Conditionals in Interaction

James Trafford 1
  • 1 University for the Creative Arts, United Kingdom of Great Britain and Northern Ireland

Abstract

There are several issues with the standard approach to the relationship between conditionals and assertions, particularly when the antecedent of a conditional is (or may be) false. One prominent alternative is to say that conditionals do not express propositions, but rather make conditional assertions that may generate categorical assertions of the consequent in certain circumstances. However, this view has consequences that jar with standard interpretations of the relationship between proofs and assertion. Here, I analyse this relationship, and say that, on at least one understanding of proof, conditional assertions may reflect the dynamics of proving, which (sometimes) generate categorical assertions. In particular, when we think about the relationship between assertion and proof as rooted in a dialogical approach to both, the distinction between conditional and categorical assertions is quite natural.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • 1. Brandom, R. Asserting, Noûs, 17 (4), 1983, pp. 637–650.

  • 2. Brandom, R. Articulating Reasons: An Introduction to Inferentialism, Cambridge, MA: Harvard University Press, 2000.

  • 3. Brandom, R. Between Saying and Doing: Towards an Analytic Pragmatism, Oxford: Oxford University Press, 2008.

  • 4. Brandom, R. Making It Explicit: Reasoning, Representing, and Discursive Commitment, Cambridge, MA: Harvard University Press, 1994.

  • 5. Díez, G. F. Kolmogorov, heyting and gentzen on the intuitionistic logical constants, Critica, 32 (96), 2000, pp. 43–57.

  • 6. Dubucs, J. Feasibility in logic, Synthese, 132(3), 2002, pp. 213–237.

  • 7. Dubucs, J. and, Marion, M. Radical anti-realism and substructural logics. In A. Rojszczak, J. Cachro, and G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science, Dortrecht: Kluwer Academic Publishers, 2003, pp. 235–249.

  • 8. Dummett, M. Truth, Proceedings of the Aristotelian Society, 59(1), 1959, pp. 141–62.

  • 9. Dummett, M. What is a theory of meaning? (ii). In. G. Evans and J. McDowell (eds.), Truth and Meaning: Essays in Semantics, Oxford: Clarendon Press, 1976.

  • 10. Dummett, M. A. E. The Logical Basis of Metaphysics, Cambridge, MA: Harvard University Press, 1991.

  • 11. Dummett, M. A. E. Origins of Analytical Philosophy, Cambridge, MA: Harvard University Press, 1993.

  • 12. Dummett, M. A E. Elements of Intuitionism, Oxford: Oxford University Press, 2000.

  • 13. Edgington, D. On conditionals, Mind, 104(414), 1995, pp. 235–329.

  • 14. Edgington, D. Conditionals, Truth and Assertion. In. I. Ravenscroft (ed.), Minds, Ethics, and Conditionals: Themes From the Philosophy of Frank Jackson, Oxford: Oxford University Press, 2009.

  • 15. Girard, J.-Y. On the meaning of logical rules i: syntax versus semantics. In. U. Berger, H. Schwichtenberg (eds.), Computational Logic, NATO ASI Series, vol 165. Springer, Berlin, Heidelberg, 1999, pp. 215–272.

  • 16. Heyting, A. Intuitionism, Amsterdam: North-Holland Pub. Co., 1971.

  • 17. Humberstone, L. The Connectives, Cambridge, MA: MIT Press, 2011.

  • 18. Lecomte, A. Ludics, dialogue and inferentialism, Baltic International Yearbook of Cognition, Logic and Communication, 8(1), 2013.

  • 19. MacFarlane, J. What is assertion? In. J. Brown and H. Cappelen (eds.), Assertion: New Philosophical Essays. Oxford: Oxford University Press, 2011.

  • 20. Marion, M. Why play logical games? In. O. Majer, A.-V. Pietarinen, and T. Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy, Berlin: Springer Verlag, 2009, pp. 3–26.

  • 21. Marion, M. Game semantics and the manifestation thesis. In. Rahman, Shahid, Primiero, Giuseppe, Marion, Mathieu (Eds.). The Realism-Antirealism Debate in the Age of Alternative Logics, Berlin: Springer, 2012, pp. 141–168.

  • 22. Per Martin-Löf. On the meanings of the logical constants and the justifications of the logical laws, Nordic Journal of Philosophical Logic, 1(1), 1996, pp. 11–60.

  • 23. Martino, E. and Usberti, G. Temporal and atemporal truth in intuitionistic mathematics, Topoi, 13(2), 1994, pp. 83–92.

  • 24. Murzi, J. Knowability and Bivalence: Intuitionistic Solutions to the Paradox of Knowability, Philosophical Studies, 149(2), 2010, pp. 269–281.

  • 25. Novaes, C. D. A dialogical, multiagent account of the normativity of logic, Dialectica, 69(4), 2015, pp. 587–609.

  • 26. Nunberg, G. The non-uniqueness of semantic solutions: Polysemy, Linguistics and Philosophy, 3(2), 1979, pp. 143–184.

  • 27. Pagin, P. Assertion, inference, and consequence. Synthese, 187(3), 2012, pp. 869–885.

  • 28. Pagin, P. Assertion. In. P. Pagin (ed.), Stanford Encyclopedia of Philosophy, 2015.

  • 29. Pagin, P. Problems with norms of assertion. Philosophy and Phenomenological Research, 91(2), 2015.

  • 30. Peirce, Ch. S. Belief and judgment, C. Hartshorne, P. Weiss. Collected papers, vol. 5, 1934, pp. 376–87.

  • 31. Prawitz, D. Meaning approached via proofs, Synthese, 148(3), 2006, pp. 507–524.

  • 32. Quine, W. V. Methods of Logic, Cambridge, MA: Harvard University Press, 1982.

  • 33. Ramsey, F. General propositions and causality. In. D. H. Mellor (ed.), Philosophical Papers, Cambridge: Cambridge University Press, 1990, pp. 145–163.

  • 34. Read, S. Proof-theoretic validity. In. C. Caret and O. Hjortland (eds.), Foundations of Logical Consequence, Oxford: Oxford University Press, 2014.

  • 35. Rescorla, M. Assertion and its constitutive norms, Philosophy and Phenomenological Research, 79(1), 2009, pp. 98–130.

  • 36. Sanford, D. H. If P, Then Q: Conditionals and the Foundations of Reasoning, London: Routledge, 2004.

  • 37. Shieh, S. On the conceptual foundations of anti-realism, Synthese, 115(1), 1998, pp. 33–70.

  • 38. Stalnaker, R. Conditional propositions and conditional assertions, In. A. Egan and B. Weatherson (eds.), Epistemic Modality, Oxford: Oxford University Press, 2009.

  • 39. Sundholm, G. Constructions, proofs and the meaning of logical constants, Journal of Philosophical Logic, 12(2), 1983, pp. 151–172.

  • 40. Trafford, J. Meaning in dialogue: An interactive approach to logic and reasoning, vol. 33, Berlin: Springer, 2016.

  • 41. Tranchini, L. Proof-theoretic semantics, paradoxes and the distinction between sense and denotation, Journal of Logic and Computation, 2014.

  • 42. Watson, G. Asserting and promising, Philosophical Studies, 117(1-2), 2004, pp. 57–77.

  • 43. Weiner, M. Must we know what we say? Philosophical Review, 114(2), 2005, pp. 227–251.

  • 44. Williamson, T. Knowing and asserting, Philosophical Review, 105(4):489–523, 1996.

  • 45. Wittgenstein, L. Philosophical Investigations, 4th Edition, transl. by Hacker and Schulte, Hoboken: Wiley-Blackwell, 2009.

OPEN ACCESS

Journal + Issues

Search