This is really only tangentially a Scientific discussion, because it deals with science.
I'd like to discuss various aspects of various "sciences." The aspects I had in mind were:1) Confidence in knowledge, 2) Status as a Science, 3) Facts and Inference, 4) The Roles of Observation, Confirmation/Repeatability, and Authority
Which sciences I pick is somewhat arbitrary. What we call "science" is arbitrary in many ways. Ultimately, each science is a study of something (and in that way we can have the "science" of anything).
But I believe what gives "science" its credibility, is the very fact that its results are so reliable. I believe what gives science its reliability is the precision of representation (which allows for the precision in testing and application) given to it by mathematics (or some equivalent proxy).
Physics is the study of "things." Ultimately, what demarcates it is what we can rigorously consider to be "things." Many make the demarcation here. "Hard sciences" study "things" while the other "sciences" study concepts that may not be "things."
Chemistry is the study of "stuff"--that is the study of "elemental" things and their interactions. The atom is the smallest unit of an element. In many ways physics and chemistry are the same, but their divergence increased when the notion of what is an "atom" froze at our current conception. Quarks, leptons, and Bosons could form an alternate concept of "atoms" and if this were the case, I doubt there would be much difference between Chemistry and Physics. But the selection of the atom for what it is was a eminently practical one for the study of interaction between elements.
Biology is the study of "living" things, not really quite the study of "life" itself. What it means to be "living" is a difficult distinction, but we know it when we see it (or at least believe we do).
I will also include many social sciences (the study of human beings and their interactions). I haven't decided which ones yet.
Also, I will divide the sciences into four categories. Mathematical sciences (pure and applied), Physical Sciences (Physics and Chemistry), Life Sciences (Biology), and Social sciences.
Again, what I include in each has a degree of arbitrariness. For instance, Computer Science could be called out separately from Applied Mathematics, but for now I am going to treat it as a subset. Also, Organic Chemistry (the study of the "stuff of life") could be included as a Life Science, but I leave it as a subset of Chemistry. Things like Geology, Astronomy, Material Science, Pharmacology, etc., I'll leave as subsets and compositions of physics and chemistry.
There is a whole host of other subjects, but I make the demarcations not by who does what, but by what is being study. So many physicists do a lot of Applied Math (that is studying certain general forms to see if they apply to reality), and biologists do applied physics (that is studying the living thing simply as thing based on physical laws), etc.
I'll be making a lot of judgment calls. Ultimately, it comes down to opinion.
Nevertheless, mine will follow.