A Concise History of Mathematics for Philosophers

Erscheinungsjahr 2019
ISBN: 978-1-108-45623-4
Verlag: Cambridge University Press

Buch, Englisch, 75 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 128 g

Reihe: Elements in the 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.

Autoren/Hrsg.

Stillwell, John

Fachgebiete

• Geisteswissenschaften Geschichtswissenschaft Geschichtswissenschaft Allgemein
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Geisteswissenschaften Philosophie Geschichte der Westlichen Philosophie

Inhaltsverzeichnis

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.