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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| Format: | Article |
| Language: | deu |
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Institute for Philosophy and Social Theory, Belgrade
2018-01-01
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| Series: | Filozofija i Društvo |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/0353-5738/2018/0353-57381803415D.pdf |
| Summary: | 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. |
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| ISSN: | 0353-5738 2334-8577 |