From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics (Synthese Library, 251)

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. Front Matter....Pages i-ix Tracking Contradictions in Geometry: The Idea of a Model from Kant to Hilbert....Pages 1-20 Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematics....Pages 21-44 Kronecker on the Foundations of Mathematics....Pages 45-52 The Mysteries of Richard Dedekind....Pages 53-96 Frege’s Letters....Pages 97-118 Frege’s Principle....Pages 119-142 Husserl and Hilbert on Completeness....Pages 143-163 Hahn’s Über die Nichtarchimedischen Grössensysteme and the Development of the Modern Theory of Magnitudes and Numbers to Measure Them....Pages 165-213 The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number....Pages 215-239 The Emergence of Descriptive Set Theory....Pages 241-262 Chance Against Constructibility....Pages 263-281 Thoralf Skolem, Hermann Weyl and “Das Gefühl der Welt als Begrenztes Ganzes”....Pages 283-329 On Tarski’s Background....Pages 331-341 Wittgenstein and Ramsey on Identity....Pages 343-371 On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle....Pages 373-425 Gödel and Husserl....Pages 427-446 Back Matter....Pages 447-472

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.

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 Godel: 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 Ramsay. Needless to say, such logically-oriented thinkers as Frege, Russell and Godel are not entirely neglected, either