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Title The prehistory of mathematical structuralism / edited by Erich H. Reck and Georg Schiemer
Published New York, NY : Oxford University Press, [2020]
©2020

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Description 1 online resource (469 pages)
Series Logic and Computation in Philosophy
Logic and computation in philosophy.
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
Summary This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic
Bibliography Includes bibliographical references and indexes
Notes Online resource; title from digital title page (viewed on April 28, 2020)
Subject Mathematics -- Philosophy.
Analysis (Philosophy) -- History
Analysis (Philosophy)
Mathematics -- Philosophy
Genre/Form History
Form Electronic book
Author Reck, Erich H., 1959- editor.
Schiemer, Georg, editor.
ISBN 0190090774
9780190641238
0190641231
9780190090777
9780190641245
019064124X