Many examples comes to mind, the most famous being the Gödel's theorems viewed as formalisations of the Liar's paradox. I just realised that the proof of non-calculability of Kolmogorov complexity is a positive rewriting of Berry's paradox. My question (perhaps to be made into collective mode) is a) what are the best examples you know ? b) (more important) is there some explication of this productivity of paradoxes (or, conversely, do you know of paradoxes with no interesting follow-up) ?



Positive results coming from paradoxes
Kritchman and Raz [adapted](http://www.ams.org/notices/201011/rtx101101454p.pdf) the surprise examination paradox (a/k/a the unexpected hanging paradox) to prove Godel's second incompleteness theorem (extending the ideas underlying Chaitin's Berry's-paradox-inspired proof of Godel's first incompleteness theorem). 


I blogged on this [here](http://www.thebigquestions.com/2011/12/15/the-big-surprise/).


