ISBN:
9789401142090
Language:
English
Pages:
Online-Ressource (XI, 250 p)
,
digital
Edition:
Springer eBook Collection. Humanities, Social Sciences and Law
Series Statement:
The Western Ontario Series in Philosophy of Science, A Series of Books in Philosophy of Science, Methodology, Epistemology, Logic, History of Science, and Related Fields 63
Parallel Title:
Erscheint auch als
Parallel Title:
Erscheint auch als
Parallel Title:
Erscheint auch als
Keywords:
Philosophy (General)
;
Science Philosophy
;
Logic, Symbolic and mathematical
;
Algebra
;
Geometry
;
History.
;
Mathematical logic.
;
Science—Philosophy.
;
Mathematics.
Abstract:
A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background
DOI:
10.1007/978-94-011-4209-0
URL:
Volltext
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