Mathematics and Logic in History and in Contemporary Thought

Ettore Carruccio,Isabel Quigly

• Editorial: Routledge
• Año: 2017
• ISBN:
  9781351506625
• Edición: 1
• Categoría: Matemáticas
• Categoría: Historia y filosofía de las matemáticas

This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.

Índice

• Cover
• Half Title
• Title
• Copyright
• Contents
• I. The Meaning, Purpose and Methods of the History of Mathematics and of Logic page
• II. Pre-Hellenic Mathematics
• III. Greek Mathematics before Euclid
• IV. The Logic of Aristotle
• V. Euclid's Elements in Hellenistic culture
• VI. Infinitesimal Methods in Classical Times: Archimedes
• VII. Introduction to Higher Geometry: Apollonius and His Followers
• VIII. Mathematics in the Roman World
• IX. The Decline of Ancient Science
• X. Mathematics and Logic in the Middle Ages
• XI. The Mathematical Renaissance and the Algebraists
• XII. Origins of Analytical Geometry and Cartesian Rationalism: Vico's Gnoseology
• XIII. Modern Infinitesimal Analysis and the Philosophical Thought of its Constructors
• XIV. From the Origins of Projective Geometry to the Development of the Erlanger Programme
• XV. Criticism of Euclid's Postulate V: Non-Euclidean Geometries
• XVI. Combinatorial Analysis and Calculus of Probability
• XVII. Sets, Functions, Curves, Non-Archimedean Geometries
• XVIII. Symbolic Logic and the Fundamentals of Arithmetic
• XIX. Hypothetical-Deductive Systems, Non-Contradictoriness, Antinomies
• XX. Problems of Contemporary Logic
• Bibliography
• Index