A Synthesis of Hempelian and Hypothetico-Deductive Confirmation


This paper synthesizes confirmation by instances and confirmation by successful predictions, and thereby the Hempelian and the hypothetico-deductive traditions in confirmation theory. The merger of these two approaches is subsequently extended to the piecemeal confirmation of entire theories. It is then argued that this synthetic account makes a useful contribution from both a historical and a systematic perspective.

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


  1. 1.

    See Kuipers (2000) for an extended discussion of qualitative versus Bayesian confirmation theory.

  2. 2.

    Definition 2 will make this notion precise in modern logical terms. See Hempel (1943) for the original account.

  3. 3.

    A generalization of the content part relation to richer languages that can be used for H-D confirmation, e.g. languages with identity, is given in Gemes (1997). The definitions below are, with the exception of Definition 2, taken from Gemes (2006). Quantifiers are treated substitutionally.

  4. 4.

    This example is due to Ken Gemes.

  5. 5.

    See Gemes (1998) and Schurz (2005) for such criticisms. Note that (SynT) avoids the most pressing criticisms raised in these papers (e.g., Gemes 1998, 7–8).


  1. Borsboom, D., & Haig, B. D. (2013). How to practise Bayesian statistics outside the Bayesian church: What philosophy for Bayesian statistical modeling? British Journal of Mathematical and Statistical Psychology, 66, 39–44.

    Article  Google Scholar 

  2. Carnap, R. (1950). The logical foundations of probability. Chicago: The University of Chicago Press.

    Google Scholar 

  3. Dietrich, F., & Moretti, L. (2005). On Coherent Sets and the Transmission of Confirmation. Philosophy of Science, 72, 403–424.

    Article  Google Scholar 

  4. Fitelson, B., & Hawthorne, J. (2010). How Bayesian confirmation theory handles the paradox of the ravens. In E. Eells, & J. Fetzer (Eds.) The place of probability in science (pp. 247–275). New York: Springer.

    Google Scholar 

  5. Gelman, A., & Shalizi, C. (2012). Philosophy and the practice of Bayesian statistics in the social sciences. In H. Kincaid (Ed.) Oxford handbook of the philosophy of the social sciences (pp. 259–273). Oxford: Oxford University Press.

    Google Scholar 

  6. Gelman, A., & Shalizi, C. (2013). Philosophy and the practice of Bayesian statistics (with discussion). British Journal of Mathematical and Statistical Psychology, 66, 8–18.

    Article  Google Scholar 

  7. Gemes, K. (1993). Hypothetico-deductivism, content and the natural axiomatisation of theories. Philosophy of Science, 60, 477–487.

    Article  Google Scholar 

  8. Gemes, K. (1997). A new theory of content II: Model theory and some alternatives. Journal of Philosophical Logic, 26, 449–476.

    Article  Google Scholar 

  9. Gemes, K. (1998). Hypothetico-deductivism: The current state of play. Erkenntnis, 49, 1–20.

    Article  Google Scholar 

  10. Gemes, K. (2006). Content and Watkins’ account of natural axiomatizations. Dialectica, 60, 85–92.

    Article  Google Scholar 

  11. Glymour, C. (1980a). Theory and evidence. Princeton: Princeton University Press.

    Google Scholar 

  12. Glymour, C. (1980b). Discussion: hypothetico-deductivism is hopeless. Philosophy of Science, 47, 322–325.

    Article  Google Scholar 

  13. Hempel, C. G. (1943). A purely syntactical definition of confirmation. Journal of Symbolic Logic, 8, 122–143.

    Article  Google Scholar 

  14. Hempel, C. G. (1945/65). Studies in the logic of confirmation. In Aspects of scientific explanation, (pp. 3-46). New York: The Free Press. Reprint from Mind 54, 1945.

  15. Huber, F. (2008). Hempel’s logic of confirmation. Philosophical Studies, 139, 181–189.

    Article  Google Scholar 

  16. Kuipers, T. (2000). From instrumentalism to constructive realism. Dordrecht: Kluwer.

    Google Scholar 

  17. Mayo, D. G. (1996). Error and the growth of experimental knowledge. Chicago and London: The University of Chicago Press.

    Google Scholar 

  18. Nicod, J. (1925). Le problème logique de l’induction. Paris: Alcan.

    Google Scholar 

  19. Popper, K. R. (1934/71). Logik der Forschung, 3rd edn. Tübingen: Mohr.

  20. Schurz, G. (1991). Relevant deduction. Erkenntnis, 35, 391-437.

    Google Scholar 

  21. Schurz, G. (2005). Bayesian H-D confirmation and structuralistic truthlikeness: Discussion and comparison with the relevant-element and the content-part approach. In R. Festa (Ed.) Logics of scientific discovery. Essays in debate with Theo Kuipers (pp. 141–159). Amsterdam: Rodopi.

    Google Scholar 

  22. Whewell, W. (1847). Philosophy of the inductive sciences, founded upon their history, Vol. II. London: Parker.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Jan Sprenger.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sprenger, J. A Synthesis of Hempelian and Hypothetico-Deductive Confirmation. Erkenn 78, 727–738 (2013). https://doi.org/10.1007/s10670-013-9487-7

Download citation


  • Malaria
  • Content Part
  • Harmonic Oscillator Model
  • Entire Theory
  • Logical Entailment