Been pondering the thread title and the OP for some time, trying to work out an answer that satisfies me. It's a deceptively complex set of issues. I am, as most of you know, a committed and unapologetic admirer of science, it's the only reliable means we've ever found for testing the truth content of ideas, but I would not for a second ever argue that it's the only way to know things. Some ideas just aren't amenable to its methods. If you want to make empirical claims about the nature of the world around us, science is what you need, but if you want to talk about human feelings, science often isn't very useful. That may be just a matter of our ignorance, maybe we don't know enough to usefully apply science's methods to human feelings, but I'm inclined to doubt that. One of the more interesting results of science, Godel's theorems, amount to a proof that science cannot know everything: any system of formal logic complex enough to include arithmetic will contain within it propositions whose truth or falsity cannot be determined. They're originally purely mathematical theorems and there's a great deal of debate about whether they can be applied more broadly, but it seems to me that if mathematics has any relationship to reality at all--and it certainly seems to--we have to concede that there are claims we can't ever know to be true or false.
Not quite a satisfactory answer yet, that's as far as I've got so far.
Not quite a satisfactory answer yet, that's as far as I've got so far.