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Fictionalism and the problem of universals in the philosophy of mathematics

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2018
2550.pdf (255.4Kb)
Authors
Đorđević, Strahinja
Article (Published version)
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Abstract
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 posit...ion (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.

Keywords:
universals / realism / philosophy of mathematics / ontology / nominalism / metaphysics / fictionalism
Source:
Filozofija i društvo, 2018, 29, 3, 415-428
Publisher:
  • Univerzitet u Beogradu - Institut za filozofiju i društvenu teoriju, Beograd

DOI: 10.2298/FID1803415D

ISSN: 0353-5738

WoS: 000445822100006

Scopus: 2-s2.0-85059215887
[ Google Scholar ]
URI
http://reff.f.bg.ac.rs/handle/123456789/2553
Collections
  • Radovi istraživača / Researcher's publications - Odeljenje za filozofiju
Institution/Community
Filozofija / Philosophy
TY  - JOUR
AU  - Đorđević, Strahinja
PY  - 2018
UR  - http://reff.f.bg.ac.rs/handle/123456789/2553
AB  - 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.
PB  - Univerzitet u Beogradu - Institut za filozofiju i društvenu teoriju, Beograd
T2  - Filozofija i društvo
T1  - Fictionalism and the problem of universals in the philosophy of mathematics
EP  - 428
IS  - 3
SP  - 415
VL  - 29
DO  - 10.2298/FID1803415D
ER  - 
@article{
author = "Đorđević, Strahinja",
year = "2018",
abstract = "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.",
publisher = "Univerzitet u Beogradu - Institut za filozofiju i društvenu teoriju, Beograd",
journal = "Filozofija i društvo",
title = "Fictionalism and the problem of universals in the philosophy of mathematics",
pages = "428-415",
number = "3",
volume = "29",
doi = "10.2298/FID1803415D"
}
Đorđević, S.. (2018). Fictionalism and the problem of universals in the philosophy of mathematics. in Filozofija i društvo
Univerzitet u Beogradu - Institut za filozofiju i društvenu teoriju, Beograd., 29(3), 415-428.
https://doi.org/10.2298/FID1803415D
Đorđević S. Fictionalism and the problem of universals in the philosophy of mathematics. in Filozofija i društvo. 2018;29(3):415-428.
doi:10.2298/FID1803415D .
Đorđević, Strahinja, "Fictionalism and the problem of universals in the philosophy of mathematics" in Filozofija i društvo, 29, no. 3 (2018):415-428,
https://doi.org/10.2298/FID1803415D . .

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