David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
South African Journal of Philosophy 30 (1):1-15 (2011)
Mathematics plays an inordinate role in the work of many of famous Western philosophers, from the time of Plato, through Husserl and Wittgenstein, and even to the present. Why? This paper points to the experience of learning or making mathematics, with an emphasis on proof. It distinguishes two sources of the perennial impact of mathematics on philosophy. They are classified as Ancient and Enlightenment. Plato is emblematic of the former, and Kant of the latter. The Ancient fascination arises from the sense that mathematics explores something ‘out there’. This is illustrated by recent discussions by distinguished contemporary mathematicians. The Enlightenment strand often uses Kant's argot: ‘absolute necessity’, ‘apodictic certainty’ and ‘a priori’ judgement or knowledge. The experience of being compelled by proof, the sense that something must be true, that a result is certain, generates the philosophy. It also creates the illusion that mathematics is certain. Kant's leading question, ‘How is pure mathematics possible?’, is easily misunderstood because the modern distinction between pure and applied is an artefact of the 19th century. As Russell put it, the issue is to explain ‘the apparent power of anticipating facts about things of which we have no experience’. More generally the question is, how is it that pure mathematics is so rich in applications? Some six types of application are distinguished, each of which engenders its own philosophical problems which are descendants of the Enlightenment, and which differ from those descended from the Ancient strand.
|Keywords||philosophy of mathematics Plato Kant|
|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.
Robert A. Holland (1992). Apriority and Applied Mathematics. Synthese 92 (3):349 - 370.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Stewart Shapiro (2000). Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press.
Emily Carson (2004). Metaphysics, Mathematics and the Distinction Between the Sensible and the Intelligible in Kant's Inaugural Dissertation. Journal of the History of Philosophy 42 (2):165-194.
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge 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.
Penelope J. Maddy (2001). Some Naturalistic Reflections on Set Theoretic Method. Topoi 20 (1):17-27.
Nicholas Rescher (2013). Kant's Neoplatonism: Kant and Plato on Mathematical and Philosophical Method. Metaphilosophy 44 (1-2):69-78.
Stephan Körner (1960/2009). The Philosophy of Mathematics: An Introductory Essay. Dover Publications.
Lisa Shabel (1998). Kant on the `Symbolic Construction' of Mathematical Concepts. Studies in History and Philosophy of Science Part A 29 (4):589-621.
William Tait (2005). The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History. OUP USA.
Frode Kjosavik (2009). Kant on Geometrical Intuition and the Foundations of Mathematics. Kant-Studien 100 (1):1-27.
Added to index2011-08-01
Total downloads195 ( #3,401 of 1,102,135 )
Recent downloads (6 months)26 ( #7,592 of 1,102,135 )
How can I increase my downloads?