If I have to believe something, it's safe to say I don't have evidence. If I do have evidence, then I know it for a fact and I don't have to have faith that it is so.My point is that you have basic assumptions and philosophical pre-commitments regarding metaphysical and epistemological matters such as the nature of reality, reason, laws of logic, explanation, certainty, universals, possibility, cause, and so on, which determine how you view evidence, and those assumptions about reality and knowledge have not and cannot be proved by empirical experience or logic, but rather it is by those beliefs that you proceed to prove everything else.
An example of this is your statement, "rejecting claims that cannot be backed with evidence is rational and justifiable. But how do you prove the claim itself? What evidence is there for it? If there isn't any evidence for it isn't it, on it's own terms a belief and therefore self-referential? Second, if believing something without evidence is irrational, is a person holding such a belief violating some sort of intellectual duty or obligation? Is such a person suffering from some sort of intellectual dysfunction?
Well, what you thing to be rational and justified depends upon your metaphysical and religious or philosophical assumptions. Your view as to what sort of creature a human being is will determine your views as to what is rational or irrational for human beings to believe and whether you think such persons are suffering from some sort of intellectual defect that deserves your approbation. Suppose you assume that the universe is a gigantic, uncreated, purposeless accident. The question then becomes, what is the evidence for the notion of matter in motion not functioning as it "ought" to function?
Ignorance of absolute truth does not allow us the freedom to invent truth, to create invisible and undetectable things and claim they exist. Our proofs must be compatible with our nature. We can't presume something exists unless we have evidence of it that is not only in our heads, but clearly demonstrable directly or indirectly.
Is a proof a visible, detectable thing? Where do these rules of thought that you espouse come from?
Cordially
Unlike those how claim "spiritual knowledge," I can show you how I know and if you have any doubts you can try it yourself. Such as "don't touch the hot stove top, but if you don't believe me, go ahead!"
Proof is a (readily) detectable and repeatable thing, not something only the "endowed" with "eyes" and "ears" can see and hear, but everyone, because we are visible, detectable creatures living in a visible and detectable world.
Now, in the course of our developing civilization, we have come to know that there are things which we cannot see or detect with our natural senses, but need special tools. The discovery of such things shows us that they, even though undetectable to our natural senses, are part of the same physical universe we see around us, and are subject to the same laws as we are, and that the differences are in degree and not in kind. Nothing "supernatural" has been discovered—ever, be it on a microscopic or cosmic scale, so then what justifies assuming that "supernatural" exists?
You write "Suppose you assume that the universe is a gigantic, uncreated, purposeless accident. The question then becomes, what is the evidence for the notion of matter in motion not functioning as it "ought" to function?"
There is no reason or justification to make such an assumption any more than to assume it is created or purposeful, because we don't know, just as no one knows what, if anything happens after this life. I simply recognize that—as of today—we don't know what this is all about with any certainty, that it is a blank page but not necessarily outside our capacity to discover. As for matter, it functions the way it functions, whether we understand why or not.