When you equal the meta sentence level and the sentence level, it is nothing special about the paradox, for it is just a contradiction between the sentence and the meta-sentence.
In Curry’s paradox, “X -> Y” is what you want to prove. So you try “if X”, to see if you can get Y.
But by letting “X = X -> Y” and if X, and X = X -> Y, then Y. You are actually doing circular proof.
Effectively you use X to prove X, which is a useless proof.
Paradox is due to the mixing of para-level (meta-level) and original level. As long as we do not allow mixing levels, there are no paradoxes. Every sentence should only be allowed to describe sentences which have lower levels.
2012.10.13 Saturday (c) All rights reserved by ACHK