Patterns of Change: Linguistic Innovations in the Development of Classical MathematicsSpringer Science & Business Media, 28 d’oct. 2008 - 262 pàgines 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. |
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analysis analytic geometry axioms Beltrami casus irreducibilis circle complex numbers concept constitutive construction curve Desargues Descartes development of geometry development of mathematics differential and integral discovery elementary arithmetic epistemic subject epistemological Euclid Euclidean geometry Euler explicit field form of language formula fractal framework Frege function fundamental geom guage history of mathematics iconic language implicit infinite instance integral calculus integrative form intersection introduced iterative geometry Kant’s Klein Kvasz Lakatos language of algebra language of geometry language of mathematics language of synthetic line segments Lobachevski logical mathematicians means methods negative numbers Nevertheless non-Euclidean geometry notion painting particular perspectivist form philosophy of mathematics picture Poincar´e point of view polynomial possible predicate calculus problem projective form projective geometry projective plane proofs quintic equations re-codings re-formulations reconstruction reified relativizations represented revolutions roots set theory solution solve space straight line structure symbolic language synthetic geometry theorem tion topology transformation variable