Bertrand Russell · Mathematics

Russell’s Paradox: The Set That Broke Set Theory

The contradiction Russell found in 1901 - the class of all classes that are not members of themselves - which shattered Frege’s logical system, exposed a crack in the foundations of mathematics, and forced Russell to invent the theory of types to escape it.

What you'll be able to recall

You learned that Russell’s paradox arises from the class R of all classes that do not contain themselves: R is a member of itself if and only if it is not. Explain how the contradiction is generated, why it broke Frege’s system, and how the theory of types was meant to block it.

Leads to Georg Cantor.

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