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enricozb | 28 days ago

Yes the type theoretic analog to Russel's (set theoretic) paradox is Girard's (as mentioned in the abstract) paradox.

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order

srcreigh|28 days ago

This is incorrect. The set paradox it’s analogous to is the inability to make the set of all ordinals. Russel’s paradox is the inability to make the set of all sets.

kibwen|28 days ago

Since we're being pedantic, Russel's paradox involves the set of all sets that don't contain themselves.

enricozb|27 days ago

Perhaps I overstated how related the two were. I was pulling mostly from the Lean documentation on Universes [0]

> The formal argument for this is known as Girard's Paradox. It is related to a better-known paradox known as Russell's Paradox, which was used to show that early versions of set theory were inconsistent. In these set theories, a set can be defined by a property.

[0]: https://lean-lang.org/functional_programming_in_lean/Functor...