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

by Ladislav Kvasz

Overview

Kvasz’s book is a contribution to the history and philosophy of mat- matics, or, as one might say, the historical approach to the philosophy of mathematics. This approach is for mathematics what the history and philosophy of science is for science. Yet the historical approach to the philosophy of science appeared much earlier than the historical approach to the philosophy of mathematics. The first significant work in the history and philosophy of science is perhaps William Whewell’s Philosophy of the Inductive Sciences, founded upon their History. This was originally published in 1840, a second, enlarged edition appeared in 1847, and the third edition appeared as three separate works p- lished between 1858 and 1860. Ernst Mach’s The Science of Mech- ics: A Critical and Historical Account of Its Development is certainly a work of history and philosophy of science. It first appeared in 1883, and had six further editions in Mach’s lifetime (1888, 1897, 1901, 1904, 1908, and 1912). Duhem’s Aim and Structure of Physical Theory appeared in 1906 and had a second enlarged edition in 1914. So we can say that history and philosophy of science was a well-established field th th by the end of the 19 and the beginning of the 20 century. By contrast the first significant work in the history and philosophy of mathematics is Lakatos’s Proofs and Refutations, which was p- lished as a series of papers in the years 1963 and 1964.

Product Details

ISBN-13:	9783764388393
Publisher:	Birkh�user Basel
Publication date:	08/27/2008
Series:	Science Networks. Historical Studies , #36
Edition description:	2008
Pages:	262
Product dimensions:	6.60(w) x 9.20(h) x 0.80(d)

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.

Editorial Reviews

From the reviews:

“This is a book on the history and philosophy of mathematics interpreted as a sequence of linguistic innovations. … Kvasz has succeeded in producing a book which synthesizes over a quarter of century of his contributions to a linguistic approach to the history and philosophy of mathematics. The book should prove of interest not only to mathematicians. It suggests new directions for the analysis of changes … resulting from cultural encounters. … The book also has explicit references … to obstacles in mathematics education.” (U. D’Ambrosio, Mathematical Reviews, Issue 2009 k)

“In this book the author expounds his ‘linguistic approach’ for reconstructing the development of mathematical disciplines from a philosophical and historical point of view. … Kvasz’ approach provides an interesting tool for philosophers and historians which should be further discussed and applied.” (Hans Fischer, Zentralblatt MATH, Vol. 1153, 2009)

From the Publisher