Overview
- One of the first confrontations of foundations of classical and foundations of constructive mathematics
- A technical and philosophical treatment of the subject
- An extensive philosophical reflection on the meaning and use of foundations in mathematics
Part of the book series: The Western Ontario Series in Philosophy of Science (WONS, volume 76)
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About this book
The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.
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Table of contents (15 chapters)
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Front Matter
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Senses of ‘Foundations of Mathematics’
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Front Matter
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Foundations of Classical Mathematics
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Front Matter
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Between Foundations of Classical and Foundations of Constructive Mathematics
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Front Matter
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Foundations of Constructive Mathematics
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Front Matter
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Editors and Affiliations
Bibliographic Information
Book Title: Foundational Theories of Classical and Constructive Mathematics
Editors: Giovanni Sommaruga
Series Title: The Western Ontario Series in Philosophy of Science
DOI: https://doi.org/10.1007/978-94-007-0431-2
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2011
Hardcover ISBN: 978-94-007-0430-5Published: 26 March 2011
Softcover ISBN: 978-94-007-3561-3Published: 21 April 2013
eBook ISBN: 978-94-007-0431-2Published: 24 March 2011
Series ISSN: 1566-659X
Series E-ISSN: 2215-1974
Edition Number: 1
Number of Pages: XII, 316
Topics: Mathematical Logic and Foundations, Philosophy of Science, Logic