From Dedekind to Gödel : essays on the development of the foundations of mathematics
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Bibliographic Information
From Dedekind to Gödel : essays on the development of the foundations of mathematics
（Synthese library, v. 251）
Kluwer Academic Publishers, c2010
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Includes bibliographical references and indexes
Description and Table of Contents
Description
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. From Dedekind to Goedel: Essays on the Development of the Foundations of Mathematics 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 Goedel are not entirely neglected, either.
Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
Table of Contents
- Preface
- J. Hintikka. Tracking Contradictions in Geometry: The Idea of a Model from Kant to Hilbert
- J. Webb. Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematics
- J. Hintikka. Kronecker on the Foundations of Mathematics
- H.M. Edwards. The Mysteries of Richard Dedekind
- D.C. McCarty. Frege's Letters
- C. Ortiz Hill. Frege's Principle
- R.G. Heck Jr. Husserl and Hilbert on Completeness
- C. Ortiz Hill. Hahn's UEber die nichtarchimedischen Groessensysteme and the Development of the Modern Theory of Magnitudes and Numbers to Measure Them
- P. Ehrlich. The Origins of Russell's Paradox: Russell, Couturat, and the Antinomy of Infinite Number
- G. H. Moore. The Emergence of Descriptive Set Theory
- A. Kanamori. Chance against Constructibility
- J. von Plato. Thoralf Skolem, Hermann Weyl and `Das Gefuhl der Welt als begrenztes Ganzes'
- W. Boos. On Tarski's Background
- J. Wolenski. Wittgenstein and Ramsey on Identity
- M. Marion. On Saying What You Really Want to Say: Wittgenstein, Goedel, and the Trisection of the Angle
- J. Floyd. Goedel and Husserl
- D. Follesdal. Index of Names. Index of Subjects and Titles.
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