@Gubiosak, I can't seem to reconcile your renewed questions. You say you're asking,
but we already answered that question.
I asked for specific counterexamples. You said,
but we already discussed logic, mathematics, and moral philosophy as potential sources of knowledge, including whether it was even meaningful to ask whether they are "scientifically testable."
The problem I have is that you reopened the debate with:
I have a problem with your replayed examples as proper to "beliefs about realities." And I have a problem understanding what types of evidence you think should apply to them.
What evidence is even needed to validate statements in categorical logical? Categorical logic doesn't require evidence and its rules don't rely upon it. Rather, categorical logic is applied
to evidence, and as such forms the backbone of the scientific method. We take it as read that categorical logic produces knowledge from combinations of propositions. It doesn't makes sense to ask what kind of evidence justifies belief in a categorical syllogism. Hence I don't think that's what you're really asking about.
What evidence is needed to validate beliefs about mathematics? Certainly basic arithmetic can be confirmed empirically. Under the common understanding of the symbols "2", "3", "5", "+", and "=" I can write 2 + 3 = 5, and confirm under that understanding that if I have two apples and acquire three more, I will have five apples.
But math includes such abstract questions as whether a set of vectors forms an orthonormal basis for a vector space. Justifying your belief that a certain set does requires nothing more than applying the contrived definitions. Knowledge in that case is merely consistency with contrived rules. Empirical verification is not possible. It makes no sense to ask what evidence supports abstract mathematics, so I don't think that's what you were asking about.
Again you have the cart before the horse. We don't use the scientific method to test propositions in mathematics. Instead we use mathematics in the scientific method. Most empirical studies that we design employ some kind of statistics model that helps us reason objectively about the likelihood of certain outcomes given the value of a variable. That helps us understand whether an effect follows a change in value. We take it as read that these models tell us what we want to know.
What evidence would justify a belief formed according to moral philosophy? Previously you gave us a toy example, but I countered with a more difficult one showing how we variously consider either
mens rea or
actus rea (alone, in the absence of the other) to variously establish moral blameworthiness—a manifest contradiction. And as such I argued that moral philosophy cannot ever produce anything more rigorous than belief, to which you had no rebuttal. I can show you empirical evidence of the belief being held by a group of people, but there is no evidence possible that the belief is true. That's because veridical truth is not something moral philosophy can attain. So no, I don't think that's what you were asking about.
And again moral philosophy applies to the practice of science in designing empirical experiences that have the potential to cause harm or be blameworthy in other ways. We don't use the scientific method to justify moral decisions, but we use moral philosophy to determine whether a desired application of the scientific method might have moral consequences.
In answering others, you added
We already discussed "subjective conscious experience," and you were unable to convince anyone that the so-called hard problem of consciousness established anything that needed separate justification. If you want to ask other people what kind of evidence justifies a subjective perception as evidence of reality, you need to provide a better argument that there's an effect requiring an explanation beyond that already given.
You are coy about "metaphysical claims about the nature of reality." So no, vague handwaving doesn't entitle you to ask for what kind of evidence justifies any particular metaphysical belief.
And again you repeat the question you've received the same answer to many times: no, we do not believe that the scientific method is the only way to get knowledge.
We already answered that question in terms of the types of claims you raised previously. You don't acknowledge any of those answers so I don't think they were really what you were interested in.
That leaves the supernatural, which you say you're "not necessarily" interested in. You told us you believe that science has properly dismissed claims of the paranormal and supernatural. But you keep revisiting your epistemological handwaving using paranormal-coded language, whose previous categorical dismissal you seem to be walking back.
Paranormal claims are touted by their claimants as a different type of belief that requires different types of evidence. Hence your repeated asking for what kinds of evidence rationally would justify these beliefs that you insist lie outside scientific inquiry hits that nail precisely on the head. You ignore the discussion of all your ill-fitting decoy examples, so we have to keep reminding you that if your plan is to discussion the epistemology of supernatural claims, just say so and quit dancing around the issue.