 After having presented a number of paradoxes of self-reference and discussed some of their underlying similarities, we will now turn to a discussion of their significance. The significance of a paradox is its indication of a flaw or deficiency in our understanding of the central concepts involved in it. In case of the semantic paradoxes, it seems that it is our understanding of fundamental semantic concepts such as truth (in the liar paradox and Grelling’s paradox) and definability (in Berry’s and Richard’s paradoxes) that are deficient. In case of the set-theoretic paradoxes, it is our understanding of the concept of a set. If we fully understood these concepts, we should be able to deal with them without being led to contradictions. 