I don’t see the problem. If someone claims they have a method that can produce knowledge, then it is reasonable to expect them to demonstrate their claim is true by using this method to produce knowledge. You disagree?
IOW, math and logic are subsumed within the scientific method. That is exactly what I wrote.
You are again begging the question, by assuming that moral positions are objective truths. Like many others who have spent time thinking about this issue, I don’t consider “Murder is wrong” to be knowledge about the world that we have discovered. Rather, it is just a rule we made up. It’s a good rule, don’t get me wrong. I like that rule. But a rule is all it is.
You seem to think the scientific method does not use human perception. You are wrong about that.
But how do we know “pain is real”? I would suggest it is thru the scientific method. We know we have a particular subjective experience in response to a number of stimuli. Other people report the same experience. In addition, non-human animals exhibit behavior that is consistent with how we would expect them to if they also had this subjective experience. All of these empirical observations support the hypothesis “Pain is real.”
It would be a mistake to think that the term “science” only refers to rigorous experiments published in peer-reviewed journal. It is, rather, a generalized approach to understanding the world, and we are using it all the time.