Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy East and West 51 (3):325 - 362 (2001)
Current formal mathematics, being divorced from the empirical, is entirely a social construct, so that mathematical theorems are no more secure than the cultural belief in two-valued logic, incorrectly regarded as universal. Computer technology, by enhancing the ability to calculate, has put pressure on this social construct, since proof-oriented formal mathematics is awkward for computation, while computational mathematics is regarded as epistemo-logically insecure. Historically, a similar epistemological fissure between computational/practical Indian mathematics and formal/spiritual Western mathematics persisted for centuries, during a dialogue of civilizations, when texts on "algorismus" and "infinitesimal" calculus were imported into Europe, enhancing the ability to calculate. It is argued here that this epistemological tension should be resolved by accepting mathematics as empirically based and fallible, and by revising accordingly the mathematics syllabus outlined by Plato.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
C. K. Raju (2001). Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in The. Philosophy East and West 51 (3):325-362.
Jean Paul Van Bendegem (2000). Alternative Mathematics: The Vague Way. Synthese 125 (1/2):19 - 31.
Charalampos Toumasis (1993). Ideas and Processes in Mathematics: A Course on History and Philosophy of Mathematics. Studies in Philosophy and Education 12 (2-4):245-256.
Jean Paul Van Bendegem (2000). Alternative Mathematics: The Vague Way. Synthese 125 (1-2):19-31.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
Sal Restivo & Wenda K. Bauchspies (2006). The Will to Mathematics: Minds, Morals, and Numbers. [REVIEW] Foundations of Science 11 (1-2):197-215.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan.
Charalampos Toumasis (1997). The NCTM Standards and the Philosophy of Mathematics. Studies in Philosophy and Education 16 (3):317-330.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
René Cori (2000). Mathematical Logic: A Course with Exercises. Oxford University Press.
Robert A. Holland (1992). Apriority and Applied Mathematics. Synthese 92 (3):349 - 370.
Added to index2011-05-29
Total downloads5 ( #178,823 of 1,089,153 )
Recent downloads (6 months)1 ( #69,735 of 1,089,153 )
How can I increase my downloads?