Element contents
Semantics and the Ontology of Number
Published online by Cambridge University Press: 26 April 2021
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 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.
Keywords
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- Online ISBN: 9781108602259Publisher: Cambridge University PressPrint publication: 20 May 2021
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