Fictionalism and the problem of universals in the philosophy of mathematics
Many long-standing problems pertaining to contemporary philosophy of mathematics can be traced back to different approaches in determining the nature of mathematical entities which have been dominated by the debate between realists and nominalists. Through this discussion conceptualism is...
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doaj-87ea8a0159cb46a89d69f1c1c43395552020-11-25T00:42:39ZdeuInstitute for Philosophy and Social Theory, BelgradeFilozofija i Društvo0353-57382334-85772018-01-0129341542810.2298/FID1803415D0353-57381803415DFictionalism and the problem of universals in the philosophy of mathematicsĐorđević Strahinja0Faculty of Philosophy, Belgrade + The History and Philosophy of Science and Technology, BelgradeMany long-standing problems pertaining to contemporary philosophy of mathematics can be traced back to different approaches in determining the nature of mathematical entities which have been dominated by the debate between realists and nominalists. Through this discussion conceptualism is represented as a middle solution. However, it seems that until the 20th century there was no third position that would not necessitate any reliance on one of the two points of view. Fictionalism, on the other hand, observes mathematical entities in a radically different way. This is reflected in the claim that the concepts being used in mathematics are nothing but a product of human fiction. This paper discusses the relationship between fictionalism and two traditional viewpoints within the discussion which attempts to successfully determine the ontological status of universals. One of the main points, demonstrated with concrete examples, is that fictionalism cannot be classified as a nominalist position (despite contrary claims of authors such as Hartry Field). Since fictionalism is observed as an independent viewpoint, it is necessary to examine its range as well as the sustainability of the implications of opinions stated by their advocates.http://www.doiserbia.nb.rs/img/doi/0353-5738/2018/0353-57381803415D.pdffictionalismuniversalsrealismnominalismphilosophy of mathematicsmetaphysicsontology |
collection |
DOAJ |
language |
deu |
format |
Article |
sources |
DOAJ |
author |
Đorđević Strahinja |
spellingShingle |
Đorđević Strahinja Fictionalism and the problem of universals in the philosophy of mathematics Filozofija i Društvo fictionalism universals realism nominalism philosophy of mathematics metaphysics ontology |
author_facet |
Đorđević Strahinja |
author_sort |
Đorđević Strahinja |
title |
Fictionalism and the problem of universals in the philosophy of mathematics |
title_short |
Fictionalism and the problem of universals in the philosophy of mathematics |
title_full |
Fictionalism and the problem of universals in the philosophy of mathematics |
title_fullStr |
Fictionalism and the problem of universals in the philosophy of mathematics |
title_full_unstemmed |
Fictionalism and the problem of universals in the philosophy of mathematics |
title_sort |
fictionalism and the problem of universals in the philosophy of mathematics |
publisher |
Institute for Philosophy and Social Theory, Belgrade |
series |
Filozofija i Društvo |
issn |
0353-5738 2334-8577 |
publishDate |
2018-01-01 |
description |
Many long-standing problems pertaining to contemporary philosophy of
mathematics can be traced back to different approaches in determining the
nature of mathematical entities which have been dominated by the debate
between realists and nominalists. Through this discussion conceptualism is
represented as a middle solution. However, it seems that until the 20th
century there was no third position that would not necessitate any reliance
on one of the two points of view. Fictionalism, on the other hand, observes
mathematical entities in a radically different way. This is reflected in the
claim that the concepts being used in mathematics are nothing but a product
of human fiction. This paper discusses the relationship between fictionalism
and two traditional viewpoints within the discussion which attempts to
successfully determine the ontological status of universals. One of the main
points, demonstrated with concrete examples, is that fictionalism cannot be
classified as a nominalist position (despite contrary claims of authors such
as Hartry Field). Since fictionalism is observed as an independent
viewpoint, it is necessary to examine its range as well as the
sustainability of the implications of opinions stated by their advocates. |
topic |
fictionalism universals realism nominalism philosophy of mathematics metaphysics ontology |
url |
http://www.doiserbia.nb.rs/img/doi/0353-5738/2018/0353-57381803415D.pdf |
work_keys_str_mv |
AT đorđevicstrahinja fictionalismandtheproblemofuniversalsinthephilosophyofmathematics |
_version_ |
1725281200901193728 |