Axiomatic Method and Category Theory

• Main Author: Rodin, Andrei (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ; 364
• Subjects: Philosophy.; Epistemology.; Category theory (Mathematics).; Homological algebra.; Mathematical logic.; Category Theory, Homological Algebra.; Mathematical Logic and Foundations.

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is...

Table of Contents:

• Introduction
• Part I A Brief History of the Axiomatic Method
• Chapter 1. Euclid: Doing and Showing
• Chapter 2. Hilbert: Making It Formal
• Chapter 3. Formal Axiomatic Method and the 20th Century Mathematics
• Chapter. 4 Lawvere: Pursuit of Objectivity
• Conclusion of Part 1
• Part II. Identity and Categorification
• Chapter 5. Identity in Classical and Constructive Mathematics
• Chapter 6. Identity Through Change, Category Theory and Homotopy Theory
• Conclusion of Part 2
• Part III. Subjective Intuitions and Objective Structures
• Chapter 7. How Mathematical Concepts Get Their Bodies. Chapter 8. Categories versus Structures
• Chapter 9. New Axiomatic Method (instead of conclusion)
• Bibliography.