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Logic without metaphysics

Zalabardo, JL; (2019) Logic without metaphysics. Synthese 10.1007/s11229-019-02124-w. (In press). Green open access

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Abstract

Standard definitions of logical consequence for formal languages are atomistic. They take as their starting point a range of possible assignments of semantic values to the extralogical atomic constituents of the language, each of which generates a unique truth value for each sentence. In modal logic, these possible assignments of semantic values are generated by Kripke-style models involving possible worlds and an accessibility relation. In first-order logic, they involve the standard structures of model theory, as sets of objects from which the extralogical symbols of the language receive their denotations. I argue that there is an alternative, holistic, approach to the task of defining logical consequence for a formal language. It specifies necessary and sufficient conditions for an assignment of truth values to all the sentences of the language to be compatible with the intended interpretation of its logical constants. It achieves this without invoking possible assignments of semantic values to the extralogical atomic constituents of the language, or the formal resources that are employed to generate these. I show how this approach can be successfully applied to modal propositional logic and to first-order logic, modal as well as nonmodal. I show that the holistic definitions of logical consequence that I supply for these languages are equivalent to the standard atomistic definitions.

Type: Article
Title: Logic without metaphysics
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11229-019-02124-w
Publisher version: http://doi.org/10.1007/s11229-019-02124-w
Language: English
Additional information: Copyright © The Author(s) 2019. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Modality, Necessity, Logical consequence, Formal semantics, Substitutional quantification, Possible worlds, Modal semantics
UCL classification: UCL
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/10069548
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