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The individuation of mathematical objects

Bahram Assadian Orcid Logo, Rob Fraser Orcid Logo

Synthese, Volume: 205, Start page: 6

Swansea University Author: Rob Fraser Orcid Logo

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DOI (Published version): 10.1007/s11229-024-04814-6

Abstract

Against mathematical platonism, it is sometimes objected that mathematical objects are mysterious. One possible elaboration of this objection is that the individuation of mathematical objects cannot be adequately explained. This suggests that facts about the numerical identity and distinctness of ma...

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Published in: Synthese
ISSN: 0039-7857 1573-0964
Published: Springer Nature 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa68644
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spelling 2025-01-03T12:11:23.4348588 v2 68644 2025-01-03 The individuation of mathematical objects b672bd356b55dba1f5d104300a083215 0000-0002-1475-1863 Rob Fraser Rob Fraser true false 2025-01-03 SOSS Against mathematical platonism, it is sometimes objected that mathematical objects are mysterious. One possible elaboration of this objection is that the individuation of mathematical objects cannot be adequately explained. This suggests that facts about the numerical identity and distinctness of mathematical objects require an explanation, but that their supposed nature precludes us from providing one. In this paper, we evaluate this nominalist objection by exploring three ways in which mathematical objects may be individuated: by the intrinsic properties they possess, by the relations they stand in, and by their underlying 'substance'. We argue that only the third mode of individuation raises metaphysical problems that could substantiate the claim that mathematical objects are somehow mysterious. Since the platonist is under no obligation to accept this thesis over the alternatives, we conclude that, at least as far as individuation is concerned, the nominalist objection has no bite. Journal Article Synthese 205 6 Springer Nature 0039-7857 1573-0964 Identity ; Individuation; Grounding; Mathematical objects; Mathematical platonism 23 12 2024 2024-12-23 10.1007/s11229-024-04814-6 COLLEGE NANME Social Sciences School COLLEGE CODE SOSS Swansea University Another institution paid the OA fee The first author acknowledges funding from UKResearch and Innovation, under the UK government’s Horizon Europe funding guarantee, Grant/AwardNumber: EP/X026949/1. 2025-01-03T12:11:23.4348588 2025-01-03T11:58:39.9788539 Faculty of Humanities and Social Sciences School of Social Sciences - Politics, Philosophy and International Relations Bahram Assadian 0000-0001-9104-310X 1 Rob Fraser 0000-0002-1475-1863 2
title The individuation of mathematical objects
spellingShingle The individuation of mathematical objects
Rob Fraser
title_short The individuation of mathematical objects
title_full The individuation of mathematical objects
title_fullStr The individuation of mathematical objects
title_full_unstemmed The individuation of mathematical objects
title_sort The individuation of mathematical objects
author_id_str_mv b672bd356b55dba1f5d104300a083215
author_id_fullname_str_mv b672bd356b55dba1f5d104300a083215_***_Rob Fraser
author Rob Fraser
author2 Bahram Assadian
Rob Fraser
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container_title Synthese
container_volume 205
container_start_page 6
publishDate 2024
institution Swansea University
issn 0039-7857
1573-0964
doi_str_mv 10.1007/s11229-024-04814-6
publisher Springer Nature
college_str Faculty of Humanities and Social Sciences
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hierarchy_top_title Faculty of Humanities and Social Sciences
hierarchy_parent_id facultyofhumanitiesandsocialsciences
hierarchy_parent_title Faculty of Humanities and Social Sciences
department_str School of Social Sciences - Politics, Philosophy and International Relations{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}School of Social Sciences - Politics, Philosophy and International Relations
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description Against mathematical platonism, it is sometimes objected that mathematical objects are mysterious. One possible elaboration of this objection is that the individuation of mathematical objects cannot be adequately explained. This suggests that facts about the numerical identity and distinctness of mathematical objects require an explanation, but that their supposed nature precludes us from providing one. In this paper, we evaluate this nominalist objection by exploring three ways in which mathematical objects may be individuated: by the intrinsic properties they possess, by the relations they stand in, and by their underlying 'substance'. We argue that only the third mode of individuation raises metaphysical problems that could substantiate the claim that mathematical objects are somehow mysterious. Since the platonist is under no obligation to accept this thesis over the alternatives, we conclude that, at least as far as individuation is concerned, the nominalist objection has no bite.
published_date 2024-12-23T08:37:24Z
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