The prehistory of mathematical structuralism / edited by Erich H. Reck and Georg Schiemer.

Format:

Book

Contributor:

Reck, Erich H., 1959- editor.

Schiemer, Georg, editor.

Series:

Oxford scholarship online.

Logic and computation in philosophy.

Oxford scholarship online

Logic and computation in philosophy

Language:

English

Subjects (All):

Mathematics--Philosophy.

Mathematics.

Structuralism.

Analysis (Philosophy)--History.

Analysis (Philosophy).

Physical Description:

1 online resource (xi, 454 pages) : illustrations.

Place of Publication:

New York : Oxford University Press, 2020.

Summary:

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 who contributed to structuralism in a methodological sense; and by re-examining a range of philosophical reflections on such contributions during the same period, which led to suggestions about logical, epistemological, and metaphysical aspects that remain relevant today.

Contents:

Introduction and overview

I. MATHEMATICAL DEVELOPMENT

Grassmann's concept structuralism

Dedekind's mathematical structuralism: from Galois Theory to numbers, sets and functions

Pasch's empiricism as methodological structuralism

Transfer principles, Klein's erlangen program, and methodological structuralism

The ways of Hilbert's axiomatics: structural and formal

Noether as mathematical structuralist

The functional roles of structures in Bourbaki

Saunders MacLane: From Principlia Mathematics throught Göttingen to the working theory of structures

II. LOGICAL AND PHILOSOPHICAL REFLECTIONS

Logical relations and diagrammatic reasoning: structuralist elements in the work of Charles Saunders Peirce

Poincaré and the prehistory of mathematical structuraism

"If numbers are to be anything at all, they must be instrinsically something": Bertrand Russell and mathematical structuralism

Cassirer's reception of Dedekind and the structuralist transformation of mathematics

Methodological frames: Paul Bernays, mathematical structuralism, and proof theory

Carnap's structuralist thesis

Explication as elimination: W.V. Quine and mathematical structuralist

Name index

Subject index.

Notes:

"This is an open access title. It is available to read and download as a free PDF version on Oxford Scholarship Online. It has been made available under a Creative Commons Attribution-Non Commercial No Derivates 4.0 International licence"--Home page.

Also issued in print: 2020.

Includes bibliographical references and index.

Description based on online resource; title from home page (viewed on June 3, 2020).

ISBN:

0-19-064124-X

0-19-009077-4