Overview

Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. This work illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Godel are not entirely neglected, either. Anyone interested in the philosophy and/or history of mathematics should find this book of interest.

Full Product Details

Author:   Jaakko Hintikka
Publisher:   Springer
Imprint:   Springer
Edition:   1996 ed.
Volume:   251
Dimensions:   Width: 21.00cm , Height: 2.60cm , Length: 29.70cm
Weight:   1.890kg
ISBN:  

9780792334842

ISBN 10:   0792334841
Pages:   460
Publication Date:   30 November 1995
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Tracking Contradictions in Geometry: The Idea of a Model from Kant to Hilbert.- Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematics.- Kronecker on the Foundations of Mathematics.- The Mysteries of Richard Dedekind.- Frege’s Letters.- Frege’s Principle.- Husserl and Hilbert on Completeness.- Hahn’s Über die nichtarchimedischen Grössensysteme and the Development of the Modern Theory of Magnitudes and Numbers to Measure Them.- The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number.- The Emergence of Descriptive Set Theory.- Chance Against Constructibility.- Thoralf Skolem, Hermann Weyl and ‘Das Gefühl der Welt als begrenztes Ganzes’.- On Tarski’s Background.- Wittgenstein and Ramsey on Identity.- On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle.- Gödel and Husserl.- Index of Names.- Index of Subjects and Titles.

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Author Information

Jaakko Hintikka is the author or co-author of thirty volumes and of some 300 scholarly articles in mathematical and philosophical logic, epistemology, language theory, philosophy of science, history of ideas and history of philosophy, including Aristotle, Descartes, Leibniz, Kant, Peirce, The Bloomsbury Group, Husserl and Wittgenstein. He has also been active in international scholarly organizations, most recently as the First Vice-President of FISP, Vice-President of IIP and Co-Chair of the American Organizing Committee of the Twentieth World Congress of Philosophy. He has been Editor-in-Chief of the International Journal Synthese and the Managing Editor of Synthese Library since 1965.

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