Eudoxos and Dedekind: On the ancient Greek theory of ratios and its relation to modern mathematics

  title={Eudoxos and Dedekind: On the ancient Greek theory of ratios and its relation to modern mathematics},
  author={Howard Stein},
  • H. Stein
  • Published 1 August 1990
  • Mathematics
  • Synthese
According to Aristotle, the objects studied by mathematics have no independent existence, but are separated in thought from the substrate in which they exist, and treated as separable i.e., are "abstracted" by the mathematician. I In particular, numerical attributives or predicates (which answer the question 'how many?') have for "substrate" multitudes with a designated unit. 'How many pairs of socks?' has a different answer from 'how many socks?'. (Cf. Metaph. XIV i 1088a5ff.: "One la… 
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