Open Access. Powered by Scholars. Published by Universities.®

Philosophy Commons

Open Access. Powered by Scholars. Published by Universities.®

Articles 1 - 2 of 2

Full-Text Articles in Philosophy

Wandering About: Analogy, Ambiguity And Humanistic Mathematics, William M. Priestley Jan 2013

Wandering About: Analogy, Ambiguity And Humanistic Mathematics, William M. Priestley

Journal of Humanistic Mathematics

This article concerns the relationship between mathematics and language, emphasizing the role of analogy both as an expression of a mathematical property and as a source of productive ambiguity in mathematics. An historical discussion is given of the interplay between the notions of logos, litotes, and limit that has implications for our understanding and teaching of Dedekind cuts and, more generally, for a humanistic notion of the role of mathematics within liberal education.


Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz Jan 2013

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

Journal of Humanistic Mathematics

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the ...