How Can Abstract Objects of Mathematics Be Known?

0511564 - FLÚ 2020 RIV GB eng J - Journal Article
Kvasz, Ladislav
How Can Abstract Objects of Mathematics Be Known?
Philosophia Mathematica. Roč. 27, č. 3 (2019), s. 316-334. ISSN 0031-8019. E-ISSN 1744-6406
Grant - others:AV ČR(CZ) AP1602
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985955
Keywords : Philosophy of matehmatics * Michael Resnik * structural realism * abstract objects
OECD category: Philosophy, History and Philosophy of science and technology
Impact factor: 0.733, year: 2019
Method of publishing: Limited access
https://academic.oup.com/philmat/article-abstract/27/3/316/5544672?redirectedFrom=fulltext

The aim of the paper is to answer some arguments raised against mathematical structuralism developed by Michael Resnik. These arguments stress the abstractness of mathematical objects, especially their causal inertness, and conclude that mathematical objects, the structures posited by Resnik included, are inaccessible to human cognition. In the paper I introduce a distinction between abstract and ideal objects and argue that mathematical objects are primarily ideal. I reconstruct some aspects of the instrumental practice of mathematics, such as symbolic manipulations or ruler-and-compass constructions, and argue that instrumental practice can secure epistemic access to ideal objects of mathematics.
Permanent Link: http://hdl.handle.net/11104/0304393