Mathematics is extremely useful in science. In fact, it is often said that mathematics is "unreasonably" effective at applying to the natural world. This is philosophically puzzling, largely because pure mathematics seems to consist of a priori, necessary truths about acausal, eternally existing mathematical objects (numbers, sets, functions, etc.). It is very difficult to see what any of this has to do with the natural world. In this class we will investigate the philosophical puzzles of applied mathematics. Special attention will be paid to the so-called Field program and related projects for explaining the applicability of mathematics. Detailed case studies will be made of classical mechanics, quantum mechanics, and the arithmetization of syntax. 2-unit option is only for Philosophy PhD students beyond the second year.
2-4 units · Letter or Credit/No Credit
Mathematics is extremely useful in science. In fact, it is often said that mathematics is "unreasonably" effective at applying to the natural world. This is philosophically puzzling, largely because pure mathematics seems to consist of a priori, necessary truths about acausal, eternally existing mathematical objects (numbers, sets, functions, etc.). It is very difficult to see what any of this has to do with the natural world. In this class we will investigate the philosophical puzzles of applied mathematics. Special attention will be paid to the so-called Field program and related projects for explaining the applicability of mathematics. Detailed case studies will be made of classical mechanics, quantum mechanics, and the arithmetization of syntax. 2-unit option is only for Philosophy PhD students beyond the second year.