Semantics and the Ontology of Number

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Semantics and the Ontology of Number

Philosophy Mathematics and Science Mathematics Philosophy of mathematics Philosophy of science

Author: Eric Snyder

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Collection: Elements in the Philosophy of Mathematics

Language: English

Published by: Cambridge University Press

Published on: 20th May 2021

Format: LCP-protected ePub

Size: 3 Mb

ISBN: 9781108653053


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.

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