The principles of mathematics

Abstract

In this chapter I shall study the main results achieved by Russell once he was able to use the techniques of Peano’s logic; then I shall compare these results with those from former unpublished manuscripts and publications. The relevant works now will be the writings, published or unpublished, from 1900 to 1903 and very especially Principles, However, I shall also resort to Principia mathematica, mainly to verify the lasting nature of these results, given that this work can be considered as the definitive version of Russell’s ‘mathematical philosophy’. At this stage the method is already clearly illustrated by an impressive list of constructive definitions, which show the great weight of Cantor’s and Peano’s techniques, which constituted a new viewpoint concerning definitions, as they were regarded according to Moore’s philosophy, although the detailed study of these definitions, as regarded as philosophically ‘constructive’ ones, is left for the next chapter (see 5.3).