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

Synthese 174 (2):225-235 (2010)
Download Edit this record How to cite View on PhilPapers
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.
PhilPapers/Archive ID
CANAPR-2
Upload history
First archival date: 2012-11-03
Latest version: 2 (2012-11-03)
View other versions
Added to PP index
2009-01-28

Total views
747 ( #6,999 of 2,445,701 )

Recent downloads (6 months)
16 ( #38,529 of 2,445,701 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.