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Semantic Assumptions in the Philosophy of Mathematics

Rob Fraser Orcid Logo

Boston Studies in the Philosophy and History of Science, Volume: 318, Pages: 43 - 65

Swansea University Author: Rob Fraser Orcid Logo

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DOI (Published version): 10.1007/978-3-319-31644-4_4

Abstract

The standard semantic analysis of sentences such as ‘The number of planets in the solar system is eight’ is that they are identity statements that identify certain mathematical objects, namely numbers. The analysis thereby facilitates arguments for a controversial philosophical position, namely real...

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Published in: Boston Studies in the Philosophy and History of Science
ISBN: 9783319316420 9783319316444
ISSN: 0068-0346 2214-7942
Published: Cham Springer International Publishing 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa68382
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spelling 2024-12-09T13:04:07.3130856 v2 68382 2024-11-29 Semantic Assumptions in the Philosophy of Mathematics b672bd356b55dba1f5d104300a083215 0000-0002-1475-1863 Rob Fraser Rob Fraser true false 2024-11-29 SOSS The standard semantic analysis of sentences such as ‘The number of planets in the solar system is eight’ is that they are identity statements that identify certain mathematical objects, namely numbers. The analysis thereby facilitates arguments for a controversial philosophical position, namely realism about mathematical objects. Accordingly, whether or not this analysis is accurate should concern philosophers greatly. Recently, several authors have offered rival analyses of sentences such as these. In this paper, I will consider a wide range of linguistic evidence and show that all of these analyses, including the standard analysis, suffer significant drawbacks. I will then outline and present further evidence in favour of my own analysis, developed elsewhere, according to which such sentences are identity statements that identify certain kinds of facts. I also defend a novel and plausible approach to the semantics of interrogative clauses that corroborates my analysis. Finally, I discuss how realists about mathematical objects should proceed in light of the arguments presented in this paper. Book chapter Boston Studies in the Philosophy and History of Science 318 43 65 Springer International Publishing Cham 9783319316420 9783319316444 0068-0346 2214-7942 6 7 2016 2016-07-06 10.1007/978-3-319-31644-4_4 COLLEGE NANME Social Sciences School COLLEGE CODE SOSS Swansea University 2024-12-09T13:04:07.3130856 2024-11-29T11:01:53.8705182 Faculty of Humanities and Social Sciences School of Social Sciences - Politics, Philosophy and International Relations Rob Fraser 0000-0002-1475-1863 1
title Semantic Assumptions in the Philosophy of Mathematics
spellingShingle Semantic Assumptions in the Philosophy of Mathematics
Rob Fraser
title_short Semantic Assumptions in the Philosophy of Mathematics
title_full Semantic Assumptions in the Philosophy of Mathematics
title_fullStr Semantic Assumptions in the Philosophy of Mathematics
title_full_unstemmed Semantic Assumptions in the Philosophy of Mathematics
title_sort Semantic Assumptions in the Philosophy of Mathematics
author_id_str_mv b672bd356b55dba1f5d104300a083215
author_id_fullname_str_mv b672bd356b55dba1f5d104300a083215_***_Rob Fraser
author Rob Fraser
author2 Rob Fraser
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container_title Boston Studies in the Philosophy and History of Science
container_volume 318
container_start_page 43
publishDate 2016
institution Swansea University
isbn 9783319316420
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issn 0068-0346
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doi_str_mv 10.1007/978-3-319-31644-4_4
publisher Springer International Publishing
college_str Faculty of Humanities and Social Sciences
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hierarchy_top_id facultyofhumanitiesandsocialsciences
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 The standard semantic analysis of sentences such as ‘The number of planets in the solar system is eight’ is that they are identity statements that identify certain mathematical objects, namely numbers. The analysis thereby facilitates arguments for a controversial philosophical position, namely realism about mathematical objects. Accordingly, whether or not this analysis is accurate should concern philosophers greatly. Recently, several authors have offered rival analyses of sentences such as these. In this paper, I will consider a wide range of linguistic evidence and show that all of these analyses, including the standard analysis, suffer significant drawbacks. I will then outline and present further evidence in favour of my own analysis, developed elsewhere, according to which such sentences are identity statements that identify certain kinds of facts. I also defend a novel and plausible approach to the semantics of interrogative clauses that corroborates my analysis. Finally, I discuss how realists about mathematical objects should proceed in light of the arguments presented in this paper.
published_date 2016-07-06T14:45:57Z
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