TITLE: Example of set which contains itself
QUESTION [40 upvotes]: I am trying to understand Russells's paradox
How can a set contain itself? Can you show example of set which is not a set of all sets and it contains itself.

REPLY [3 votes]: I think part of the answer to Russell's Paradox has to do with the distinction between a set as a collection of things and the "name" of the set. A set that actually contains itself would be in an infinite regression of things. 
"The set that contains everything" if it actually contained itself (not just its "name"; but literally everything) is almost a kind of divide by zero error.
This is not an unusual confusion, when the name of a thing comes to be a placeholder for the thing itself -- you can play with the symbol and forget that the substance of what it is actually composed of has some reality.
This can work in lists of other symbols, as in the example of catalogues or other such lists that only include references and not actual objects.
I'm not a mathematician, but am interested in the philosophy of representation and reality.