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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