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What ‘the number of planets is eight’ means

Rob Fraser Orcid Logo

Philosophical Studies, Volume: 172, Issue: 10, Pages: 2757 - 2775

Swansea University Author: Rob Fraser Orcid Logo

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DOI (Published version): 10.1007/s11098-015-0443-z

Abstract

The following sentence is true only if numbers exist: (1) The number of planets is eight. It is true; hence, numbers exist.’ So runs a familiar argument for realism about mathematical objects. But this argument relies on a controversial semantic thesis: that ‘The number of planets’ and ‘eight’ are s...

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Published in: Philosophical Studies
ISSN: 0031-8116 1573-0883
Published: Springer Science and Business Media LLC 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa68379
first_indexed 2024-11-29T13:46:45Z
last_indexed 2024-11-29T13:46:45Z
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spelling 2024-11-29T11:54:08.2738703 v2 68379 2024-11-29 What ‘the number of planets is eight’ means b672bd356b55dba1f5d104300a083215 0000-0002-1475-1863 Rob Fraser Rob Fraser true false 2024-11-29 SOSS The following sentence is true only if numbers exist: (1) The number of planets is eight. It is true; hence, numbers exist.’ So runs a familiar argument for realism about mathematical objects. But this argument relies on a controversial semantic thesis: that ‘The number of planets’ and ‘eight’ are singular terms standing for the number eight, and the copula expresses identity. This is the ‘Fregean analysis’. I show that the Fregean analysis is false by providing an analysis of sentences such as (1) that best explains the available linguistic data, and according to which no terms in (1) purport to stand for numbers. Journal Article Philosophical Studies 172 10 2757 2775 Springer Science and Business Media LLC 0031-8116 1573-0883 1 10 2015 2015-10-01 10.1007/s11098-015-0443-z http://dx.doi.org/10.1007/s11098-015-0443-z COLLEGE NANME Social Sciences School COLLEGE CODE SOSS Swansea University 2024-11-29T11:54:08.2738703 2024-11-29T09:05:35.0392806 Faculty of Humanities and Social Sciences School of Social Sciences - Politics, Philosophy and International Relations Rob Fraser 0000-0002-1475-1863 1
title What ‘the number of planets is eight’ means
spellingShingle What ‘the number of planets is eight’ means
Rob Fraser
title_short What ‘the number of planets is eight’ means
title_full What ‘the number of planets is eight’ means
title_fullStr What ‘the number of planets is eight’ means
title_full_unstemmed What ‘the number of planets is eight’ means
title_sort What ‘the number of planets is eight’ means
author_id_str_mv b672bd356b55dba1f5d104300a083215
author_id_fullname_str_mv b672bd356b55dba1f5d104300a083215_***_Rob Fraser
author Rob Fraser
author2 Rob Fraser
format Journal article
container_title Philosophical Studies
container_volume 172
container_issue 10
container_start_page 2757
publishDate 2015
institution Swansea University
issn 0031-8116
1573-0883
doi_str_mv 10.1007/s11098-015-0443-z
publisher Springer Science and Business Media LLC
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
url http://dx.doi.org/10.1007/s11098-015-0443-z
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description The following sentence is true only if numbers exist: (1) The number of planets is eight. It is true; hence, numbers exist.’ So runs a familiar argument for realism about mathematical objects. But this argument relies on a controversial semantic thesis: that ‘The number of planets’ and ‘eight’ are singular terms standing for the number eight, and the copula expresses identity. This is the ‘Fregean analysis’. I show that the Fregean analysis is false by providing an analysis of sentences such as (1) that best explains the available linguistic data, and according to which no terms in (1) purport to stand for numbers.
published_date 2015-10-01T20:49:41Z
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