Responding to Lanny Arvan.
Interesting ramble covering (as usual) a lot of ground.
People who have studied the foundations of probability and the foundations of logic recognize a certain arbitrariness to those disciplines.
Probability, in particular, can be interpreted three major ways (charaterized by Reichenbach, Carnap and Ramsay) resulting in three different semantics. When one says 'the world is improbable', does one mean, (a) as compared to all previous worlds, (b) as compared to all logically possible worlds, or (c) as compared to all the worlds we are willing to place money on?
My own perspective, in both cosmology and economics, that research (properly so-called), calculation and measurement will only take you so far. A significant proportion of the cosmologists' or the economists' output is based, not on measurement, but on recognition. Sometimes we see this acknowledged with code-phrases ("this year's economy is similar to what we say in 1992") but more often is not explicitly acknowledged at all.
The thing with recognition is, there are no rules regarding domain. Everything is relevant, because the variables are so intertwined, there is no real saying what is salient and what is coincidental. The person who first noticed a sine wave (properly a property of electricity and oceans) in economic data was operating on the principle of recognition, as was Pascal when he said (with no real knowledge of the alternatives) that this is the "best of all possible worlds".
Teaching, I think, is more an art of recognition than of measurement, which is why the best teachers can identify the students with the most potential before even the first exam result comes in, and why teachers can learn more and more about their discipline even without doing 'research'. The acquisition of a capacity to 'recognize' is a function of the accumulation of experience, preferably as diverse and as difficult as possible.
Recognition, properly so-called, is a logical process, not magic or intuition. When you pick out the face of your spouse from a crowd of people at an airport, this is not some random event or happenstance, but a knowable and identifiable process of human cognition. We can understand that *some* process is taking place, even if we cannot measure that phenomenon except by the grossest indicators.
I think that what we'll find, after enough investigation, is that measurement in both economics and education has been employment more for political purposes than for research purposes.
Which, of course, is what people with enough experience in both fields have long since recognized.