Frege, Neo-Logicism and Applied Mathematics

Peter Clark
University of Melbourne
A little over one hundred years ago , Frege wrote to Russell in the following terms1: I myself was long reluctant to recognize ranges of values and hence classes; but I saw no other possibility of placing arithmetic on a logical foundation. But the question is how do we apprehend logical objects? And I have found no other answer to it than this, We apprehend them as extensions of concepts, or more generally, as ranges of values of functions. I have always been aware that there are difficulties connected with this, and your discovery of the contradiction has added to them; but what other way is there?
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DOI 10.1007/978-1-4020-2196-1_11
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