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.

Aristotle’s prohibition rule on kind-crossing and the definition of mathematics as a science of quantities / P. Cantù. - In: SYNTHESE. - ISSN 0039-7857. - (2008 Nov 04). ((Intervento presentato al convegno The Classical Model of Science : The Axiomatic Method, the Order of Concepts and the Hierarchy of Sciences : International conference tenutosi a Amsterdam nel 2007 [10.1007/s11229-008-9419-2].

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

P. Cantù
Primo
2008

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.
Prohibition-rule on kind-crossing ; Aristotle ; Mathematics ; Quantity ; Magnitude ; Mathesis universalis
Vrije Universiteit Amsterdam
http://www.springerlink.com/content/32318507373161l6
Article (author)
File in questo prodotto:
File Dimensione Formato  
Cantùrev.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 139.92 kB
Formato Adobe PDF
139.92 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/55705
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 9
social impact