This paper analyses proofs of impossibility of epistemology formulated by Leonard Nelson. He proposed two such demonstrations. The first proof tries to show that no criterion of knowledge is possible. Nelson's second argument considers the sentence B "A is a piece of knowledge' as being synthetic (in Kantian sense). On the other hand, Epistemology cannot employ problematic premises. Hence, it consists of analytic sentences. Now, epistemology is impossible because synthetic sentence cannot be derived from purely analytic ones. The analysis conducted in the papers intends to locate Nelson's arguments in contemporary discussions about the status of epistemology. In particular, it is argued that the second proof deserves attention of contemporary epistemologists.