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The prehistory of mathematical structuralism /

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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 reco...

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Bibliographic Details
Corporate Author: Oxford University Press
Other Authors: Reck, Erich H., 1959- (Editor), Schiemer, Georg (Editor)
Format: eBook
Language:English
Published: New York, NY : Oxford University Press, [2020]
Series:Logic and computation in philosophy.
Subjects:
Mathematics > Philosophy.
Analysis (Philosophy) > History.
Mathématiques > Philosophie.
Philosophie analytique > Histoire.
Analysis (Philosophy)
Mathematics > Philosophy
Electronic books.
History
Online Access:Connect to the full text of this electronic book
Table of 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.