Aristotle's prohibition rule on kind-crossing and the definition of mathematics as a science of quantities
Graduate studies at Western
Synthese 174 (2):225 - 235 (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.|
|Keywords||Prohibition-rule on kind-crossing Mathesis universalis Aristotle Mathematics Quantity Magnitude|
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