Why Can't There Be Numbers

Bibliographic Data

ID5052457
AuthorsDavid Builes (0000-0002-7302-3284, Philosophy, New York University, USA, corresponding author)
Year2021
Volume72
Issue1
Pages65-76
Publication date2021-12-06
Open AccessYes
TypeARTICLE
VenueThe Philosophical Quarterly (JOURNAL)
Journal identifiersISSN: 0031-8094 • E-ISSN: 1467-9213
PublisherOxford University Press (PUBLISHER • GB)
DOI10.1093/pq/pqab017
OpenAlexW3145567746
LanguageEN
Citations received1
References cited42

Platonists affirm the existence of abstract mathematical objects, and Nominalists deny the existence of abstract mathematical objects. While there are standard arguments in favor of Nominalism, these arguments fail to account for the necessity of Nominalism. Furthermore, these arguments do nothing to explain why Nominalism is true. They only point to certain theoretical vices that might befall the Platonist. The goal of this paper is to formulate and defend a simple, valid argument for the necessity of Nominalism that seeks to precisify the widespread intuition that mathematical objects are somehow 'spooky' or 'mysterious

Argument (complex analysis) · Epistemology · Intuition · Nominalism · Nothing · Simple (philosophy) · Computability, Logic, AI Algorithms · History and Theory of Mathematics · Philosophy · Philosophy and Theoretical Science

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