David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Topoi 29 (1):15-27 (2010)
The foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the foundational analysis with an often disregarded aspect (the cognitive and historical constitution of mathematical structures) and because of the provable incompleteness of proof principles also in the analysis of deduction. For the purposes of our investigation, we will hint here to a philosophical frame as well as to some recent experimental studies on numerical cognition that support our claim on the cognitive origin and the constitutive role of mathematical intuition.
|Keywords||Numerical cognition Mathematical intuition Foundations of mathematics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
William P. Banks & David K. Hill (1974). The Apparent Magnitude of Number Scaled by Random Production. Journal of Experimental Psychology 102 (2):353.
Véronique Izard & Stanislas Dehaene (2008). Calibrating the Mental Number Line. Cognition 106 (3):1221-1247.
Jeff Paris & Leo Harrington (1977). A Mathematical Incompleteness in Peano Arithmetic. In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. 90--1133.
Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene (2004). Exact and Approximate Arithmetic in an Amazonian Indigene Group. Science 306 (5695):499-503.
Prentice Starkey, Elizabeth S. Spelke & Rochel Gelman (1990). Numerical Abstraction by Human Infants. Cognition 36 (2):97-127.
Citations of this work BETA
No citations found.
Similar books and articles
Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.
Andrei Rodin (2010). How Mathematical Concepts Get Their Bodies. Topoi 29 (1):53-60.
Thomas Mormann (2009). Completions, Constructions, and Corollaries. In H. Pulte, G. Hanna & H.-J. Jahnke (eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Springer.
Helen De Cruz & Johan De Smedt (2010). The Innateness Hypothesis and Mathematical Concepts. Topoi 29 (1):3-13.
Mark McEvoy (2007). Kitcher, Mathematical Intuition, and Experience. Philosophia Mathematica 15 (2):227-237.
Helen De Cruz (2007). An Enhanced Argument for Innate Elementary Geometric Knowledge and its Philosophical Implications. In Bart Van Kerkhove (ed.), New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific.
Elaine Landry (2011). How to Be a Structuralist All the Way Down. Synthese 179 (3):435 - 454.
David S. Henley (1995). Syntax-Directed Discovery in Mathematics. Erkenntnis 43 (2):241 - 259.
Michael Potter (2007). What is the Problem of Mathematical Knowledge? In Michael Potter, Mary Leng & Alexander Paseau (eds.), Mathematical Knowledge.
Added to index2010-01-23
Total downloads86 ( #17,044 of 1,140,287 )
Recent downloads (6 months)3 ( #60,710 of 1,140,287 )
How can I increase my downloads?