Download e-book for kindle: Architecture of Modern Mathematics: Essays in History and by J. Ferreirós, J. J. Gray

By J. Ferreirós, J. J. Gray

ISBN-10: 0198567936

ISBN-13: 9780198567936

This edited quantity, aimed toward either scholars and researchers in philosophy, arithmetic and heritage of technological know-how, highlights best advancements within the overlapping parts of philosophy and the background of contemporary arithmetic. it's a coherent, extensive ranging account of ways a few subject matters within the philosophy of arithmetic has to be reconsidered within the gentle of the newest ancient examine, and the way a couple of old bills will be deepened through embracing philosophical questions.

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Additional resources for Architecture of Modern Mathematics: Essays in History and Philosophy

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The effort of thinking through what von Staudt was doing in that book seems to have been a major source for Klein to place the emphasis he did on the role of transformations of figures in geometry in his Erlangen Program of 1872, not because the Geometrie der Lage does so clearly and forcefully, but because the book is quite obscure. Von Staudt took the primitive figures of geometry to be points, lines, and planes, which are somehow moved around in a way that sends points to points, lines to lines and planes to planes.

The central difficulty, if such it be, presented by the proofs of many theorems in pure mathematics is that, according to most philosophies of mathematics, such proofs are timelessly valid and intellectually accessible across cultures to anyone with sufficient ability and time, and their conclusions are therefore timelessly true. Accordingly, a theorem and its proof are 27 Feferman [1998]. 28 Introduction paradigmatic ahistorical objects, and the defining activity of the mathematician admits historical enquiry only in ways devoid of philosophical substance.

The purely logical aspect of mathematical work is not, for a mathematician, the whole story, and so it cannot suffice for the historian of mathematics. Mathematics is concerned with concepts, and these concepts can be unclear and subject to refinement. A sound logical elucidation of a mathematical concept may well not help one to analyse how that concept came about and how it changed, and therefore not help the philosopher interested in how mathematics develops. Even if this or that piece of mathematics can be distilled into set theory, it is likely that its imperfectly formed antecedents cannot be, and not only 28 See for instance, Feferman’s In the Light of Logic, p.

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Architecture of Modern Mathematics: Essays in History and Philosophy by J. Ferreirós, J. J. Gray

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