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Semantics and the Ontology of Number Eric Snyder

Semantics and the Ontology of Number By Eric Snyder

Semantics and the Ontology of Number by Eric Snyder


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Summary

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 outlines a recent debate between substantivalists and adjectivalists regarding the semantic function of number words in numerical statements.

Semantics and the Ontology of Number Summary

Semantics and the Ontology of Number by Eric Snyder

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.

Table of Contents

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

Additional information

NLS9781108456258
9781108456258
1108456251
Semantics and the Ontology of Number by Eric Snyder
New
Paperback
Cambridge University Press
2021-05-20
75
N/A
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