I'm having a look at intuitionistic approach to mathematics, and stumbled upon a derivation of Russell's Paradox that doesn't use the LEM. (Why did mathematicians take Russell's paradox seriously?) What was the Intuitionistic response to this? How did they overcome Russell's paradox? Cheers!
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1For Intuitionistic Set Theory; but - as you said - Russell's Paradox does not need LEM; thus also Intuitionsitic ST msut in some way "restrict" the comprehension principle. See the detail into the Supplement Axioms of CZF and IZF; as you can see, there is Separation. – Mauro ALLEGRANZA Oct 24 '15 at 13:48
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1Intuistionsitic ST adopts Intuitionsitic Logic; thus, as a rule of thumb, it must avoid all Set-theoretic principles incompatible with intuitionistic logic. – Mauro ALLEGRANZA Oct 24 '15 at 13:50