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Full 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 Gödel: 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 Gödel 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.
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.
