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Some Comments on Ian Rumfitt’s Bilateralism

Kürbis, N; (2016) Some Comments on Ian Rumfitt’s Bilateralism. Journal of Philosophical Logic , 45 (6) pp. 623-644. 10.1007/s10992-016-9395-9. Green open access

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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.

Type: Article
Title: Some Comments on Ian Rumfitt’s Bilateralism
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10992-016-9395-9
Publisher version: https://doi.org/10.1007/s10992-016-9395-9
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Negation, Denial, Classical logic, Intuitionist logic Harmony, Proof-theoretic semantics
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10071968
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