Graduate studies at Western
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|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Similar books and articles
Jamie Tappenden (1995). Geometry and Generality in Frege's Philosophy of Arithmetic. Synthese 102 (3):319 - 361.
Ian J. Dove (2009). Towards a Theory of Mathematical Argument. Foundations of Science 14 (1-2):136-152.
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.
Dennis Lomas (2002). What Perception is Doing, and What It is Not Doing, in Mathematical Reasoning. British Journal for the Philosophy of Science 53 (2):205-223.
Andrew Aberdein (2013). Mathematical Wit and Mathematical Cognition. Topics in Cognitive Science 5 (2):231-250.
Valeria Giardino (2010). Intuition and Visualization in Mathematical Problem Solving. Topoi 29 (1):29-39.
Danielle Macbeth (2007). Striving for Truth in the Practice of Mathematics: Kant and Frege. Grazer Philosophische Studien 75 (1):65-92.
Volker Peckhaus (1999). 19th Century Logic Between Philosophy and Mathematics. Bulletin of Symbolic Logic 5 (4):433-450.
Lyn D. English (ed.) (1997). Mathematical Reasoning: Analogies, Metaphors, and Images. L. Erlbaum Associates.
Alonzo Church (1942). Elementary Topics in Mathematical Logic. Brooklyn, N.Y. [Brooklyn.
Zenon Kulpa (2009). Main Problems of Diagrammatic Reasoning. Part I: The Generalization Problem. [REVIEW] Foundations of Science 14 (1-2):75-96.
Added to index2011-05-26
Total downloads29 ( #48,285 of 751,826 )
Recent downloads (6 months)2 ( #38,076 of 751,826 )
How can I increase my downloads?