Synthese 88 (2):119 - 126 (1991)
|Abstract||The distinction between analytic and synthetic propositions, and with that the distinction between a priori and a posteriori truth, is being abandoned in much of analytic philosophy and the philosophy of most of the sciences. These distinctions should also be abandoned in the philosophy of mathematics. In particular, we must recognize the strong empirical component in our mathematical knowledge. The traditional distinction between logic and mathematics, on the one hand, and the natural sciences, on the other, should be dropped. Abstract mathematical objects, like transcendental numbers or Hilbert spaces, are theoretical entities on a par with electromagnetic fields or quarks. Mathematical theories are not primarily logical deductions from axioms obtained by reflection on concepts but, rather, are constructions chosen to solve some collection of problems while fitting smoothly into the other theoretical commitments of the mathematician who formulates them. In other words, a mathematical theory is a scientific theory like any other, no more certain but also no more devoid of content.|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4).
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan.
Dale Jacquette (2006). Applied Mathematics in the Sciences. Croatian Journal of Philosophy 6 (2):237-267.
Leon Horsten, Philosophy of Mathematics. Stanford Encyclopedia of Philosophy.
Added to index2009-01-28
Total downloads20 ( #61,609 of 549,694 )
Recent downloads (6 months)1 ( #63,425 of 549,694 )
How can I increase my downloads?