For a while now I've been trying hard to understand philosophical viewpoints that defer from mine. Somewhere along the line I've picked up or developed a lot of the LW-typical viewpoints (not sure if this was because of LW, or if I developed them earlier and that's what later attracted me to LW), but I know there are a lot of smart people out there who disagree with those viewpoints. I've tried to read articles and books on this, but they either don't address what I'm looking for somehow, or they're so technical that I have a hard time following them. I've also talked at some length with a philosophy professor, but our conversations often seem to end with me still being confused and the professor being confused about what it is I might be confused about.

I'm thinking maybe it'll help to get some input from people who do intuitively agree with my viewpoints, hence this post. So, can someone please tell me what the central arguments or motivations are for promoting the following:

Epistemology:

• Trusting philosophical intuitions and/or the way people use words to the point of making strong metaphysical claims about the world, despite the findings of cognitive science / evolutionary psychology / experimental philosophy / etc. that there doesn't seem to be any good reason to trust those intuitions / ways of talking
• Not looking at the world in a probabilistic way
• Using personal preference or personal intuitions as priors instead of some objective measure along the lines of Solomonoff Induction

Ontology / philosophy of mind:

• Moral realism
• Mathematical Platonism
• Libertarian free will (I'm looking for arguments other than those from religion)
• The view that there actually exist abstract "tables" and "chairs" and not just particles arranged into those forms
• The existence of non-physical minds (I'm looking for arguments other than the argument from the Hard Problem of Consciousness)

I suspect I'm having trouble with the ontology issues because of my trouble understanding the epistemology issues. Specifically, I keep getting the impression that most (all?) of the arguments for the ontology issues boil down to trusting philosophical intuitions and/or the way people use words. Something along the following lines:

I intuitively feel that there really are objective morals (or: objective mathematics, actual free will, tables and chairs, minds).

Therefore, there really are objective morals (etc.).

Or the equivalent using the way people talk about things.

But this just seems totally ludicrous to me. If we trust cognitive science, evolutionary psychology, etc., and if those fields give us perfectly plausible reasons for why we might intuitively feel this way / talk this way, even if it didn't reflect the truth, then what could possibly be your motivation for sticking to your intuitions anyway and using them to support some grand metaphysical theory?

The only thing I can think of is that people who support using intuitions like this say, "well, you're also ultimately basing yourself on intuitions for things like logic, existence of mind-independent objects, Occamian priors, and all the other viewpoints that you view as intuitively plausible, so I can jolly well use whatever intuitions I feel like too." But although I can hear such words and why they sound reasonable in a sense, they still seem totally crazy to me, although I'm not 100% sure why.

Any help would be appreciated.