David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Topoi 29 (1):53-60 (2010)
When the traditional distinction between a mathematical concept and a mathematical intuition is tested against examples taken from the real history of mathematics one can observe the following interesting phenomena. First, there are multiple examples where concepts and intuitions do not well fit together; some of these examples can be described as “poorly conceptualised intuitions” while some others can be described as “poorly intuited concepts”. Second, the historical development of mathematics involves two kinds of corresponding processes: poorly conceptualised intuitions are further conceptualised while poorly intuited concepts are further intuited. In this paper I study this latter process in mathematics during the twentieth century and, more specifically, show the role of set theory and category theory in this process. I use this material for defending the following claims: (1) mathematical intuitions are subject to historical development just like mathematical concepts; (2) mathematical intuitions continue to play their traditional role in today's mathematics and will plausibly do so in the foreseeable future. This second claim implies that the popular view, according to which modern mathematical concepts, unlike their more traditional predecessors, cannot be directly intuited, is not justified.
|Keywords||Mathematical intuition Embodiment of concepts Set theory Category theory|
|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
Gottlob Frege & Eike-Henner W. Kluge (1973). On the Foundations of Geometry and Formal Theories of Arithmetic. Philosophical Review 82 (2):266-269.
René Descartes & Franz Hals (1927). La Géométrie. Revue de Métaphysique et de Morale 34 (4):3-4.
Citations of this work BETA
No citations found.
Similar books and articles
E. Brian Davies (2005). A Defence of Mathematical Pluralism. Philosophia Mathematica 13 (3):252-276.
Giuseppe Longo & Arnaud Viarouge (2010). Mathematical Intuition and the Cognitive Roots of Mathematical Concepts. Topoi 29 (1):15-27.
David Corfield (2003). Towards a Philosophy of Real Mathematics. Cambridge University Press.
Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. [REVIEW] Foundations of Science 15 (1):29-48.
Irina Starikova (2007). Picture-Proofs and Platonism. Croatian Journal of Philosophy 7 (1):81-92.
Elaine Landry (2011). How to Be a Structuralist All the Way Down. Synthese 179 (3):435 - 454.
Helen De Cruz & Johan De Smedt (2010). The Innateness Hypothesis and Mathematical Concepts. Topoi 29 (1):3-13.
Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.
Added to index2009-07-31
Total downloads39 ( #91,909 of 1,780,191 )
Recent downloads (6 months)4 ( #140,973 of 1,780,191 )
How can I increase my downloads?