Patterns of change: linguistic innovations in the development of classical mathematics

The book offers a reconstruction of linguistic innovations in the history of mathematics. It argues that there are at least three ways in which the language of mathematics can be changed. As illustration of changes of the first kind,called re-codings, is the development along the line: synthetic geometry, analytic geometry, fractal geometry, and set theory. In this development the mathematicians changed the very way of constructing geometric figures. As illustration of changes of the second kind, called relativization, is the development of synthetic geometry along the line: Euclid’s geometry, projective geometry, non-Euclidean geometry, Erlanger program up to Hilbert’s Grundlagen der Geometrie. Changes of the third kind, called re-formulations are for instance the changes that can be seen on the different editions of Euclid’s Elements. Perhapsthe best known among them is Playfair’s change of the formulation of the fifth postulate. Focuses on changes of language in the history of mathematics Introduces exact tools of formal logic for the reconstruction of the historical development of the language of mathematics Offers two rather universal patterns of development INDICE: Preface.- Introduction.- Re-codings as the first pattern of changein mathematics.- Historical description of re-codings.- Philosophical reflections on re-codings.- Relativizations as the second pattern of change in mathematics.- A Historical description of relativizations in synthetic geometry.- Historical description of relativizations in algebra.- Philosophical reflectionson relativizations.- Re-formulations as a third pattern of change in mathematics.- Re-formulations and concept-formation.- Re-formulations and problem-solving.- Re-formulations and theory-building.- Mathematics and change.- The question of revolutions in mathematics (Kuhn).- The question of mathematical research programs (Lakatos).- The question of stages of cognitive development (Piaget).- Notes.- Bibliography.

• ISBN: 978-3-7643-8839-3
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 265
• Fecha Publicación: 01/07/2008
• Nº Volúmenes: 1
• Idioma: Inglés