Semantics and the Ontology of Number

Download or read book Semantics and the Ontology of Number written by Eric Snyder and published by Cambridge University Press. This book was released on 2021-05-20 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.