The authors believe that the problem of applicability can be approached in two ways. One approach derives from the fact that the empirical world has been the source of many mathematical concepts, and claims that arithmetic captures reality in the same way as common empirical disciplines. Its miraculous applicability can then be explained by the greater universality of the concepts used. Such an approach is designated a poste¬riori. The other approach to the problem of applicability, designated a priori, assumes that arithmetic is not grounded empirically, in fact it is already there before all expe¬rience. Upon analysis, both approaches authors’ view, these merits and shortcomings were already noticed by Frege. Though his conception is to be classiﬁed as an a priori approach, he – unlike his predecessors – also learned much from proponents of a posteriori conceptions.
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