Keynes’ mathematical Treatise addresses what some call ‘radical uncertainty’, which he thought endemic in world affairs and whose appreciation underpinned much of his later work. In contrast, the mainstream view in economics, as elsewhere, has been that even if radical uncertainty exists, either there is in principle nothing that can ever be done about it, or that even if one could in theory do something about it then the institutions required would be unreliable, and one would be better off without them. Thus the mainstream has worked as if it were realistic to ignore even the possibility of radical uncertainty. But one needs some conceptualisation of radical uncertainty, such as Keynes’, before one can make such judgments. This paper presents an interpretation, to inform debate. The viewpoint taken here is mathematical, but this is not to deny the value of other views.