Much has been made of Frank H. Knight's (1921: p.20, Ch.7) famous distinction between "risk" and "uncertainty". In Knight's interpretation, "_risk_" refers to situations where the decision-maker can assign mathematical probabilities to the randomness which he is faced with. In contrast, Knight's "_uncertainty_" refers to situations when this randomness "cannot" be expressed in terms of specific mathematical probabilities. As John Maynard Keynes was later to express it:
"By `uncertain' knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty...The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence...About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know." (J.M. Keynes, 1937)
Nonetheless, many economists dispute this distinction, arguing that Knightian risk and uncertainty are one and the same thing. For instance, they argue that in Knightian uncertainty, the problem is that the agent _does not_ assign probabilities, and not that she actually _cannot_, i.e. that uncertainty is really an epistemological and not an ontological problem, a problem of "knowledge" of the relevant probabilities, not of their "existence". Going in the other direction, some economists argue that there are actually no probabilities out there to be "known" because probabilities are really only "beliefs". In other words, probabilities are merely subjectively-assigned expressions of beliefs and have no necessary connection to the true randomness of the world (if it is random at all!).
Nonetheless, some economists, particularly Post Keynesians such as G.L.S. Shackle (1949, 1961, 1979) and Paul Davidson (1982, 1991) have argued that Knight's distinction is crucial. In particular, they argue that Knightian "uncertainty" may be the only relevant form of randomness for economics - especially when that is tied up with the issue of time and information. In contrast, situations of Knightian "risk" are only possible in some very contrived and controlled scenarios when the alternatives are clear and experiments can conceivably be repeated -- such as in established gambling halls. Knightian risk, they argue, has no connection to the murkier randomness of the "real world" that economic decision-makers usually face: where the situation is usually a unique and unprecedented one and the alternatives are not really all known or understood. In these situations, mathematical probability assignments usually cannot be made. [....]
<http://cepa.newschool.edu/het/essays/uncert/intrisk.htm>