| I don't know if someone already said this, in this thread; there is a lot to read and understand.
One way to avoid Russell's Paradox is to prove that it isn't a paradox at all.
One way we can do this (prove it's not a paradox) is by proving that it's based on a false assumption; that sets can contain themselves, more specifically, sets have the ability to contain themselves. How do we do this? We need to prove that a set cannot contain itself; that it cannot exist if it contains itself.
A second way to do this (prove it's not a paradox) is by proving that it's based on a false assumption; that a set cannot contain itself; a set does not have the ability to contain itself. How do we do this? We need to prove that a set must contain itself; that a set cannot exist without containing itself.
If you can prove that either (one or the other) assumption is incorrect, the paradox will fall apart since it is based on a false assumption
Answering the question "Does the set of all sets contain itself?" is important since, in my opinion, it is the only set with the possibility of containing itself.  |