Fictionalism and the problem of universals in the philosophy of mathematics
Апстракт
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.
Кључне речи:
universals / realism / philosophy of mathematics / ontology / nominalism / metaphysics / fictionalismИзвор:
Filozofija i društvo, 2018, 29, 3, 415-428Издавач:
- Univerzitet u Beogradu - Institut za filozofiju i društvenu teoriju, Beograd
DOI: 10.2298/FID1803415D
ISSN: 0353-5738
WoS: 000445822100006
Scopus: 2-s2.0-85059215887
Институција/група
Filozofija / PhilosophyTY - 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 . .