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

Philosophia Mathematica 20 (1):58-85 (2012)
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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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Danielle Macbeth
Haverford College

Citations of this work

Manipulative imagination: how to move things around in mathematics.Valeria Giardino - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):345-360.

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References found in this work

Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Tractatus Logico-Philosophicus.Ludwig Wittgenstein - 1956 - Revista Portuguesa de Filosofia 12 (1):109-110.
The iconic logic of Peirce's graphs.Sun-Joo Shin - 2002 - Cambridge, Mass.: MIT Press.
The Iconic Logic of Peirce's Graphs.Sun-joo Shin - 2003 - Transactions of the Charles S. Peirce Society 39 (1):127-133.

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