Paul Rusnock. Bolzano's philosophy and the emergence of modern mathematics. Studien zur österreichischen philosophie [studies in austrian philosophy], vol. 30. amsterdam & atlanta: Editions rodopi, 2000. Isbn 90-420-1501-2. Pp. 218 [Book Review]

Philosophia Mathematica 14 (3):362-364 (2006)
Bernard Bolzano , one of the leading figures of the Bohemian Enlightenment, made important contributions both to mathematics and philosophy which were virtually unknown in his lifetime and are still largely unacknowledged today. As a mathematician, he was a pioneer in the clarification and rigorization of mathematical analysis; as a philosopher, he may be considered a forerunner of the analytic movement later to emerge with Frege and Russell.Rusnock's account of Bolzano's work is laid out in five chapters and two appendices. The introductory first chapter consists of an overview of Bolzano's philosophy and his account of scientific theories. For Bolzano, the importance of such theories—as in mathematics—is their formal structure. Unlike his philosophical predecessors, Bolzano held that the goal of scientific presentation is not to maximize certainty, but rather to set out the objective order of truth.Chapter 2 is an analysis of Bolzano's early work, Contributions to a Better Founded Presentation of Mathematics, in which a number of his characteristic doctrines concerning mathematics are adumbrated. In sharp contradistinction to Kant, Bolzano thought that the methodology of mathematics is logic, and that mathematics should be founded independently of epistemology. In the Contributions Bolzano formulates a ‘thoroughgoing refutation of Kant's account of mathematical knowledge’, repudiating in particular …
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DOI 10.1093/philmat/nkl014
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