Aristotle's prohibition rule on kind-crossing and the definition of mathematics as a science of quantities

Paola Cantù

pp. 225-235

in: Arianna Betti, Willem de Jong (eds), The classical model of science I, Synthese 174 (2), 2010.

Abstract

The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements, to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior analytics is used to distinguish between conceptions that share the same name but are substantively different: for example the search for a broader genus including all mathematical objects; the search for a common character of different species of mathematical objects; and the effort to treat magnitudes as numbers.

Cited authors

Descartes René

Aristoteles

Proclus