The essay begins with a taxonomy of the major contexts in which the notion of ‘style’ in mathematics has been appealed to since the early twentieth century. These include the use of the notion of style in comparative cultural histories of mathematics, in characterizing national styles, and in describing mathematical practice. These developments are then related to the more familiar treatment of style in history and philosophy of the natural sciences where one distinguishes ‘local’ and ‘methodological’ styles. It is argued that the natural locus of ‘style’ in mathematics falls between the ‘local’ and the ‘methodological’ styles described by historians and philosophers of science. Finally, the last part of the essay reviews some of the major accounts of style in mathematics, due to Hacking and Granger, and probes their epistemological and ontological implications.As Mancosu says later in the article "this entry is the first attempt to encompass in a single paper the multifarious contributions to this topic". So it is wide-open for further philosophical investigation!
Tuesday, July 7, 2009
Mancosu on Mathematical Style
Paolo Mancosu continues his innovative work in the philosophy of mathematics with a thought-provoking survey article on Mathematical Style for the Stanford Encyclopedia of Philosophy. From the introductory paragraph: