I studied both (λ-calculus and Set Theory) academically and the description IS disjointed and difficult to read. I get what OP is trying to say because I already understand these concepts.<p>But even though the isomorphism between the Y combinator and Russell's paradox is elegant, the paradox is actually very deep (much deeper than the idea of a fixed point) -- that's why it took someone until the early 20th century to formalize it. For an awesome (and mind-blowing) explanation of the paradox, see Halmos' Naive Set Theory (botom of page 6): <a href="http://sistemas.fciencias.unam.mx/~lokylog/images/stories/Alexandria/Logica%20y%20Conjuntos/Paul%20R.Halmos%20-%20Naive%20Set%20Theory.pdf" rel="nofollow">http://sistemas.fciencias.unam.mx/~lokylog/images/stories/Al...</a>
I've read that languages for mathematical reasoning (such as Coq) are not Turing-complete to avoid issues like this. We can tolerate the possibility of infinite loops when we actually execute a program and see that it returns an answer, but apparently programs used as proofs aren't actually run, so type-checking needs to eliminate this sort of paradox.
Good stuff. A bit of googling got me to Curry's Paradox [0] which is really just a different statement of this. Self-reference breaks things.<p>[0] <a href="http://en.wikipedia.org/wiki/Curry%27s_paradox#Existence_problem" rel="nofollow">http://en.wikipedia.org/wiki/Curry%27s_paradox#Existence_pro...</a>