Philosophy in the modern world a new history of western philosophy, volume 4 (new history of western philosophy) ( PDFDrive ) (1) 60

PEIRCE TO STRAWSON member of itself, then it is a member of itself A system that leads to such a paradox cannot be logically sound The second volume of Grundgesetze was already in press when Russell’s letter arrived Utterly downcast, Frege described the paradox in an appendix, and attempted to patch the system by weakening the guilty axiom But this revised system in its turn proved inconsistent After retiring from Jena in 1918 Frege seems to have given up his belief that arithmetic can be derived from logic, and returned to the Kantian view that it is, like geometry, synthetic a priori We now know that the logicist programme can never be carried out The path from the axioms of logic to the theorems of arithmetic is barred at two points First, as Russell showed, the naive set theory that was part of Frege’s logical basis was inconsistent in itself Second, the notion of ‘axioms of arithmetic’ was itself called in question when it was later shown (by the Austrian mathematician Kurt Goădel in 1931) that it was impossible to give arithmetic a complete and consistent axiomatization Nonetheless, Frege’s philosophical legacy was enormous He often compared the mathematician to a geographer who maps new continents His own career as a thinker resembled that of Christopher Columbus as an explorer Just as Columbus failed to find a passage to India but made Europe acquainted with a whole new continent, so Frege failed to derive arithmetic from logic, but made innovations in logic and advances in philosophy that permanently changed the whole map of both subjects Like Columbus, Frege succumbed to discouragement and depression; he was never to know that he was the founder of an influential philosophical movement But he did not give up all hope that his work had value: leaving his papers to his son just before his death in 1925 he wrote, ‘Do not despise the pieces I have written Even if all is not gold, there is gold in them.’ Psychology and Pragmatism in William James William James (1842–1910) was six years older than Frege, but he began his philosophical career quite late in life He was born in New York, the son of a Swedenborgian theologian and the elder brother of the celebrated novelist Henry James He was educated partly in America and partly in Europe, where he attended schools in France and Germany For a while 43