IRIS Institutional Research Information System - AIR Archivio Istituzionale della Ricerca

IRIS è il sistema di gestione integrata dei dati della ricerca (persone, progetti, pubblicazioni, attività) adottato dall'Università degli Studi di Milano.

AIR nasce in UNIMI nel 2006 con lo scopo di raccogliere, documentare e conservare le informazioni sulla produzione scientifica dell'Università degli Studi di Milano e costituisce di fatto l'Anagrafe della ricerca dell'Ateneo.

This PhD thesis analyzes a change in the definition of mathematics in the 19th century: from science of quantities to science of forms. A comparison of the concepts of quantity, magnitude, number, form, and structure, which have not always been sufficiently distinguished in the literature on the 19th century, shows interesting connections between philosophy, geometry and algebra. The first part is devoted to a historical and philosophical analysis of the notion of magnitude, especially to its geometrical origin in Greek mathematics, to its algebraic development in the 14th century – which changes the notion of magnitude (quantity) into the notion of a general magnitude (quantity) –, and to the comparison with Descartes's and Leibniz's remarks on operations and relations. The analysis of some works of Wolff, d'Alembert, Euler and Gauss – texts that appear for the first time in an Italian translation in the Appendix – shows that magnitudes, when mathematics is defined as Grössenlehre, are extensive quantities defined by an equality relation and by an additive operation that characterizes the relation of the parts to the whole. The second part of the research (chapters 4-6) is entirely devoted to an analysis of the epistemology of Hermann Grassmann, and in particular to the notion of an extensive magnitude that he develops in the Ausdehnungslehre (some passages of the 1844 and 1862 editions are also translated into Italian in the Appendix). The aim of the work is to show the intimate connection between the mathematical research and the philosophical conception of Grassmann, which is considered as an original contribution to the foundation of a theory of extensive magnitudes independently from numbers and from a theory of measurement.

La matematica da scienza delle grandezze a teoria delle forme : l'Ausdehnungslehre di H. Grassmann ; S. Bozzi, D. Palladino. - Milano : Università degli studi di Milano. DIPARTIMENTO DI FILOSOFIA, 2003 Feb 13. ((14. ciclo, Anno Accademico 2001/2002.

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