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.
It would be interesting to see what various high school textbooks propose for both a definition of science and scientific method. Against those definitions I would like to test the contention of some that "it is not science unless it is based upon proven facts." I've always thought it to be the part of science to explore reality on the basis of reasonable guesses and thereby arrive at the facts.
I would contend that both intelligence and design are quantifiable to a degree. Also that the manner and degree to which they manifest themselves is highly dependent upon the observer. But I know you will not receive these on face value.
My vocation (parts and service representative) makes it difficult to plot out in writing a detailed thesis on the subject, but I do hope to propose a series of definitions and questions to assist in a better understanding between us.
Here comes that guy with his hammer again!!!!