Frege, neo-logicism and applied mathematics

Peter Clark

pp. 169-183

in: Friedrich Stadler (ed), Induction and deduction in the sciences, Berlin, Springer, 2004

Abstract

A little over one hundred years ago (the letter is dated July 28, 1902), 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?

Cited authors

Frege Gottlob