The Prehistory of Mathematical Structuralism

by Reck, Erich H.; Schiemer, Georg

• ISBN13: 9780190641221
• ISBN10: 0190641223
• Format: Hardcover
• Copyright: 2020-06-01
• Publisher: Oxford University Press

Author Biography

Erich H. Reck is Professor of Philosophy at the University of California at Riverside. He is the author of a number of articles in the philosophy of mathematics, the history and philosophy of logic, and the history of 19th/20th-century philosophy. In addition, he is the editor, or co-editor, of several related collections of essays: From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy (OUP, 2002); Frege's Lectures on Logic: Carnap's Student Notes, 1910-1914 (Open Court, 2004); Gottlob Frege: Critical Assessments of Leading Philosophers, Vols. I-IV (Routledge, 2005); The Historical Turn in Analytic Philosophy (Palgrave Macmillan, 2013); and Logic, Philosophy of Mathematics, and their History: Essays in Honor of W.W. Tait (College Publications, 2018). Currently he is working on a book on the mathematician and philosopher of mathematics Richard Dedekind.

Georg Schiemer is Assistant Professor at the Department of Philosophy at the University of Vienna as well as external fellow at the Munich Center for Mathematical Philosophy at LMU Munich. He is currently principal investigator of the project "The Roots of Mathematical Structuralism" funded by an ERC Starting Grant. His research focuses on the history and philosophy of mathematics and early analytic philosophy. He is also interested in the history and philosophy of logic and formal philosophy of science.

Table of Contents

1. Erich Reck & Georg Schiemer: The Prehistory of Mathematical Structuralism: Introduction and Overview

Part I: Mathematical Developments
2. Paola Cantù: Grassmann's Concept Structuralism
3. José Ferreirós & Erich Reck: Dedekind's Mathematical Structuralism: From Galois Theory to Numbers, Sets, and Functions
4. Dirk Schlimm: Pasch's Empiricism as Methodological Structuralism
5. Georg Schiemer: Transfer Principles, Klein's Erlangen Program, and Methodological Structuralism
6. Wilfried Sieg: The Ways of Hilbert's Axiomatics: Structural and Formal
7. Audrey Yap: Noether as Mathematical Structuralist
8. Gerhard Heinzmann & Jean Petitot: The Functional Role of Structures in Bourbaki
9. Colin McLarty: Saunders Mac Lane: From Principia Mathematica through Göttingen to the Working Theory of Structures

Part II: Logical and Philosophical Reflections
10. Jessica Carter: Logic of Relations and Diagrammatic Reasoning: Structuralist Elements in the Work of Charles Sanders Peirce
11. Janet Folina: Poincaré and the Pre-History of Mathematical Structuralism
12. Jeremy Heis: 'If Numbers Are To Be Anything At All, They Must Be Intrinsically Something': Bertrand Russell and Mathematical Structuralism
13. Erich Reck: Cassirer's Reception of Dedekind and the Structuralist Transformation of Mathematics
14. Wilfried Sieg: Methodological Frames: Paul Bernays, Mathematical Structuralism, and Proof Theory
15. Georg Schiemer: Carnap's Structuralist Thesis
16. Sean Morris: Explication as Elimination: W.V. Quine and Mathematical Structuralism