Semantics and the Ontology of Number
Seiten
2021
Cambridge University Press (Verlag)
9781108456258 (ISBN)
Cambridge University Press (Verlag)
9781108456258 (ISBN)
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.
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.
1. Introduction; 2. Substantivalism and Adjectivalism; 3. Polymorphism and the Ontology of Number.
| Erscheinungsdatum | 17.05.2021 |
|---|---|
| Reihe/Serie | Elements in the Philosophy of Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 152 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Naturwissenschaften | |
| ISBN-13 | 9781108456258 / 9781108456258 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Von Logik und Mengenlehre bis Zahlen, Algebra, Graphen und …
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 104,90
Grundlagen für das Bachelor-Studium
Buch | Hardcover (2023)
Hanser (Verlag)
CHF 55,95
