Patterns of Change Linguistic Innovations in the Development of Classical Mathematics /

• Main Author: Kvasz, Ladislav (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2008.
• Series: Science Networks. Historical Studies ; 36
• Subjects: Mathematics.; History.; History of Mathematical Sciences.

This book offers a reconstruction of linguistic innovations in the history of mathematics; innovations which changed the ways in which mathematics was done, understood and philosophically interpreted. It argues that there are at least three ways in which the language of mathematics has been changed...

Table of Contents:

• Preface
• Introduction
• Re-codings as the first pattern of change in 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 reflections on 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.