David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Friends of Wisdom Newsletter (6):1-6 (2010)
For over thirty years I have argued that all branches of science and scholarship would have both their intellectual and humanitarian value enhanced if pursued in accordance with the edicts of wisdom-inquiry rather than knowledge-inquiry. I argue that this is true of mathematics. Viewed from the perspective of knowledge-inquiry, mathematics confronts us with two fundamental problems. (1) How can mathematics be held to be a branch of knowledge, in view of the difficulties that view engenders? What could mathematics be knowledge about? (2) How do we distinguish significant from insignificant mathematics? This is a fundamental philosophical problem concerning the nature of mathematics. But it is also a practical problem concerning mathematics itself. In the absence of the solution to the problem, there is the danger that genuinely significant mathematics will be lost among the unchecked growth of a mass of insignificant mathematics. This second problem cannot, it would seem, be solved granted knowledge-inquiry. For, in order to solve the problem, mathematics needs to be related to values, but this is, it seems, prohibited by knowledge-inquiry because it could only lead to the subversion of mathematical rigour. Both problems are solved, however, when mathematics is viewed from the perspective of wisdom-inquiry. (1) Mathematics is not a branch of knowledge. It is a body of systematized, unified and inter-connected problem-solving methods, a body of problematic possibilities. (2) A piece of mathematics is significant if (a) it links up to the interconnected body of existing mathematics, ideally in such a way that some problems difficult to solve in other branches become much easier to solve when translated into the piece of mathematics in question; (b) it has fruitful applications for (other) worthwhile human endeavours. If ever the revolution from knowledge to wisdom occurs, I would hope wisdom mathematics would flourish, the nature of mathematics would become much more transparent, more pupils and students would come to appreciate the fascination of mathematics, and it would be easier to discern what is genuinely significant in mathematics (something that baffled even Einstein). As a result of clarifying what should count as significant, the pursuit of wisdom mathematics might even lead to the development of significant new mathematics.
|Keywords||Philosophy of Mathematics Platonism Logicism Mathematical Significance Mathematics and Values|
|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
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 (1993). Ideas and Processes in Mathematics: A Course on History and Philosophy of Mathematics. Studies in Philosophy and Education 12 (2-4):245-256.
Michael D. Resnik (1997). Mathematics as a Science of Patterns. New York ;Oxford University Press.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
Corfield David (1998). Beyond the Methodology of Mathematics Research Programmes. Philosophia Mathematica 6 (3):272-301.
Charalampos Toumasis (1997). The NCTM Standards and the Philosophy of Mathematics. Studies in Philosophy and Education 16 (3):317-330.
Michael Heller (1997). Essential Tension: Mathematics - Physics - Philosophy. [REVIEW] Foundations of Science 2 (1):39-52.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Penelope J. Maddy (2001). Some Naturalistic Reflections on Set Theoretic Method. Topoi 20 (1):17-27.
Added to index2011-05-24
Total downloads77 ( #22,830 of 1,692,210 )
Recent downloads (6 months)12 ( #18,548 of 1,692,210 )
How can I increase my downloads?