What are the meanings of number expressions, and what can they tell us about questions of central importance to the philosophy of mathematics, specifically 'Do numbers exist?' This Element attempts to shed light on this question by outlining a recent debate between substantivalists and adjectivalists regarding the semantic function of number words in numerical statements. After highlighting their motivations and challenges, I develop a comprehensive polymorphic semantics for number expressions. I argue that accounting for the numerous meanings and how they are related leads to a strengthened argument for realism, one which renders familiar forms of nominalism highly implausible.
By:
Eric Snyder Imprint: Cambridge University Press Country of Publication: United Kingdom Dimensions:
Height: 228mm,
Width: 152mm,
Spine: 5mm
Weight: 152g ISBN:9781108456258 ISBN 10: 1108456251 Series:Elements in the Philosophy of Mathematics Pages: 75 Publication Date:20 May 2021 Audience:
Professional and scholarly
,
Undergraduate
Format:Paperback Publisher's Status: Active
1. Introduction; 2. Substantivalism and Adjectivalism; 3. Polymorphism and the Ontology of Number.
