Fictionalism and the Problem of Universals in the Philosophy of Mathematics

Filozofija I Društvo 29 (3):415-428 (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. 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 fictionalism, universals, realism, nominalism, philosophy of mathematics, metaphysics, ontology
Categories No categories specified
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DOI 10.2298/FID1803415D
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The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford University Press.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.

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