Semantics and the Ontology of Number

Erscheinungsjahr 2021
ISBN: 978-1-108-45625-8
Verlag: Cambridge University Press

Buch, Englisch, 75 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 150 g

Reihe: Elements in the Philosophy of Mathematics

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.

Autoren/Hrsg.

Snyder, Eric

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Geisteswissenschaften Philosophie Philosophie: Allgemeines, Methoden
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

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