Logic, Counterexamples, and Translation

  • Roy T. CookEmail author
Part of the Outstanding Contributions to Logic book series (OCTR, volume 9)


In “Is Logic Empirical” (Putnam 1968), Putnam formulates an empirical argument against classical logic—in particular, an apparent counterexample to the distributivity laws. He argues further that this argument is also an argument in favor of quantum logic. Here we challenge this second conclusion, arguing instead that counterexamples in logic are counterexamples not to particular inferences, but to logics as a whole. The key insight underlying this argument is that what counts as a legitimate translation from natural language to formal language is dependent on the background logic being assumed. Hence, in the face of a counterexample, one can move to a logic that fails to validate the inference seemingly counter-instanced, or one can move to a logic where the best translation of the natural language claims involved in the counterexample are no longer best translated as an instance of the inference in question.


  1. Beall, J., & Restall, G. (2006). Logical pluralism. Oxford: Oxford University Press.zbMATHGoogle Scholar
  2. Ben-Menahem, Y. (Ed.). (2005). Hilary Putnam. Cambridge: Cambridge University Press.Google Scholar
  3. Caspers, M., Heunen, C., Landsman, N., & Spitters, B. (2009). Intuitionistic quantum logic of an \(n\)-level system. Foundations of Physics, 39, 731–759.MathSciNetCrossRefGoogle Scholar
  4. Cook, R. (2014). Should anti-realists be anti-realists about anti-realism? Erkenntnis, 79, 233–258.MathSciNetCrossRefGoogle Scholar
  5. Cohern, R., & Wartofsky, M. (Eds.). (1968). Boston studies in the philsoophy of science (Vol. 5). Dordrecht: D Reidel.Google Scholar
  6. Dummett, M. (1976). Is logic empirical? In Lewis 1976 (pp. 45–68), reprinted in (Dummett 1978, (pp. 269–289)).Google Scholar
  7. Dummett, M. (1978). Truth and other enigmas. London: Duckworth.Google Scholar
  8. Dunn, J., & Hardegree, G. (2001). Algebraic methods in philosophical logic. Oxford: Oxford University Press.zbMATHGoogle Scholar
  9. Etchemendy, J. (1999). The concept of logical consequence. Stanford: CSLI.zbMATHGoogle Scholar
  10. Gardner, M. (1971). Is quantum logic really logic? Philosophy of Science, 38(4), 508–529.CrossRefGoogle Scholar
  11. Gibbons, P. (1987). Particles and paradoxes: The limits of quantum logic. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  12. Hellman, G. (1980). Quantum logic and meaning. Proceedings of the Philosophy of Science Association, 2, 493–511.Google Scholar
  13. Humberstone, L. (2011). The connectives. Cambridge: MIT Press.zbMATHGoogle Scholar
  14. Lewis, H. (Ed.). (1976). Contemporary British philosophy, \(4\)th series. London: Allen and Unwin.Google Scholar
  15. Maudlin, T. (2005). The tale of quantum logic. In Ben-Menahem 2005 (pp. 156–187).Google Scholar
  16. Putnam, H. (1968). Is logic empirical? In Cohen & Wartofsky 1968 (pp. 216–241), reprinted as The logic of quantum mechanics. (In Putnam 1975 (pp. 174–197)).Google Scholar
  17. Putnam, H. (1975). Mathematics, matter, and method: Philosophical papers (Vol. I). Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  18. Quine, W. (1951). Two dogmas of empiricism. The Philosophical Review, 60, 20–43. (reprinted in Quine 1953 (pp. 20–46)).Google Scholar
  19. Quine, W. (1953). From a logical point of view. Camrbridge: Harvard University Press.zbMATHGoogle Scholar
  20. Tarski, A. (1983). Logic, semantics, metamathematics (2nd ed.). Indianapolis: Hackett.Google Scholar
  21. Troelstra, A., & van Dalen, D. (1988). Constructivism in mathematics (Vol. 1). Amsterdam: Elsevier.zbMATHGoogle Scholar
  22. Weatherson, B. (2003). From classical to intuitionistic probability. Notre Dame Journal of Formal Logic, 44(2), 111–123.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of MinnesotaMinneapolisUSA

Personalised recommendations