A Concise History of Mathematics for Philosophers
Seiten
2019
Cambridge University Press (Verlag)
978-1-108-45623-4 (ISBN)
Cambridge University Press (Verlag)
978-1-108-45623-4 (ISBN)
Presents an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. Ranges from 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.
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.
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.
Preface; 1. Irrational numbers and geometry; 2. Infinity in Greek mathematics; 3. Imaginary numbers; 4. Calculus and infinitesimals; 5. Continuous functions and real numbers; 6. From non-Euclidean geometry to arithmetic; 7. Set theory and its paradoxes; 8. Formal systems; 9. Unsolvability and incompleteness.
| Erscheinungsdatum | 11.06.2019 |
|---|---|
| Reihe/Serie | Elements in the Philosophy of Mathematics |
| Zusatzinfo | Worked examples or Exercises; 20 Halftones, black and white |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 150 x 230 mm |
| Gewicht | 100 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Geschichte der Philosophie |
| Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik | |
| ISBN-10 | 1-108-45623-5 / 1108456235 |
| ISBN-13 | 978-1-108-45623-4 / 9781108456234 |
| Zustand | Neuware |
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