I think you overlook the central point: The assessment that x>y is based on learned information about x and y, and the assessment that a is a smaller problem th

I think you overlook the central point: The assessment that x>y is based on learned information about x and y, and the assessment that a is a smaller problem than b ditto. You may argue that the x, y, a and b are wrong, and therefore the conclusions is wrong. Well, fine, as you please. What I'm saying is that learning about x, y, a and b, then forming conclusions, is a high-information mode.