Journal of Philosophical Logic

, Volume 39, Issue 3, pp 255–274 | Cite as

Inferentializing Semantics

  • Jaroslav Peregrin


The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of proof-theoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones.


Inference Proof theory Model theory Inferentialism Semantics 


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  1. 1.
    Brandom, R. (1994). Making it explicit. Cambridge: Harvard University Press.Google Scholar
  2. 2.
    Buss, S. R. (1998). Handbook of proof theory. Amsterdam: Elsevier.Google Scholar
  3. 3.
    Carnap, R. (1943). Formalization of logic. Cambridge: Harvard University Press.Google Scholar
  4. 4.
    Dunn, J. M., & Hardegree, G. M. (2000). Algebraic methods in philosophical logic. Oxford: Clarendon.Google Scholar
  5. 5.
    Gentzen, G. (1934). Untersuchungen über das logische Schliessen I. Mathematische Zeitschrift, 39, 176–210.CrossRefGoogle Scholar
  6. 6.
    Gentzen, G. (1936). Untersuchungen über das logische Schliessen II. Mathematische Zeitschrift, 41, 405–431.CrossRefGoogle Scholar
  7. 7.
    Hardegree, D. M. (2005). Completeness and super-valuations. Journal of Philosophical Logic, 34, 81–95.CrossRefGoogle Scholar
  8. 8.
    Kahle, R., & Schroeder-Heister, P. (2006). Proof-theoretic semantics. Synthèse, 148, 503–506.CrossRefGoogle Scholar
  9. 9.
    Kreisel, G. (1964). Hilbert’s programme. In P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics (pp. 157–180). Englewood Cliffs: Prentice-Hall.Google Scholar
  10. 10.
    Kreisel, G. (1968). A survey of proof theory. Journal of Symbolic Logic, 33, 321–388.CrossRefGoogle Scholar
  11. 11.
    Murzi, J., & Hjortland, O. T. (2009). Inferentialism and the categoricity problem: reply to Raatikainen. Analysis, 69, 480–488.Google Scholar
  12. 12.
    Peregrin, J. (1997). Language and its models. Nordic Journal of Philosophical Logic, 2, 1–23.Google Scholar
  13. 13.
    Peregrin, J. (2006). Meaning as an inferential role. Erkenntnis, 64, 1–36.CrossRefGoogle Scholar
  14. 14.
    Peregrin, J. (2008). An Inferentialist approach to semantics. Philosophy Compass, 3, 1208–1223.CrossRefGoogle Scholar
  15. 15.
    Prawitz, D. (2006). Meaning approached via proofs. Synthèse, 148, 507–524.CrossRefGoogle Scholar
  16. 16.
    Prior, A. N. (1960/61). Runabout inference ticket. Analysis, 21, 38–39.CrossRefGoogle Scholar
  17. 17.
    Raatikainen, P. (2008). On rules of inference and the meanings of logical constants. Analysis, 68, 282–287.CrossRefGoogle Scholar
  18. 18.
    Read, S. (2004). Identity and harmony. Analysis, 64, 113–119.CrossRefGoogle Scholar
  19. 19.
    Restall, G. (2000). Introduction to substructural logics. London: Routledge.Google Scholar
  20. 20.
    Tarski, A. (1933). Pojęcie prawdy v językach nauk dedukcyjnych. (Warsawa) (English translation The Concept of Truth in Formalized Languages in Tarski (1956), pp. 152–278).Google Scholar
  21. 21.
    Tarski, A. (1936). Über den Begriff der logischen Folgerung. Actes du Congrés International de Philosophique Scientifique, 7, 1–11. (English translation On the Concept of Logical Consequence in Tarski (1956), pp. 409–420).Google Scholar
  22. 22.
    Tarski, A. (1939). O ugruntowaniu naukowej semantyki. Przeglad Filosoficzny, 39, 50–57 (English translation The establishment of Scientific Semantics in Tarski (1956), pp. 401–408).Google Scholar
  23. 23.
    Tarski, A. (1956). Logic, semantics, metamathematics. Oxford: Clarendon.Google Scholar
  24. 24.
    Tennant, N. (2007). Existence and identity in free logic: a problem for inferentialism?’. Mind, 116, 1055–1078.Google Scholar
  25. 25.
    van Fraassen, B. C. (1971). Formal semantics and logic. New York: Macmillan.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Logic, Institute of PhilosophyAcademy of Sciences of the Czech RepublicPraha 1Czech Republic

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