Russell’s Universalism and Topic-Specificity

Abstract

A tension runs across all the six preceding chapters. On one hand, we have claimed that Russell wanted to provide his readers with more than a formally perfect substitute for the mathematical concept he considered; on the other hand, we have insisted on the fact that he never expound the additional criteria he used to select his favourite analysis from among the many possible ones. Russell’s decisions were not arbitrary; in each case, reasons were provided to justify the choices. But these justifications were always tied up to some local and topic-specific considerations, and they were not grounded on any general criteria. Thus, we saw in the last chapter that Applic, one of the best candidates to play the role of a criterion, was no more than a guiding rule of thumb. In other words, in the picture I have painted of PoM and PM so far, there is a maladjustment between Russell’s general characterization of logical analysis (as a formally perfect, or truth-preserving, translation of the mathematical theorems into the logical language) and his own practice of analysis (which takes into account non-formal aspects of the mathematics he analysed).