Tony Lawson’s work on probability and uncertainty is both an important contribution to the heterodox canon as well as a notable early strand of his ongoing enquiry into the nature of social reality. In keeping with most mainstream and heterodox discussions of uncertainty in economics, however, Lawson focuses on situations in which the objects of uncertainty are imagined and can be stated in a way that, potentially at least, allows them to be the subject of probability judgments. This focus results in a relative neglect of the kind of uncertainties that flow from the existence of possibilities that do not even enter the imagination and which are therefore ruled out as the subject of probability judgments. This paper explores uncertainties of the latter kind, starting with and building on Donald Rumsfeld’s famous observations about known unknowns and unknown unknowns. Various connections are developed, first with Nassim Taleb’s Black Swan, and then with Lawson’s Keynes-inspired interpretation of uncertainty.