1)Recursion is apparently a very important aspect of Godel's thinking in his On Formally Undecidable Propositions of Principia Mathematica and Related Systems. There is also something recursive about Godel's essay in Albert Einstein: Philosopher-Scientist The Library of Living Philosophers, Volume 7. There he describes what appears to be the possibility of time travel in a rotating universe. That's pretty recursive.
2) Paul has linked to this. It is most interesting to see the analogy between the prisoner's dilemma and behaviour in general. It is as if we are prisoners. But there is this key difference: the prisoner's dilemma is a one-off. Behaviour is day to day. So after years of people choosing to do unto others as they would be done unto and finding that no one else is making that choice, what is the rational move then? Imagine the prisoner chooses not to rat out the other prisoner, but the other prisoner chooses to rat her or him out. The silent prisoner gets 5 years, the rat goes free. After five years the prisoner is offered the same dilemma. If she or he rats out the other its a maximum of one more year and possible immediate freedom. Silence gets a six month minimum more with a possibility of 5 years more. So the prisoner goes all altruistic and remains silent, and gets another 5. The altruistic behaviour looks more and more nutty.