@cyrnosofia: Crispin Wright showed that logicism was not dead after Russell’s paradox. He gave it a new route, now called neo-Fregeanism, by replacing Frege’s broken foundation with a more careful abstraction principle Crispin Wright argued that this verdict was too pessimistic. Together with Bob Hale, he proposed that Frege's mistake lay not in the general logicist idea, but in the particular principle he chose. Instead of Basic Law V, Wright focused on Hume's Principle, which states: The number of Fs is equal to the number of Gs if and only if the Fs and the Gs can be put into one-to-one correspondence For example, there are three apples and three oranges because the apples can be paired with the oranges one by one, with none left over. Hume's Principle thus provides a criterion for when two collections have the same number. Wright's key insight was that if one assumes ordinary second-order logic together with Hume's Principle, one can derive the axioms of arithmetic. This result—later rigorously established by George Boolos and known as Frege's Theorem—showed that arithmetic could still be grounded in logical principles without appealing to Frege's inconsistent Basic Law V. George Boolos played an important role in demonstrating the strength of this approach. The resulting position became known as neo-Fregeanism. It preserves the central ambition of logicism—that arithmetic is objective and fundamentally logical—while avoiding the contradiction that ruined Frege's original system. Wright did not claim that Frege had been entirely vindicated. Rather, he argued that Russell's paradox destroyed only one route to logicism, not the project itself. #philosophy #logic #ontology #mathematics #philosophytok

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Tuesday 23 June 2026 14:51:47 GMT