Yes please! I'd like to get the post moved to the math section if possible, as I'd like to challenge the mathematicians among us fairly with this case as well. Thank you for your attempt to help, Carrock. However, I'm still struggling. You start your post with the words, "A non mathematical example". As soon as you start the argument with this presumption, the rules of the (rigid) set theory are no longer applicable (at least according to my logical thinking). The librarian is free to include a reference in the catalogue (of catalogues which don't include themselves) to itself, for instance. Or, he/she could just throw the whole lot into the bin out of pure frustration, for that is a tap into the vastness of possibilities that root out of human imagination. In real-life, a human being can come-up with solutions outside of set theory logic for such practical problems. The gist of my argument is that (I feel) your example example is not a fair real-life implementation of Russel's paradox. P.S. I didn't understand the last part of your post: "* and will learn from SF if my understanding is inadequate."
Greetings everyone, This is my very first post here, and it comes out of pure curiosity. I see that the OP's argument draws from Russel's paradox. However, I'm having a very hard time "imagining" a set of all sets that is not a member of itself. On the contrary, I can perfectly imagine a set of all cats (like a big balloon filled with cats, for instance). The challenge for me is that Russel's paradox is an abstract mathematical concept, and I am not able to imagine anything physical out of it. Quoting the OP, "...from the very conceivable idea that you can group whatever you want together." Again, although grouping things is conceiveable for me, a set of all sets that is not a member of itself is not physically conceivable for me. The thread title reads, "If I can imagine it, it is a possibility." Anyone who wishes to help me out here is grandly welcomed!