Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice

Philosophia Mathematica 20 (1):58-85 (2012)
Abstract
Throughout its long history, mathematics has involved the use ofsystems of written signs, most notably, diagrams in Euclidean geometry and formulae in the symbolic language of arithmetic and algebra in the mathematics of Descartes, Euler, and others. Such systems of signs, I argue, enable one to embody chains of mathematical reasoning. I then show that, properly understood, Frege’s Begriffsschrift or concept-script similarly enables one to write mathematical reasoning. Much as a demonstration in Euclid or in early modern algebra does, a proof in Frege’s concept-script shows how it goes
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Andrew Aberdein (2010). Observations on Sick Mathematics. In Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.), Philosophical Perspectives on Mathematical Practice. College Publications. 269--300.
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