Philosophy of Mathematics from the Pythagoreans to Euclid

This Element discusses the characteristics of mathematical knowledge and the employability of mathematical methods.

Barbara M. Sattler (Author)

9781009578905, Cambridge University Press

Hardback, published 22 May 2025

80 pages
23.5 x 16 x 1 cm, 0.262 kg

This Element looks at the very beginning of the philosophy of mathematics in Western thought. It covers the first reflections on attempts to untie mathematics from its practical usage in administration, commerce, and land-surveying and discusses the first ideas to see mathematical structures as constituents underlying the physical world in the Pythagoreans. The first two sections focus on the epistemic status of mathematical knowledge in relation to philosophical knowledge and on the various ontological positions ancient Greek philosophers in early and classical times ascribe to mathematical objects – from independent and separate entities to mere abstractions and idealisations. Section 3 discusses the paradigmatic role mathematical deductions have played for philosophy, the role of mathematical diagrams, and mathematical methods of interest for philosophers. Section 4, finally, investigates a couple of individual concepts that are fundamental for both philosophy and mathematics, such as infinity.

Introduction
1. Ontology: the status of mathematical objects
2. Epistemology: mathematical knowledge versus philosophical knowledge
3. Methodology
4. Central concepts
References.

Subject Areas: Philosophy [HP]