Journal of Philosophical Logic

, Volume 45, Issue 6, pp 623–644 | Cite as

Some Comments on Ian Rumfitt’s Bilateralism

Article

Abstract

Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of ‘exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use’ (Rumfitt Mind109, 781–823 (4): 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of bilateral logic which also meets those requirements. Thus Rumfitt cannot claim that only classical bilateral rules of inference succeed in imparting a coherent sense onto the connectives. My system can be extended to classical logic by adding the intuitionistically unacceptable half of a structural rule Rumfitt uses to codify the relation between assertion and denial. Thus there is a clear sense in which, in the bilateral framework, the difference between classicism and intuitionism is not one of the rules of inference governing negation, but rather one of the relation between assertion and denial.

Keywords

Negation Denial Classical logic Intuitionist logic Harmony Proof-theoretic semantics 

References

  1. 1.
    Ferreira, F. (2008). The co-ordination principles: A problem for bilateralism. Mind, 117, 1051 –1057.CrossRefGoogle Scholar
  2. 2.
    Gibbard, P. (2002). Price and Rumfitt on rejective negation and classical logic. Mind, 111, 297 –303.CrossRefGoogle Scholar
  3. 3.
    Humberstone, L. (2000). The revival of rejective negation. Journal of Philosophical Logic, 29, 331–381.CrossRefGoogle Scholar
  4. 4.
    Rumfitt, I. (2000). “Yes” and “No”. Mind, 109, 781–823.CrossRefGoogle Scholar
  5. 5.
    Rumfitt, I. (2002). Unilateralism disarmed: A reply to Dummett and Gibbard. Mind, 111, 305–312.CrossRefGoogle Scholar
  6. 6.
    Rumfitt, I. (2008). Co-ordination principles: A reply. Mind, 117, 1059–1063.CrossRefGoogle Scholar
  7. 7.
    Smiley, T. (1996). Rejection. Analysis, 56, 1–9.CrossRefGoogle Scholar
  8. 8.
    Tennant, N. (1999). Negation, absurdity and contrariety. In D. Gabbay, & H. Wansing (Eds.), What is Negation? (pp. 199–222). Dortrecht: Kluwer.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of PhilosophyBirkbeck College, University of LondonLondonUK

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