"[T]he opposition and conflict between the 'natural scientific' and the more 'spiritual scientifically' oriented medical traditions in a deeper sense appears as an expression of the difference between the perspectives you come to when you develop a thought-sight experience or a will-touch experience in a too one-sided way."
-Sune Nordwall
It is no mystery to me that some assume a rigorous definition of science for themselves, and most likely practice science within a strict discipline. Hence we get statements like, "It is not dealing with proven facts, so it is not science." We need to deal with that, and we need to ask whether public schools can accomodate a wider definition of science.
I would also like to add the following questions which I would like to hear you out on:
1.) Can intelligence be quantified? If so, on what basis? If not, why not?
2.) Can design be quantified? If so, on what basis? If not, why not?
No, because there is no objective basis. We can certaintly rate people, and even animals on scale according to their ability to solve puzzles, but this is just a self-definition. You are saying that intelligence is what I measure with my test of intelligence. It's useful, though, if your test measures a skill needed in a real application.
2.) Can design be quantified? If so, on what basis? If not, why not?
Give it a try. Attempt to give us an objective basis.
Well, here I'll put on my Feyerabend hat, and question whether a strict discipline of this sort exists, and whether such a discipline would be a good thing. Physicists tend to do science in quite different ways from biologists and from chemists., Even within any given discipline, some of us are cautious; some take huge leaps. Some tend to fly by the seat of their pants; some insist of theoretical rigor. Some try to look at the big picture; others focus on details. And I can give you good historical instances where science done from each of these perspectives was essential to solving an important problem.
Science has a very limited philosophical underpinnings. An insistence on openness and honesty; an insistence that theories must be broadly consistent with, and explanatory of, observations; reproducibility, self-consistency, and rationality, and that's it. Try to put science in a tighter philosophical straitjacket than that, and you'll choke it to death. My problem with high-school textbooks is not that they omit to discuss the scientific method; it's that the scientific method they claim exists is in many cases a fiction.
Can intelligence be quantified? If so, on what basis? If not, why not?
Within limits. we can apply tests of general intelligence to humans; despite the abhorrence of the left, these are largely reproducible and valid. We can do cross-species experiments to compare the intelligence of animals.
Can design be quantified? If so, on what basis? If not, why not?
Dembski claims it can, but I'm highly skeptical. It's akin to asking if one can tell if a given number is random. Take the nth digit of pi to base 10. If you use that as a way to select a one-digit number with equal probabilities of being anything from 0 to 9, it's essentially random. Someone who doesn't know what you're doing has no better than 1 in 10 odds of guessing the number. On the other hand, anyone with a computer who knows what algorithm you're using can calculate it with 100% probability. There really aren't any random numbers; there are only random processes. And, in the same way, there is no way to tell if an entity is designed, without looking at how it came to be.