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The Prehistory of Mathematical Structuralism

Erich H. Reck and Georg Schiemer

Abstract

Since the 1960s, there has been a vigorous and ongoing debate about structuralism in English-speaking philosophy of mathematics. But structuralist ideas and methods go back further in time; that is, there is a rich prehistory to this debate, also in the German- and French-speaking literature. In the present collection of essays, this prehistory is explored in a twofold way: by reconsidering various mathematicians in the 19th and early 20th centuries (Grassmann, Dedekind, Pasch, Klein, Hilbert, Noether, Bourbaki, and Mac Lane) who contributed to structuralism in a methodological sense; and by r ... More

Keywords: mathematics, philosophy, structuralism, structure, methodology, metaphysics, 19th century, 20th century

Bibliographic Information

Print publication date: 2020 Print ISBN-13: 9780190641221
Published to Oxford Scholarship Online: June 2020 DOI:10.1093/oso/9780190641221.001.0001

Authors

Affiliations are at time of print publication.

Erich H. Reck, editor
Professor of Philosophy, University of California at Riverside

Georg Schiemer, editor
Assistant Professor, Department of Philosophy, University of Vienna

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Contents

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1 Introduction and Overview

Erich H. Reck and Georg Schiemer

Part I Mathematical Developments

8 The Functional Role of Structures in Bourbaki

Gerhard Heinzmann and Jean Petitot

Part II Logical and Philosophical Reflections