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Patterns of Change

Linguistic Innovations in the Development of Classical Mathematics

  • Book
  • © 2008

Overview

Authors:
  1. Ladislav Kvasz

    1. Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia
      Faculty of Education, Charles University, Praha, Czech Republic

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    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Science Networks. Historical Studies (SNHS, volume 36)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Introduction

    Pages 1-10

  3. Re-coding as the First Pattern of Change in Mathematics

    Pages 11-105

  4. Relativizations as the Second Pattern of Change in Mathematics

    Pages 107-223

  5. Re-Formulations as a Third Pattern of Change in Mathematics

    Pages 225-238

  6. Mathematics and Change

    Pages 239-251

  7. Back Matter

    Pages 253-261
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Keywords

About this book

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 ?rst signi?cant 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 ?rst 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 ?eld th th by the end of the 19 and the beginning of the 20 century. By contrast the ?rst signi?cant 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.

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)

Authors and Affiliations

  • Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia

    Ladislav Kvasz

  • Faculty of Education, Charles University, Praha, Czech Republic

    Ladislav Kvasz

Bibliographic Information

  • Book Title: Patterns of Change

  • Book Subtitle: Linguistic Innovations in the Development of Classical Mathematics

  • Authors: Ladislav Kvasz

  • Series Title: Science Networks. Historical Studies

  • DOI: https://doi.org/10.1007/978-3-7643-8840-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkh�user Basel 2008

  • Hardcover ISBN: 978-3-7643-8839-3Published: 17 July 2008

  • eBook ISBN: 978-3-7643-8840-9Published: 28 October 2008

  • Series ISSN: 1421-6329

  • Series E-ISSN: 2296-6080

  • Edition Number: 1

  • Number of Pages: XVIII, 262

  • Topics: History of Mathematical Sciences

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