Review of Symbolic Logic 1 (1):16-41 (2008)
|Abstract||My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one observation is immediate: the march of the centuries has produced an amusing reversal of philosophical fortunes. Let me begin there. In the beginning, that is, in Plato, mathematical knowledge was sharply distinguished from ordinary perceptual belief about the world. According to Plato’s metaphysics, mathematics is the study of eternal and unchanging abstract Forms,1 while science is uncertain and changeable opinion about the world of mere becoming. Indeed, in Plato’s lights, of the two, only mathematics deserves to be called ‘knowledge’ at all! Of course if sense perception cannot give us knowledge, if mathematics is not about perceivable things, then Plato owes us an account of how we ordinary humans achieve this wonderful insight into the properties of the abstract world of Forms. Plato’s answer is that we do not actually acquire mathematical knowledge at all; rather, we recollect it from a time before birth, when our souls, unencumbered by physical bodies, were free to commune with the Forms, and not just the mathematical ones, either – also Truth, Beauty, Justice, the Good, and so on.2 Whatever appeal this position may have held for the ancient Greeks, it will not begin to satisfy a contemporary, scientiﬁcally minded philosopher..|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Jean De Groot (2006). A Husserlian Perspective on Empirical Mathematics in Aristotle. Proceedings of the American Catholic Philosophical Association 80:91-99.
A. Quale (2012). On the Role of Constructivism in Mathematical Epistemology. Constructivist Foundations 7 (2):104-111.
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4).
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Eugene Wigner (1960). The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications in Pure and Applied Mathematics 13:1-14.
Dale Jacquette (2006). Applied Mathematics in the Sciences. Croatian Journal of Philosophy 6 (2):237-267.
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.
Ian Hacking (2011). Why is There Philosophy of Mathematics AT ALL? South African Journal of Philosophy 30 (1):1-15.
Added to index2009-01-28
Total downloads44 ( #25,360 of 549,122 )
Recent downloads (6 months)1 ( #63,361 of 549,122 )
How can I increase my downloads?