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Full-Text Articles in Philosophy of Science
Mathematicians Versus Philosophers In Recent Work On Mathematical Beauty, Viktor Blåsjö
Mathematicians Versus Philosophers In Recent Work On Mathematical Beauty, Viktor Blåsjö
Journal of Humanistic Mathematics
Recent attempts at defining mathematical beauty fall roughly into two schools of thought. One takes its starting point in the subjective experience of the mathematician and characterises mathematical beauty in cognitive terms. The other seeks to reduce beauty to objective notions such as truth, symmetry, or simplicity. This second approach is popular among analytic philosophers, who are committed to seeing mathematics and science as prototypically rational enterprises. I criticise this stance on the grounds that this commitment makes its supporters approach beauty in mathematics not with a genuine desire to sympathetically understand it, but with the preconceived goal of explaining …
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
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 …