"[Gottlob Frege] had set himself the task of defining the fundamental concept of arithmetic—i.e. number—in terms that succeeded in 'stripping off' all the 'irrelevant accretions that veil it from the eye of the mind', and so displaying it 'in its pure form'. For his purposes, it was beside the point to ask how men's actual use of number-conceptions had developed historically, or what differences anthropologists had found between the methods of counting and figuring used in different cultures; such factual studies merely chronicled the changing meanings of number-words in our historical gropings towards fully adequate or 'pure' number-conceptions. A rationally based arithmetic, by contrast, must concern itself with the ideal and final system of number-concepts, and this will provide a unique intellectual standard, or template, for judging all men's earlier and cruder proto-arithmetical creations. The analysis of number concepts must therefore be undertaken using the instruments of logic alone. It calls for the construction and interpretation of a rigorous axiomatic system already being worked out for arithmetic by... Peano. Frege's Foundations of Arithmetic served as a philosophical example which was soon followed by others. The program... became a model for Bertrand Russell's work on philosophical logic, and for half a century's research on philosophy of science..."