The Indispensability Argument and Multiple Foundations for Mathematics Export

@article{citeulike:2967299, abstract = {One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set2013theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is that these latter issues are of direct relevance to philosophical arguments connected to the applicability of mathematics. In particular, the possibility of there being distinct alternative foundations for mathematics blocks the standard argument from the indispensable role of mathematics in science to the existence of specific mathematical objects.}, address = {Xavier University, Ohio}, author = {Baker, Alan}, citeulike-article-id = {2967299}, citeulike-linkout-0 = {http://dx.doi.org/10.1111/1467-9213.00295}, citeulike-linkout-1 = {http://www.ingentaconnect.com/content/bpl/phiq/2003/00000053/00000210/art00004}, citeulike-linkout-2 = {http://www3.interscience.wiley.com/cgi-bin/abstract/118872593/ABSTRACT}, doi = {10.1111/1467-9213.00295}, issn = {1467-9213}, journal = {Philosophical Quarterly}, keywords = {mathematics, metaphysics, philosophy}, month = {January}, number = {210}, pages = {49--67}, posted-at = {2008-07-06 14:26:59}, priority = {0}, publisher = {Blackwell Publishing}, title = {The Indispensability Argument and Multiple Foundations for Mathematics}, url = {http://dx.doi.org/10.1111/1467-9213.00295}, volume = {53}, year = {2003} }

TY - JOUR ID - citeulike:2967299 L3 - citeulike-article-id:2967299 N2 - One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set2013theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is that these latter issues are of direct relevance to philosophical arguments connected to the applicability of mathematics. In particular, the possibility of there being distinct alternative foundations for mathematics blocks the standard argument from the indispensable role of mathematics in science to the existence of specific mathematical objects. IS - 210 JF - Philosophical Quarterly SN - 1467-9213 AD - Xavier University, Ohio EP - 67 TI - The Indispensability Argument and Multiple Foundations for Mathematics PB - Blackwell Publishing VL - 53 SP - 49 KW - mathematics KW - metaphysics KW - philosophy AU - Baker, Alan PY - 2003/01// UR - http://dx.doi.org/10.1111/1467-9213.00295 ER -