現代数学哲学・数学史論文集<br>The Architecture of Modern Mathematics : Essays in History and Philosophy

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現代数学哲学・数学史論文集
The Architecture of Modern Mathematics : Essays in History and Philosophy

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  • 製本 Hardcover:ハードカバー版／ページ数 456 p.
  • 言語 ENG
  • 商品コード 9780198567936
  • DDC分類 510.9

基本説明

Contents- J. Tappenden: The Riemannian background to Frege's philosophy; J. Avigad: Methodology and metaphysics in the development of Dedekind's theory of ideals; P. Mancosu: Tarski on models and logical consequence; M. Epple: Felix Hausdorff's 'considered empiricism'; H. Benis-Sinaceur: From Kant to Hilbert: French philosophy of concepts in the beginning of the 20th Century; J. J. Gray: Modern mathematics as a cultural phenomenon; and more.

Full Description

This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.

Contents

INTRODUCTION ; REINTERPRETATIONS IN THE HISTORY AND PHILOSOPHY OF FOUNDATIONS ; Frege and the role of historical elucidation: Methodology and the foundations of mathematics ; Riemann's Habilitationsvortrag at the crossroads of mathematics, physics and philosophy ; The Riemannian background to Frege's philosophy ; Axiomatics, Empiricism, and Anschauung in Hilbert's conception of geometry: Between arithmetic and general relativity ; EXPLORATIONS INTO THE EMERGENCE OF MODERN MATHEMATICS ; Methodology and metaphysics in the development of Dedekind's theory of ideals ; Emmy Noether's "set-theoretic" topology: from Dedekind to the rise of functors ; Tarski on models and logical consequence ; A path to the epistemology of mathematics: Homotopy theory ; ALTERNATIVE VIEWS AND PROGRAMS IN THE PHILOSOPHY OF MATHEMATICS ; Felix Hausdorff's 'considered empiricism' ; Practice-related symbolic realism in H. Weyl's mature view of mathematical knowledge ; From Kant to Hilbert: French philosophy of concepts in the beginning of the 20th Century. ; Relative consistency and accessible domains, (Synthese, vol. 84, 1990) ; CODA ; Modern mathematics as a cultural phenomenon