A concise history of mathematics for philosophers
John Stillwell.
Bok Engelsk 2019 · Electronic books.
| Utgitt | Cambridge University Press
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| Omfang | 1 online resource (69 pages) : : digital, PDF file(s).
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| Utgave | 1st ed.
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| Opplysninger | Title from publisher's bibliographic system (viewed on 30 May 2019).. - Cover -- Title page -- Copyright page -- A Concise History of Mathematics for Philosophers -- Contents -- Preface -- 1 Irrational Numbers and Geometry -- Preview -- 1.1 The Pythagorean Theorem -- 1.2 Irrationality -- 1.3 Operations on Lengths and Numbers -- 1.4 Axiomatics -- 1.5 Philosophical Issues -- 2 Infinity in Greek Mathematics -- Preview -- 2.1 Irrationality and Non-termination -- 2.2 Areas and Volumes -- 2.3 The Method of Exhaustion -- 2.4 The Theory of Proportions -- 2.5 Archimedes and Actual Infinity -- 2.6 Philosophical Issues -- 3 Imaginary Numbers -- Preview -- 3.1 Quadratic and Cubic Equations -- 3.2 Bombelli's Algebra of Imaginary Numbers -- 3.3 The Convenience of Imaginary Numbers -- 3.4 Realizing the Imaginary -- 3.5 Philosophical Issues -- 4 Calculus and Infinitesimals -- Preview -- 4.1 Infinite Series -- 4.2 Algebraic Geometry -- 4.3 Infinitesimal Calculus -- 4.4 Infinitesimals: Criticism and Avoidance -- 4.5 Complex Analysis -- 4.6 Philosophical Issues -- 5 Continuous Functions and Real Numbers -- Preview -- 5.1 The Fundamental Theorem of Algebra -- 5.2 The Intermediate Value Theorem -- 5.3 Definition of Real Numbers -- 5.4 Counter-intuitive Curves -- 5.5 Philosophical Issues -- 6 From Non-Euclidean Geometry to Arithmetic -- Preview -- 6.1 The Parallel Axiom -- 6.2 Non-Euclidean Geometry -- 6.3 The Impact of Non-Euclidean Geometry -- 6.4 Arithmetization of Geometry -- 6.5 Vector Geometry -- 6.6 Philosophical Issues -- 7 Set Theory and Its Paradoxes -- Preview -- 7.1 Before Cantor -- 7.2 Cantor's Diagonal Argument -- 7.3 Higher Infinities -- 7.4 Aftermath of the Diagonal Argument -- 7.5 Philosophical Issues -- 8 Formal Systems -- Preview -- 8.1 Hilbert -- 8.2 The Systems of Peano and Zermelo -- 8.3 Frege's System for Logic -- 8.4 Completeness and Incompleteness -- 8.5 Philosophical Issues -- 9 Unsolvability and Incompleteness.. - Preview -- 9.1 Computability -- 9.2 Unsolvability -- 9.3 Incompleteness -- 9.4 The Incompleteness of Set Theory -- 9.5 Philosophical Issues -- Bibliography.. - This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 1-108-61012-9
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