I've previously noted that some of the deepest philosophical disagreements are traceable to differing assumptions about what needs to be explained.
A reductionist might assume that we simply need to explain the third-personal empirical data: e.g. the facts that we have certain brain states, make certain vocalizations, etc. They then deny the reality of any further philosophical phenomena (e.g. irreducible qualia, normativity, etc.) on the grounds of parsimony: none of that is necessary to explain the scientific data. You don't need to posit moral facts in order to explain the occurrence of moral intuitions.
That's true enough. I don't think scientific inquiry should lead us to believe in moral realism. But I also don't think that science exhausts all there is to know. The philosophical 'data' may be more expansive than the empirical data, since we may know things other than third-personal observational facts. For an obvious example, I know that I'm phenomenally conscious. This datum calls out for explanation. For another example: we can (I assume) also know various moral/normative truths, in which case the search for a systematic moral/normative theory would be well-motivated (despite the fact that it wouldn't help explain the limited subset of data that the reductionist exclusively concerns himself with).
There are also various facts about epistemic normativity which call out for explanation. For example, I take it as given that rational induction is possible. We ought to believe that an emerald first observed after 2020 will be green, not grue. Such differences in 'projectability' may motivate positing objective structure: arguably, the reason why we can project 'green' but not 'grue' is because the former property is metaphysically privileged in an important sense. It is a more "natural" property, in the sense that collections of green things are (in respect of their colour) objectively more similar than collections of grue things.
So, realists (of various stripes) will dispute the reductionist's limited construal of 'the data to be explained'. This raises the difficult question: how can we make dialectical progress in resolving such fundamental disagreements? Are there generally acceptable moves for supporting or undermining the inclusion of a particular claim as "given"?
It seems there must be some constraints here. Something has gone badly wrong with the person who takes the existence of the Flying Spaghetti Monster as a datum. This seems like a belief that should be undermined by skeptical probing, if it does no essential work in explaining anything else. But then why can't the skeptic likewise dispense with any other self-contained cluster of beliefs (say, normative beliefs; or even empirical beliefs!), if they do no essential work in explaining anything else? What is it that makes empirical beliefs (and, arguably, normative beliefs) indispensable in this way?
I'm unsure what to say about this. My best attempt at an answer is to appeal to transcendental / "may as well" arguments. At least in case of epistemic normativity: anti-skepticism is a precondition for successful inquiry, so we may as well take it on faith. If we're wrong, we're screwed anyway; but if we're right -- if we have any chance at all of attaining knowledge -- then this assumption positions us to make the most of it. (Cf. Intellectual Black Holes.)
A similar argument applies to practical normativity: we may as well assume there's something we ought to do (then work out what it would be, and act accordingly). It's only on this assumption that our choices matter -- that we ever act rightly or wrongly -- so this is the only possibility that is worth taking into account.
It's less clear whether any such neutral justification can be given for the assumption of first-personal subjective experience. In this case, it's more of a Moorean fact: something we're more certain of than we are of any argument to the contrary. The inescapability thus looks to be merely psychological: there's little I could say to someone with different beliefs -- e.g. a self-identified "zombie" -- to convince them that they're really conscious. (One of my undergrad professors insisted that he has no idea what all this talk of 'subjective experience' is about.)
This shouldn't necessarily undermine the belief. We have little option but to reason from what personally strikes us as true -- even if others think differently, that shouldn't make it impossible for us to come to justified beliefs. But, on the other hand, nor should we want subjective certainty to suffice for justification: someone might be irrationally certain that the FSM exists, after all. The difficulty is that, at the bedrock level, there are no neutral arguments left to distinguish between the various positions. It looks like we must simply make a stab in the dark and insist that certain views (our own, if we're lucky) are brutely justified and others aren't.
It would be nice if we could say something a little more illuminating.