ABSTRACT
At the beginning of the seventh chapter of his authoritative survey of mathematical logic, G. T. Kneebone makes this striking observation on Russell’s Principia: ‘For all the inspiration that Principia Mathematica has communicated to the logicians and philosophers of mathematics of the twentieth century, and for all its rich fecundity as a source of concepts and symbolic devices, this great work remains, in the literature of the foundations of mathematics, a lone classic without progeny.’ 2 In this chapter I propose to examine some of the ideas which have dominated thinking about the foundations of mathematics during the sixty years which have elapsed since the publication of the first edition of Principia to see what, if anything, they owe to Russell and what they tell us of the reasons for the abandonment of Russell’s programme of logicism to which Kneebone alludes.
