Abstractionism

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

Francesca Boccuni (Author), Luca Zanetti (Author)

9781009509794, Cambridge University Press

Hardback, published 6 February 2025

86 pages
23.5 x 16 x 1 cm, 0.268 kg

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.

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.

Subject Areas: Philosophy [HP]