Aristotelianism in the philosophy of mathematics
Studia Neoaristotelica 8 (1):3-15 (2011)
| Abstract | Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, is a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree, a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity. | |||||||||
| Keywords | Philosophy of mathematics Aristotelianism quantity structure | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,701 |
| External links |
  Try with proxy. |
| Through your library | Configure |
Similar books and articlesJames Franklin (2009). Aristotelian Realism. In A. Irvine (ed.), The Philosophy of Mathematics (Handbook of the Philosophy of Science series). North-Holland Elsevier.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan.
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
José Ferreirós Domínguez & Jeremy Gray (eds.) (2006). The Architecture of Modern Mathematics: Essays in History and Philosophy. Oxford University Press.
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.
Paola Cantù, Bolzano Versus Kant: Mathematics as a Scientia Universalis. Philosophical Papers Dedicated to Kevin Mulligan.
Roman Duda (2000). Integralność matematyki. Filozofia Nauki 1.
Peter Milne (1994). The Physicalization of Mathematics: Review of J. Bigelow, The Reality of Numbers: A Physicalist's Philosophy of Mathematics; P. Maddy, Realism in Mathematics; Y. Solomon, The Practice of Mathematics; J. P. Van Bendegem, Finite Empirical Mathematics: Outline of a System. [REVIEW] British Journal for the Philosophy of Science 45 (1):305-340.
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
Michael Heller (1997). Essential Tension: Mathematics - Physics - Philosophy. Foundations of Science 2 (1):39-52.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
Michael D. Resnik (1997). Mathematics as a Science of Patterns. New York ;Oxford University Press.
Charalampos Toumasis (1997). The NCTM Standards and the Philosophy of Mathematics. Studies in Philosophy and Education 16 (3):317-330.
Analytics
Monthly downloads |
Added to index2012-01-08Total downloads15 ( #78,648 of 549,090 )Recent downloads (6 months)3 ( #25,722 of 549,090 )How can I increase my downloads? |
My notes
Discussion
