Journal Article

The History of Algebra and the Development of the Form of its Language†

Ladislav Kvasz

in Philosophia Mathematica

Volume 14, issue 3, pages 287-317
Published in print October 2006 | ISSN: 0031-8019
Published online January 2006 | e-ISSN: 1744-6406 | DOI: http://dx.doi.org/10.1093/philmat/nkj017
The History of Algebra and the Development of the Form of its Language†

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This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwārizmī, Cardano, and Descartes to Euler, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language and analyzes the changes of this language in the course of history. It turns out that the most fundamental epistemological changes in the development of algebra can be interpreted as changes of the pictorial form (in the sense of Wittgenstein's Tractatus) of the symbolic language of algebra. Thus the paper develops further the method of reconstruction which the author introduced for the analysis of the development of geometry.

Journal Article.  14050 words. 

Subjects: Philosophy of Mathematics and Logic ; Mathematics

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