ABSTRACT
In the preceding chapter I discussed a fundamental issue of Grundgesetze der Arithmetik already, namely value ranges. They were properly introduced in ‘Funktion und Begriff’ and, in some sense their discussion belonged with that of the notions of ‘function’, ‘concept’ and ‘object’. In the remaining two chapters, I will be concerned with other philosophical issues discussed by Frege in Grundgesetze der Arithmetik and in other (usually later) works. In this chapter, some fundamental themes of Frege’s philosophy take central stage, while in the last chapter I will round my critical exposition with some other less central but not less interesting themes. As we saw in Chapters 2 and 3, Frege’s views can be assessed sometimes while analysing his criticism of other views. In Chapter 2, I expounded Frege’s criticism both of psychologistic conceptions of mathematics and of what I called there the ‘naturalistic views of mathematics’. But such criticism did not refute two less vulnerable views very popular in the academic quarters of those days. Firstly, there is the psychologistic view of logic. For a logicist like Frege, his refutation of psychologism in mathematics in Die Grundlagen der Arithmetik would not be conclusive if it were not completed by a refutation of psychologism in logic. In fact, if arithmetic were independent of psychology but logic were not independent of psychology, it would be unheard of to try to derive arithmetic from logic. Thus, the refutation of psychologism in logic was an extremely important and unavoidable task for Frege, and he sets out to accomplish it in the Preface to Grundgesetze der Arithmetik. Secondly, there is the formalist conception of mathematics, whose refutation by Frege is dispersed in different writings extending over some three decades. Already at the end of Die Grundlagen der Arithmetik Frege criticizes formalism in arithmetic, but he elaborates such criticism with more details both in the second volume of Grundgesetze der Arithmetik and in shorter writings, beginning with his 1885 paper ‘Über formale Theorien der Arithmetik’.1
