Journal of Philosophical Logic

, Volume 43, Issue 1, pp 171–179 | Cite as

Reinflating Logical Consequence

Article

Abstract

Shapiro (Philos Q 61:320–342, 2011) argues that, if we are deflationists about truth, we should be deflationists about logical consequence. Like the truth predicate, he claims, the logical consequence predicate is merely a device of generalisation and more substantial characterisation, e.g. proof- or model-theoretic, is mistaken. I reject his analogy between truth and logical consequence and argue that, by appreciating how the logical consequence predicate is used as well as the goals of proof theory and model theory, we can be deflationists about truth but not logical consequence.

Keywords

Deflationism Truth Logical consequence Entailment Model theory Proof theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Beall, J. (2009). Spandrels of truth. Oxford: OUP.CrossRefGoogle Scholar
  2. 2.
    Beall, J., & Murzi, J. (2012). Two flavors of Curry paradox. The Journal of Philosophy, forthcoming.Google Scholar
  3. 3.
    Beall, J., & Restall, G. (2006). Logical pluralism. Oxford: Clarendon Press.Google Scholar
  4. 4.
    Boolos, G. (1975). On second-order logic. Journal of Philosophy, 72, 509–527.CrossRefGoogle Scholar
  5. 5.
    Etchemendy, J. (1990). The concept of logical consequence. Cambridge: Harvard University Press.Google Scholar
  6. 6.
    Etchemendy, J. (2008). Reflections on consequence. In D. Patterson (Ed.), New essays on Tarski and philosophy (pp. 263–299). Oxford: Clarendon Press.CrossRefGoogle Scholar
  7. 7.
    Field, H. (2008). Saving truth from paradox. Oxford: OUP.CrossRefGoogle Scholar
  8. 8.
    Field, H. (2009). What is the normative role of logic? Proceedings of the Aristotelian Society, 83, 251–268.CrossRefGoogle Scholar
  9. 9.
    Horsten, L. (2011). The Tarskia turn: Deflationism and axiomatic truth. Cambridge: MIT Press.CrossRefGoogle Scholar
  10. 10.
    Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716.CrossRefGoogle Scholar
  11. 11.
    Priest, G. (2006). In contradiction (2nd ed.) Oxford: Clarendon Press.CrossRefGoogle Scholar
  12. 12.
    Prior, A.N. (1971). Objects of thought. Oxford: Clarendon Press.CrossRefGoogle Scholar
  13. 13.
    Quine, W. (1980). Grammar, truth, and logic. In S. Kanger, & S. Öhman (Eds.), Philosophy and grammar (pp. 17–28). Dordrecht: D. Reidel.CrossRefGoogle Scholar
  14. 14.
    Shapiro, L. (2011). Deflating logical consequence. The Philosophical Quarterly, 61, 320–342.CrossRefGoogle Scholar
  15. 15.
    Shapiro, S. (2005). Logical consequence, proof theory, and model theory. In S. Shapiro (Ed.), The Oxford handbook of philosophy of mathematics and logic (pp. 651–670). New York: OUP.CrossRefGoogle Scholar
  16. 16.
    Smiley, T. (1958). Entailment and deducibility. Proceedings of the Aristotelian Society, 59, 233–254.Google Scholar
  17. 17.
    Tarski, A. (1936). On the concept of logical consequence. In Logic, semantics, metamathematics (2nd ed., pp. 409–420). Indianapolis: Hackett. Trans. J. Woodger.Google Scholar
  18. 18.
    van Bentham, J. (2011). The dynamic world of Martin Stokhof. In C. Dutilh Novaes, & J. van der Does (Eds.), Festschrift for Martin Stokhof.Google Scholar
  19. 19.
    Wright, C. (1999). Truth: a traditional debate reviewed. In S. Blackburn, & K. Simmons (Eds.), Truth (pp. 203–238). Oxford: OUP.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Faculty of PhilosophyUniversity of CambridgeCambridgeUK

Personalised recommendations