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Bilateralist Detours: From Intuitionist to Classical Logic and Back

Kürbis, N; (2017) Bilateralist Detours: From Intuitionist to Classical Logic and Back. Logique & Analyse , 60 (239) pp. 301-316. 10.2143/LEA.239.0.32371556. Green open access

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Abstract

There is widespread agreement that while on a Dummettian theory of meaning the justified logic is intuitionist, as its constants are governed by harmonious rules of inference, the situation is reversed on Huw Price's bilateralist account, where meanings are specified in terms of primitive speech acts assertion and denial. In bilateral logics, the rules for classical negation are in harmony. However, as it is possible to construct an intuitionist bilateral logic with harmonious rules, there is no formal argument against intuitionism from the bilateralist perspective. Price gives an informal argument for classical negation based on a pragmatic notion of belief, characterised in terras of the differences they make to speakers' actions. The main part of this paper puts Price's argument under close scrutiny by regimenting it and isolating principles Price is committed to. It is shown that Price should draw a distinction between A or → A making a difference. According to Price, if A makes a difference to us, we treat it as decidable. This material allows the intuitionist to block Price's argument. Abandoning classical logic also brings advantages, as within intuitionist logic there is a precise meaning to what it might mean to treat A as decidable: it is to assume A v →A.

Type: Article
Title: Bilateralist Detours: From Intuitionist to Classical Logic and Back
Open access status: An open access version is available from UCL Discovery
DOI: 10.2143/LEA.239.0.32371556
Publisher version: http://virthost.vub.ac.be/lnaweb/ojs/index.php/Log...
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.
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/10071964
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