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18 - Philosophy, science and medicine

from PART IV - PHYSICS AND METAPHYSICS

Published online by Cambridge University Press:  28 March 2008

By
Giuseppe Cambiano
Edited by
Keimpe Algra ,
Jonathan Barnes ,
Jaap Mansfeld  and
Malcolm Schofield
Giuseppe Cambiano
Affiliation:
University of Turin
Keimpe Algra
Affiliation:
Universiteit Utrecht, The Netherlands
Jonathan Barnes
Affiliation:
Université de Genève
Jaap Mansfeld
Affiliation:
Universiteit Utrecht, The Netherlands
Malcolm Schofield
Affiliation:
University of Cambridge
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Summary

Philosophy and mathematics

The relationship between philosophy and mathematics appears to be less close in the Hellenistic age than in previous centuries. The mathematicians proceeded with their work without any explicit adhesion to philosophical doctrines or any reply to the theoretical and epistemological problems raised by the Epicureans and the sceptics when dealing with mathematics. In the fifth century AD the Neo-platonist Proclus saw Euclid as a Platonist, because his Elements concluded with the construction of regular polyhedrons, the basis of the cosmic structure outlined by Plato in the Timaeus (Eucl. 68.20–3; 70.22–71.5). But there is no proof that Euclid meant to direct the whole of his writing towards the creation of a cosmology.

Another level on which Proclus tried to show Euclidean geometry's dependence on philosophy was the formal structure of the Elements. This was based on the distinction between a small number of principles, assumed at the outset without demonstration and listed in the first book as definitions, common notions and postulates, and a body of propositions reached deductively starting from the principles. Proclus highlighted a correspondence between this structure and the theory of science formulated by Aristotle, particularly in the Posterior Analytics, and also between Euclid's principles and those mentioned by Aristotle (Eucl. 76.6–77.2). It is in fact possible to make out some parallelism: for example, Aristotle includes among the principles used by mathematicians Euclid's third common notion, which is that if equals are subtracted from equals, the remainders will be equal (APo. 76a41).

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The Cambridge History of Hellenistic Philosophy , pp. 585 - 614
Publisher: Cambridge University Press
Print publication year: 1999

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