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)|
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
Bernd Buldt, Benedikt Löwe & Thomas Müller (2008). Towards a New Epistemology of Mathematics. Erkenntnis 68 (3):309 - 329.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Simon B. Duffy (2009). The Role of Mathematics in Deleuze's Critical Engagement with Hegel. International Journal of Philosophical Studies 17 (4):563 – 582.
Sal Restivo & Wenda K. Bauchspies (2006). The Will to Mathematics: Minds, Morals, and Numbers. [REVIEW] Foundations of Science 11 (1-2):197-215.
L. P. Steffe (2010). Consequences of Rejecting Constructivism: “Hold Tight and Pedal Fast”. Commentary on Slezak's “Radical Constructivism: Epistemology, Education and Dynamite”. Constructivist Foundations 6 (1):112-119.
Robert D. Heslep (2012). Education for Computers. Studies in Philosophy and Education 31 (4):357-364.
Steve Gerrard (1991). Wittgenstein's Philosophies of Mathematics. Synthese 87 (1):125-142.
Jean Paul Van Bendegem (2000). Alternative Mathematics: The Vague Way. Synthese 125 (1/2):19 - 31.
C. K. Raju (2001). Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā. Philosophy East and West 51 (3):325 - 362.
Added to index2009-01-28
Total downloads12 ( #183,461 of 1,696,616 )
Recent downloads (6 months)0
How can I increase my downloads?