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)|
References found in this work BETA
A Theory of Magnitude: Common Cortical Metrics of Time, Space and Quantity.V. Walsh - 2003 - Trends in Cognitive Sciences 7 (11):483-488.
Exact and Approximate Arithmetic in an Amazonian Indigene Group.Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene - 2004 - Science 306 (5695):499-503.
The Mental Representation of Parity and Number Magnitude.Stanislas Dehaene, Serge Bossini & Pascal Giraux - 1993 - Journal of Experimental Psychology: General 122 (3):371.
Numerical Abstraction by Human Infants.Prentice Starkey, Elizabeth S. Spelke & Rochel Gelman - 1990 - Cognition 36 (2):97-127.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
Citations of this work BETA
No citations found.
Similar books and articles
Category Theory: The Language of Mathematics.Elaine Landry - 1999 - Philosophy of Science 66 (3):27.
What is the Problem of Mathematical Knowledge?Michael Potter - 2007 - In Michael Potter, Mary Leng & Alexander Paseau (eds.), Mathematical Knowledge.
An Enhanced Argument for Innate Elementary Geometric Knowledge and its Philosophical Implications.Helen De Cruz - 2007 - In Bart Van Kerkhove (ed.), New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific.
Kitcher, Mathematical Intuition, and Experience.Mark McEvoy - 2007 - Philosophia Mathematica 15 (2):227-237.
The Innateness Hypothesis and Mathematical Concepts.Helen De Cruz & Johan De Smedt - 2010 - Topoi 29 (1):3-13.
Completions, Constructions, and Corollaries.Thomas Mormann - 2009 - In H. Pulte, G. Hanna & H.-J. Jahnke (eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Springer.
Intuition and Visualization in Mathematical Problem Solving.Valeria Giardino - 2010 - Topoi 29 (1):29-39.
Added to index2010-01-23
Total downloads147 ( #32,033 of 2,168,630 )
Recent downloads (6 months)3 ( #127,283 of 2,168,630 )
How can I increase my downloads?