Christopoulou Demetra（In his work, Hermann Weyl （1926） addresses the issue of abstraction principles, an issue that has been broadly discussed during the last decades with regard to the Neo-Fregean program. This pa...Christopoulou Demetra（In his work, Hermann Weyl （1926） addresses the issue of abstraction principles, an issue that has been broadly discussed during the last decades with regard to the Neo-Fregean program. This paper aims to show off the way Weyl＇s account of abstraction could offer a reply to Benacerraf＇s （1973） challenge to realism. Benacerraf argued that mathematical realism is not associated with a plausible epistemology about human access to abstract objects. Weyl deals with the method of abstraction by investigating certain cases of Fregean abstraction principles. He thinks that we can introduce shapes of geometrical images, integers mod m, circles, directions of lines etc. by means of certain creative acts of consciousness, especially intentionality towards proper relations between the elements of an initial domain. Weyl puts emphasis on intentions towards certain invariant characteristics of items that are involved in equivalence relations. Further, he claims that those invariants are transformed into ideal objects through a finite process that is involved in intuition. This paper, in the first place, attempts to make explicit Weyl＇s phenomenological leanings. Secondly, it argues that Weyl＇s explanation of how ideal mathematical objects become present to mind can address the epistemic issue concerning mathematical knowledge and can also be associated with a particular view which is implicit in his philosophy and retains realistic elements. Hence, it can address Benacerraf＇s problem.展开更多
文摘Christopoulou Demetra（In his work, Hermann Weyl （1926） addresses the issue of abstraction principles, an issue that has been broadly discussed during the last decades with regard to the Neo-Fregean program. This paper aims to show off the way Weyl＇s account of abstraction could offer a reply to Benacerraf＇s （1973） challenge to realism. Benacerraf argued that mathematical realism is not associated with a plausible epistemology about human access to abstract objects. Weyl deals with the method of abstraction by investigating certain cases of Fregean abstraction principles. He thinks that we can introduce shapes of geometrical images, integers mod m, circles, directions of lines etc. by means of certain creative acts of consciousness, especially intentionality towards proper relations between the elements of an initial domain. Weyl puts emphasis on intentions towards certain invariant characteristics of items that are involved in equivalence relations. Further, he claims that those invariants are transformed into ideal objects through a finite process that is involved in intuition. This paper, in the first place, attempts to make explicit Weyl＇s phenomenological leanings. Secondly, it argues that Weyl＇s explanation of how ideal mathematical objects become present to mind can address the epistemic issue concerning mathematical knowledge and can also be associated with a particular view which is implicit in his philosophy and retains realistic elements. Hence, it can address Benacerraf＇s problem.
