Over at Marginal Revolutions, Tyler Cowen tries to show how we can "operationalize Knightian uncertainty". His response, is not so much a measure of Knightian Uncertainty, but a strategic implication. Basically he suggests we try more varied actions, and therefore have better success by putting resources into low-odds ventures. It is true, of course, that if you try many different things, your odds of discovering penicillin, X-rays, or Viagra, are greater, merely because you are allocating more resources to finding productive payoffs. But is it cost effective? If you wish to find a strategy to create wealth, is it a good investment to go to the library and randomly allocate time reading from various books within the dewey decimal system? I'm not convinced, and I have not seen any studies demonstrating this.

Barkley Rosser notes that Keynes's conception of uncertainty is more formal, and easier to quantify. I disagree. All the definitions notwithstanding, he basically states two extremes: that proposition a given evidence h is a/h=0 when h excludes a, and a/h=1 when evidence h implies a with certainty, leaves a lot of wiggle room for how a/h behaves when not equal to 0 or 1. Keynes then goes on to prove all sorts of things relating to joint probabilities being less the total probabilities, or that confidence in probabilities increases our belief in them. It isn't helpful to define a functions endpoints, then intimate vague things about what goes on in between, you don't need algebra to do that, sort of like his function of inflation he gave in the General Theory. In the end, Keynes states in his 1937 QJE article:

By ‘uncertain’ knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is merely probable. The game of roulette is no subject, in this sense, to uncertainty; nor is the prospect of a Victory bond being drawn. Or, again, the expectation of life is only slightly uncertain. Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of an European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealthowners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know (Keynes Collected Writings Chapter 14, pp. 113-114).

So in the end, Keynes's conception is just as murky as Knight's definition, the Treatise of Probability doesn't make it any less so. I thought Knight made uncertainty more interesting by noting that to the degree it is quantified it is no longer a 'risk' in the traditional intuitive sense, merely an expense or benefit that you can rationally, and objectively accrue. A businessman makes profits in cases where his judgment concerns something truly uncertain, and thus not amenable to some accountant merely pointing out his actions are like playing the lottery with an expected value. I find this on one hand very profound, but on the other, utterly unhelpful.

While it is true that you any new business idea, from Google to Tartar-control Crest, exploits Knightian uncertainty (you couldn't quantify Google's expected return in 1998), it is not clear that merely doing something unexpected generates higher returns on average because the set of uncertain actions includes so many things, a potentially infinite set (eg, I may put money into digging for gold in my back yard, giving money to Nigerian email spammers, investing in penny stocks, starting a business selling penis-enlargement herbs,etc.).

People have been talking about Knightian uncertainty for a long time, but in the end, people must write about uncertainty by assuming some kind of density function, which then makes it different than Knightian uncertainty. So it's more philosophy than science. I have been intrigued with the idea for many years, and perhaps it is an unsolvable paradox unworthy of too much contemplation.