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Koshkin 18 minutes ago [-]
> a set can contain itself
Can it?
> a term can have only one type... Due to this law, types cannot contain themselves
Doesn't look like one follows from the other...
bombcar 14 minutes ago [-]
The set of all sets that contain itself ;)
Koshkin 9 minutes ago [-]
Except such set is empty and thus does not contain itself.
chromacity 6 hours ago [-]
It's a great introduction, but I find the premise a bit funny. It starts with Russell's paradox, insinuates that solving it within set theory makes set theory complex (it doesn't, you basically just restrict what can be used to build a set), and then introduces a system that is fundamentally more complex.
Koshkin 3 minutes ago [-]
But from the standpoint of a Haskell programmer Category Theory is simple!
layer8 1 hours ago [-]
Regarding Russell’s paradox, its dual is also interesting: Consider the set D := { s | s ∈ s }, the set of sets that do contain themselves. Does D contain itself? It might or it might not, neither causes a contradiction. Tnis shows that you don’t need an antinomy for a set comprehension to be ill-defined.
xanderlewis 32 minutes ago [-]
Why is it ill-defined? As you said, there's no contradiction.
Can it?
> a term can have only one type... Due to this law, types cannot contain themselves
Doesn't look like one follows from the other...
Also, in the usual ZF set theory, it's empty.