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Non-representational mathematical realism

Frapolli, MJ; (2015) Non-representational mathematical realism. Theoria , 30 (3) pp. 331-348. 10.1387/theoria.14105. Green open access

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Abstract

This paper is an attempt to convince anti-realists that their correct intuitions against the metaphysical inflationism derived from some versions of mathematical realism do not force them to embrace non-standard, epistemic approaches to truth and existence. It is also an attempt to convince mathematical realists that they do not need to implement their perfectly sound and judicious intuitions with the anti-intuitive developments that render full-blown mathematical realism into a view which even Gödel considered objectionable (Gödel 1995, p. 150). I will argue for the following two theses: (i) that realism, in its standard characterization, is our default position, a position in agreement with our pre-theoretical intuitions and with the results of our best semantic theories, and (ii) that most of the metaphysical qualms usually related to it depends on a poor understanding of truth and existence as higher-order concepts.

Type: Article
Title: Non-representational mathematical realism
Open access status: An open access version is available from UCL Discovery
DOI: 10.1387/theoria.14105
Publisher version: http://doi.org/10.1387/theoria.14105
Language: English
Additional information: THEORIA is a non-profit editorial venture. It is published by the University of the Basque Country (UPV/EHU Press) under a Creative Commons Licence. It is part of the Open Journal System (OJS) and all its papers (from 2003 onwards) are freely available on-line. THEORIA is published under a Creative Commons Licence: Attribution-Noncommercial-No Derivative Works 4.0 Generic
Keywords: abstract entities, anti-realism, existence, numbers, realism, representationalism, truth
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/1545654
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