Fictionalism and the Problem of Universals in the Philosophy of Mathematics

Strahinja Đorđević

doi:10.2298/FID1803415D

Authors

Strahinja Đorđević Faculty of Philosophy, University of Belgrade; The History and Philosophy of Science and Technology, University of Belgrade;

DOI:

https://doi.org/10.2298/FID1803415D

Keywords:

fictionalism, universals, realism, nominalism, philosophy of mathematics, metaphysics, ontology

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 20^thcentury 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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