Abstractionism

List of contents

1. Introduction; 2. Mathematical Abstractionism; 3. Philosophical Abstractionism I: Semantics; 4. Philosophical Abstractionism II: Ontology; 5. Philosophical Abstractionism III: Epistemology; 6. New Directions in Philosophical; Abstractionism; References.

Summary

The aim of this Element is to provide an overview of abstractionism in the philosophy of mathematics. The authors distinguish between mathematical abstractionism, which interprets mathematical theories on the basis of abstraction principles, and philosophical abstractionism, which attributes a philosophical significance to mathematical abstractionism. They then survey the main semantic, ontological, and epistemological theses that are associated with philosophical abstractionism. Finally, the authors suggest that the most recent developments in the debate pull abstractionism in different directions.

Foreword

This Element is a comprehensive overview on the debate on abstraction principles; logico-mathematical material explained accessibly.

Product details

• Authors: Francesca Boccuni, Luca Zanetti, Luca (Scuola Universitaria Superiore Iuss Zanetti
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.01.2025
• EAN: 9781009509794
• ISBN: 978-1-0-0950979-4
• No. of pages: 86
• Series: Elements in the Philosophy of Mathematics
• Subjects: Humanities, art, music > Philosophy; Non-fiction book > Philosophy, religion > Philosophy: general, reference works; PHILOSOPHY / General, Philosophy: metaphysics & ontology, Philosophy of Mathematics, Philosophy: metaphysics and ontology, Philosophy: epistemology & theory of knowledge, Philosophy: logic, Philosophy: epistemology and theory of knowledge