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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.
About the author
Ladislav Kvasz studied mathematics and philosophy at Comenius University. He spent longer sojourns at the University of Vienna, King's College London, University of California at Berkeley and Technical University in Berlin. His book Patterns of Change (2008) was awarded the International Fernando Gil Prize for the Philosophy of Science. He is interested in the changes of the formal language of science and the consequences which linguistic innovations (such as invention of variables, or introduction of functions) had on scientific method and thought.
Summary
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.
Additional text
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)
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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)
