Some Comments on Ian Rumfitt’s Bilateralism

Journal of Philosophical Logic 45 (6):623-644 (2016)
Authors
Nils Kürbis
King's College London
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.
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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