 From the two theorems above we see that in the areas of provability and computability the paradoxes of self-reference turn into limitation results: there are limits to what can be proven and what can be computed. This is actually quite similar to what happened in the areas of semantics, set theory and epistemology: The paradoxes of self-reference turned into theorems showing that there are limits to which properties we can consistently assume a truth predicate to have (Tarski’s theorem), a set theory to have (inconsistency of naive set theory), and a knowledge predicate to have (Montague’s theorem). It is hard to accept these limitation results, because most of them conflict with our intuitions and expectations. The central role played by self-reference in all of them makes them even harder to accept, and definitely more puzzling. However, we are forced to accept them, and forced to accept the fact that in these areas we cannot have all we might (otherwise) reasonably ask for. 