Journal of Philosophical Logic 45 (6):623-644 (2016)
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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’ : 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.
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Keywords | Negation Denial Classical logic Intuitionist logic Harmony Proof-theoretic semantics |
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DOI | 10.1007/s10992-016-9395-9 |
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References found in this work BETA
The Revival of Rejective Negation.Lloyd Humberstone - 2000 - Journal of Philosophical Logic 29 (4):331-381.
Price and Rumfitt on Rejective Negation and Classical Logic.Peter Gibbard - 2002 - Mind 111 (442):297-304.
View all 7 references / Add more references
Citations of this work BETA
Bilateralism Does Not Provide a Proof Theoretic Treatment of Classical Logic.Michael Gabbay - 2017 - Journal of Applied Logic 25:S108-S122.
Reprint Of: A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
Bilateralist Detours: From Intuitionist to Classical Logic and Back.Nils Kürbis - 2017 - Logique Et Analyse 60 (239):301-316.
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