By J. Ferreirós, J. J. Gray
This edited quantity, geared toward either scholars and researchers in philosophy, arithmetic and historical past of technology, highlights best advancements within the overlapping components of philosophy and the background of contemporary arithmetic. it's a coherent, extensive ranging account of the way a couple of subject matters within the philosophy of arithmetic needs to be reconsidered within the gentle of the most recent ancient learn, and the way a few ancient debts should be deepened via embracing philosophical questions.
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Extra info for Architecture of Modern Mathematics: Essays in History and Philosophy
The German case was the ﬁrst to be studied in any detail. In Berlin, a university created at the start of the nineteenth century in the spirit of neo-humanism and where mathematics was run, from roughly 1850 to 1890 by Kummer, Kronecker, and Weierstrass, the ethos was that of analysis, number theory, and algebra. These were subjects with strong intellectual connections to Gauss, they ﬁtted the neo-humanist ethos because they set no great store by applications, and they established deep roots in the German mathematical psyche as a result.
Accordingly, a theorem and its proof are 27 Feferman . 28 Introduction paradigmatic ahistorical objects, and the deﬁning activity of the mathematician admits historical enquiry only in ways devoid of philosophical substance. To this challenge, the historian can reply ﬁrst that it is well to insist on the distinction between what it is for something to be proved, and for something to be true. It has been clear since the acceptance of non-Euclidean geometry that mathematics is capable of building up distinct theories, each of them consistent on their own but which are mutually inconsistent.
It takes one place, admittedly over a long period of time, and studies it in considerable detail, drawing lessons about how teaching and training shaped the practice of generations of graduates. The place is Cambridge, between the end of the eighteenth century and the First World War, and Warwick argues that such detailed studies are the best way to trace the evolution of mathematical practice, the articulation of paradigms (here he has new points to make about the Kuhnian idea of normal science) and the way mathematical physicists read and respond to others – those in the school and those outside.