Steve Russ. The mathematical works of Bernard Bolzano. Oxford: Oxford university press, 2004. Pp. XXX + 698. Isbn 0-19-853930- [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 14 (3):352-362 (2006)
In his book on The Mathematics of Great Amateurs Coolidge starts the chapter on Bolzano saying that he included Bolzano because it seemed interesting to him ‘that a man who was a remarkable pulpit orator, only removed from his chair for his political opinions, should have thought so far into the deepest problems of a science which he never taught in a professional capacity’ [Coolidge, 1990, p. 195]. In fact, considering Bolzano's poor health and his enormous productivity in his ‘professional areas’, the results, the breadth and the extent of this ‘great amateur's’ thoughts on mathematics, and its proper scientific presentation are simply astonishing. Even this new selection of more than 650 printed pages of text, well edited and translated by Steve Russ, represents only a part of Bolzano's legacy on mathematical topics: the complete German edition of Bolzano's writings, the Bernard Bolzano-Gesamtausgabe edited by J. Berg, E. Morscher, B. van Rootselaar, and others is projected to include over 120 volumes of which more than 36 volumes will contain his mathematical works. About 25 volumes have been published so far in this mathematical subseries including Bolzano's extensive Miscellanea Mathematica .To most readers of this journal, Bolzano will be well-known for his contributions to logic—his ‘logic of variation’ is viewed as a precursor of the modern semantic conception of logical consequence—and his contributions to the foundations of calculus, especially his ‘purely analytic proof’ of the intermediate-value theorem and the Bolzano-Weierstrass theorem, or his early discovery of a counterintuitive function which is continuous in its domain, but nowhere-differentiable.Despite his lifelong interest in the foundations of mathematics, Bolzano studied theology and taught philosophy of religion in his native city, Prague, from 1805 until his dismissal in 1820. Part of Bolzano's duties …
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