In his outstanding book Knowledge and its Limits, Williamson claims that we have inductive evidence for some negative theses concerning the prospects of defining knowledge, like this: knowing cannot be defined in accordance with a determinate traditional conjunctive scheme; defends a theory of mental states, mental concepts and the relations between the two, from which we would obtain additional, not merely inductive, evidence for this negative thesis; and presents an alternative definition of knowledge. Here I consider these issues and extract (...) two relevant conclusions: Williamson's theory of states and concepts only supports the negative thesis because this theory would explain too much, since it imposes implausible necessary limitations on possible uses of concepts and linguistic expressions. So, there is no appropriate non-inductive evidence for the negative thesis. Williamson's own definition of knowledge is at risk. (shrink)