1. When I referred to "randomly made-up laws", I didn't mean a reality the actual laws of which are somehow random, but the rules we make up for how the world supposedly works, so the distinction is between laws we derive from past observation and laws we just make up instead.

As for your use of "investigation": Could you explain how you would investigate something that is not reproducible, or in general how you would investigate something in a way that leads to results that do not depends on empiricism?

I would think that as soon as you throw out empricism, you throw out investigation. If some event is completely random ("not reproducible"), that by definition means that you cannot know or deduce any rule for why/how it happened, which in turn means that you cannot even try to cause such an event or know where to look in order to observe it, so I don't see how you would "investigate" under such circumstances.

So, while I agree that there might be things you cannot investigate with empiricism, I would think that almost by definition, you cannot investigate those things at all, as investigation relies on empiricism.

2. No, I don't fail to notice that, very much the opposite. What I thought I stated very explicitly is that if empiricism does not work, assuming that it does work gives you the same expected outcome as assuming that it doesn't work. So, the actual outcome indeed likely would differ depending on whether you assume that empiricism works or doesn't work, so if you assume that it does work, you incur an opportunity cost of those possibilities that might lead to a better outcome - but you have no way to distinguish those from the choices that lead to worse outcome, and on average ("expected outcome"), assuming empiricism gives you as good an expected outcome as any other choice.

As for that "if you can't influence it" thing: I don't get your point, but I think I was a bit ambiguous, so let me rephrase my point: "find me anyone who seriously disagrees with that and also thinks that it matters whether you believe in some god or not and would argue about it (if you can't influence the future anyhow, and thus can't influence whether you believe or not, why should it matter?)".

As for your last example: I think you are contradicting yourself? I do understand it correctly that beauty also is one of those things that you think is not easily measured with a scientific mindframe? And yet, you explain one possible scientific approach to beauty? I would think it's almost trivial to measure all of those scientifically - in just the way you describe. It's all kinda about what people like - and the only reliable way to figure out what people like is empirical: You ask them and you observe their reactions to different circumstances. What would you suggest instead?

Really, I think you may want to think about what it actually is that you suggest to use instead of empiricism wherever you think empiricism does not apply. Just saying "something else that is not empiricism" is easy, but what would that look like? Have a close look at whatever you think the alternative is, whether there is any component of a known concept or a rule of how/why/when things happen or what some action will result in it. If there isn't, then how do you even formulate it? If there is, check whether there is any reason to prefer it over its opposite. If there isn't, then why don't you believe the opposite? If there is, that probably is where empiricism is hiding.