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Single Idea 10047

[from 'Mathematical logic and theory of types' by Bertrand Russell, in 6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory ]

Full Idea

Unfortunately, Russell's new logic, as well as preventing the deduction of paradoxes, also prevented the deduction of mathematics, so he supplemented it with additional axioms, of Infinity, of Choice, and of Reducibility.

Gist of Idea

Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms

Source

report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Alan Musgrave - Logicism Revisited §2

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.102


A Reaction

The first axiom seems to be an empirical hypothesis, and the second has turned out to be independent of logic and set theory.