Rohloff, Waldemar (Author)
The topic of the dissertation is the applicability of mathematics. The dissertation is centered around the works of Kant and Frege who represent a distinctive approach to the problem of the applicability of mathematics. Their approach is characterized by a number of shared assumptions. Both philosophers claim that mathematics is dependent for its content on the possibility of applications without which it would be empty. Both philosophers offer an account of applicability which explains this feature of mathematics in terms of its a priori content. Finally, both philosophers offer an account of applicability which is itself knowable a priori. Based on these common assumptions I characterize their distinctive approach as an a priori account of applicability. The dissertation is structured around two questions which I pose to each of the philosophers. The first concerns the relationship between the applicability of mathematics and their larger philosophical projects. With respect to Kant, this means assessing the relationship between the applicability of mathematics and his transcendental idealism. With respect to Frege it involves assessing the relationship between the applicability of mathematics and his logicism. The second question concerns the details of their accounts of applicability. As is shown in the dissertation, Kant's account of applicability makes essential use of a common synthesis underlying empirical and mathematical cognition. For Frege, his account of the applicability of mathematics (specifically arithmetic) involves an epistemological and mathematical inquiry into the foundations of arithmetic.
...MoreDescription Cited in Diss. Abstr. Int. A 68/07 (2008). Pub. no. AAT 3274350.
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