Hence why Russell’s paradox makes reference to the set of all sets that do not contain themselves, rather than just some sets that don’t contain themselves.
(Now, of course, mathematicians don’t use naive set theory anymore, but ZFC, which solves the problem.)
Love it—mainly because it invokes one of my favourite paradoxes.
If you preach hypocrisy, and you are in fact hypocritical, than you’re not a hypocrite. And if you aren’t a hypocrite, then you are.
The paradox arises only if you aren’t hypocritical about anything else.
Hence why Russell’s paradox makes reference to the set of all sets that do not contain themselves, rather than just some sets that don’t contain themselves.
(Now, of course, mathematicians don’t use naive set theory anymore, but ZFC, which solves the problem.)