Semantics and the Ontology of Number

What are the meanings of number expressions, what can they tell us about questions central to the philosophy of mathematics?

Eric Snyder (Author)

9781108456258, Cambridge University Press

Paperback / softback, published 20 May 2021

75 pages
22.8 x 15.2 x 0.5 cm, 0.152 kg

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.

1. Introduction
2. Substantivalism and Adjectivalism
3. Polymorphism and the Ontology of Number.

Subject Areas: Philosophy of science [PDA], Philosophy of mathematics [PBB], Mathematics [PB], Mathematics & science [P], Philosophy [HP]