inductive logic, part I. In R. Carnap, & R. Jeffrey (Eds.), Studies in inductive logic and probability (Vol. 1, pp. 33–165). Berkeley: University of California Press.

  9. 9.

    Carnap, R. (1980). A basic system of inductive logic, part II. In R. C. Jeffrey (Ed.), Studies in inductive logic and probability (Vol. 2, pp. 7–155). University of California Press.

  10. 10.

    Congdon, P. (2007). Bayesian statistical modelling (2nd ed.). Wiley.

  11. 11.

    de Finetti, B. (1937). La prevision: Ses lois logiques, ses sources subjectives. Annales de l’Institut Henri P oincaré, 7, 1–68. English translation in [23].

  12. 12.

    de Finetti, B. (2008). Philosophical lectures on probability. Springer.

  13. 13.

    Fine, T. L. (1973). Theories of probability. Academic.

  14. 14.

    Freudenthal, H. (1974). The crux of course design in probability. Educational Studies in Mathematics, 5, 261–277. Errata in vol. 6, p. 125 (1975).

  15. 15.

    Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003). Bayesian data analysis (2nd ed.). Chapman & Hall.

  16. 16.

    Goodman, N. (1979). Fact, fiction, and forecast (3rd ed.). Hackett.

  17. 17.

    Hájek, A. (2003). What conditional probability could not be. Synthese, 137, 273–323.

    Article  Google Scholar 

  18. 18.

    Hájek, A. (2007). Interpretations of probability. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. http://plato.stanford.edu/archives/fall2007/entries/probability-interpret/.

  19. 19.

    Jeffrey, R.. (1971). Probability measures and integrals. In R. Carnap, & R. Jeffrey (Eds.), Studies in inductive logic and probability (Vol. 1, pp. 167–223). Berkeley: University of California Press.

  20. 20.

    Jeffrey, R.. (1992). Probability and the art of judgment. Cambridge University Press.

  21. 21.

    Keynes, J. M.. (1921). A treatise on probability. Macmillan. Reprinted with corrections 1948.

  22. 22.

    Kolmogorov, A. N. (1933). Grundbegriffe der wahrscheinlichkeitsrechnung. English translation: Foundations of probability. Trans. Nathan Morrison. Chelsea (1956).

  23. 23.

    Kyburg, Jr., H. E., & Smokler, H. E. (Eds.) (1980). Studies in subjective probability (2nd ed.). Krieger.

  24. 24.

    Maher, P. (1996). Subjective and objective confirmation. Philosophy of Science, 63, 149–173.

    Article  Google Scholar 

  25. 25.

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

    Article  Google Scholar 

  26. 26.

    Maher, P. (2004). Probability captures the logic of scientific confirmation. In C. R. Hitchcock (Ed.), Contemporary debates in philosophy of science (pp. 69–93). Blackwell.

  27. 27.

    Maher, P. (2006). The concept of inductive probability. Erkenntnis, 65, 185–206.

    Article  Google Scholar 

  28. 28.

    Maher, P. (2009). Physical probability. In C. Glymour, W. Wang, & D. Westerståhl (Eds.), Logic, methodology and philosophy of science: Proceedings of the thirteenth international congress (pp. 193–210). College Publications.

  29. 29.

    Pearl, J.. (1990). Jeffrey’s rule, passage of experience, and Neo-Bayesianism. In H. E. Kyburg, Jr., R. P. Loui, & G. N. Carlson (Eds.), Knowledge representation and defeasible reasoning (pp. 245–265). Kluwer.

  30. 30.

    Roeper, P., & Leblanc, H. (1999). Probability theory and probability logic. University of Toronto Press.

  31. 31.

    von Wright, G. H. (1957). The logical problem of induction (2nd ed.). Blackwell.

  32. 32.

    Zabell, S. L. (1997). Confirming universal generalizations. Erkenntnis, 45, 267–283.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Patrick Maher.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Maher, P. Explication of Inductive Probability. J Philos Logic 39, 593–616 (2010). https://doi.org/10.1007/s10992-010-9144-4

Download citation


  • Inductive probability
  • Explication
  • Carnap