Semantics and the Ontology of Number
by
Eric Snyder
Book Details
Format
Paperback / Softback
Book Series
Elements in the Philosophy of Mathematics
ISBN-10
1108456251
ISBN-13
9781108456258
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
May 20th, 2021
Print length
75 Pages
Weight
150 grams
Dimensions
15.10 x 22.70 x 1.20 cms
Product Classification:
PhilosophyMathematicsPhilosophy of mathematicsPhilosophy of science
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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.
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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