Halting problem
If running R and making it look at a copy of itself does not run forever, then Q answered "yes, if we run this program and make it look at a copy of itself it will run forever". But Q said this when looking at R itself. So what Q actually said is: "yes, if we run R and make it look at a copy of itself it will run forever". So: If R running on a copy of itself does not run forever, then it does run forever. This is impossible.