PEIRCE TO STRAWSON The number two was treated in turn as the class of classes equivalent to the class whose members are (a) the members of the class used to define one, plus (b) any object not a member of that defining class In this way the numbers can be defined one after the other, and each number is a class of classes of individuals However, the natural number series can be continued thus ad infinitum only if the number of objects in the universe is itself infinite For if there are only n individuals then there will be no classes with n ỵ members, and so no cardinal number n ỵ Russell accepted this and therefore added to his axioms an axiom of infinity, i.e the hypothesis that the number of objects in the universe is not finite Whether or not this hypothesis is true, it is surely not a truth of pure logic, and so the need to postulate it appears to nullify the logicist project of deriving arithmetic from logic alone Russell’s later philosophy of mathematics was presented to the world in two remarkable works The first, more technical, presentation was written in collaboration with his former tutor A N Whitehead and appeared in three volumes between 1910 and 1913 under the title Principia Mathematica The second, more popular work, Introduction to Mathematical Philosophy, was written while he was serving a prison sentence for his activities as an antiwar protester in 1917 By this time, Russell had achieved distinction outside the philosophy of mathematics in areas that were later to become major preoccupations of British philosophers His early work, along with that of Moore, is often said to have inaugurated a new era in British philosophy, the era of ‘analytic philosophy’ Even though the impetus to the analytic style of thinking can be traced back, as Russell himself was happy to admit, to the work of Frege, it was Moore who first gave currency, in the twentieth century, to the term ‘analysis’ itself as the mark of a particular way of philosophizing ‘Analysis’ was, first and foremost, an anti-idealist slogan: instead of accepting the necessity of understanding a whole before one could understand its parts, Moore and Russell insisted that the right road to understanding was to analyse wholes by taking them to pieces But what was it that was to be taken to pieces—things or signs? Initially, both Moore and Russell saw themselves as analysing concepts, not language—concepts that were objective realities independent of the mind ‘Where the mind can distinguish elements’, Russell wrote in 1903, ‘there must be different 51