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11 - Anachronism and incommensurability:words, concepts, contexts, and intentions

Published online by Cambridge University Press:  19 July 2021

Niccolò Guicciardini
Affiliation:
Università degli Studi di Milano
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Summary

Historians are constantly confronted with the twin problems of translating texts and interpreting their meanings. When mathematicians like Georg Cantor or Abraham Robinson demonstrate the consistency of concepts that, since the paradoxes of Zeno and Democritus, have been assumed to be paradoxical notions like infinitesimals or the actual infinite, how should the works of earlier mathematicians be regarded, who either used such concepts or believed they had proven their impossibility? Is it anachronistic to use nonstandard analysis or transfinite numbers to “rehabilitate” or explain the works of Leibniz, Euler, Cauchy, or Peirce, for example, as recent mathematicians, historians, and philosophers of mathematics have attempted? At the other extreme, chronologically, how may ideas readily accepted in the West – like incommensurable numbers, parallel lines, and similar triangles – but foreign to traditional Chinese mathematics have adversely affected the interpretations of ancient Chinese mathematical works?

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Anachronisms in the History of Mathematics
Essays on the Historical Interpretation of Mathematical Texts
, pp. 307 - 357
Publisher: Cambridge University Press
Print publication year: 2021

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