David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
ASCS09: Proceedings of the 9th Conference of the Australasian Society for Cognitive Science (pp. 254-260). Sydney: Macquarie Centre for Cognitive Science (2010)
We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept
|Keywords||philosophy of mathematics geometrical figures and drawings Aristotle and Plato on 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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Pierre Cassou-Nogués (2006). Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics. Theoria 21 (1):89-104.
Stewart Shapiro (1983). Mathematics and Reality. Philosophy of Science 50 (4):523-548.
Stewart Shapiro (2000). Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press.
C. McLarty (2012). Introduction: Hypotheses and Progress. Philosophia Mathematica 20 (2):135-142.
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
Anne Newstead & Franklin James, The Epistemology of Geometry I: The Problem of Exactness. ASCS 2009 Proceedings of the 9th Australasian Society for Cognitive Science Conference.
Anne Newstead & Franklin James, The Epistemology of Geometry I: The Problem of Exactness. Proceedings of the Australasian Society for Cognitive Science 2009.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan
Added to index2010-05-07
Total downloads66 ( #51,671 of 1,725,999 )
Recent downloads (6 months)3 ( #231,316 of 1,725,999 )
How can I increase my downloads?