It was pointed out earlier - and forgive me, but I forget by whom - that "burden of proof" really only applies if you're trying to convince the other person that you're right and they're wrong. Any time you fail to change the other person's mind, for whatever reason (be it adequately articulated or not), they've failed "burden of proof." Essentially: "you haven't convinced me, personally, so you have failed to burden of proof."
Or have they? Is it fair to say that if the argument doesn't convince some specific individual that burden of proof has not been met? Is it fair for the YEC to say "you haven't convinced me that evolution is true, so you've failed burden of proof?" then proceed to dismiss the whole thing as a bunch of ruddy nonsense?
This is the whole purpose of debate. When I say that theism "hasn't met its burden of proof", I am specifically saying "no piece or pieces of evidence, nor no argument, ever presented to me for the existence of a God or Gods has, I feel, been convincing enough to me, personally". I feel that the claim of the existence of a God is a particularly extraordinary one, and thus requires an extraordinary degree of evidence that has yet to be provided. I've seen lots of arguments, and every single one I have found significant flaws with. I've seen lots of supposed evidence, and I have found every single one to be either lacking or completely erroneous.
What would be nice is if we could follow and see the merit in arguments that are not our own and recognize that the other party has indeed provided proofs. Whether or not you personally agree with all of it is a separate thing entirely.
Again, this is the point of the whole "burden of proof" argument - it's that you have to support the claim you are making with positive proofs. If someone makes a claim, you cannot just assume that there is proof for it - the claim needs to be sufficiently supported before it can reasonably be believed.
I do not agree with classical monotheism, but their theologians have fantastic argumentation to buttress their theology. As far as I'm concerned, they've satisfied "burden of proof."
This makes no sense. If they have met their burden of proof, you would agree with their claims. Evidently, you aren't convinced of their position, so you cannot say that their claims have met their burden of proof for you, personally. Having arguments that support your position does not mean that those arguments are sufficient to satisfy that particular argument's burden of proof.
Claiming they haven't is just silly to me, and something that I find quite off-putting in a discussion. Honestly, the moment someone throws that phrase "burden of proof" out there in the context of informal, online discussions or debates my usual response is to roll my eyes and wait for the inevitable "but you didn't convince me, so you failed burden of proof."
Sorry, that's just how burden of proof - or any argument anywhere ever about anything - works.
There is a difference between "having" burden of proof, and "meeting" a burden of proof. Here is the difference:
Person A makes a claim.
Person B questions claim.
Person A must support their claim with evidence, as they hold the burden of proof to support their position. This is having the burden of proof.
Person A makes a claim that the sky is green.
Person B questions claim.
Person A presents evidence for his claim by showing a picture of the sky being green. The picture has clearly been photoshopped, and is therefore insufficient evidence on which to reach the conclusion that Person A's claim is accurate. Person A has not met their burden of proof.
I don't think this standard works for a large number of philosophical or religious discussions, though. Relatively few philosophical or religious ideas are falsifiable, but this does not mean there are not adequate proofs or arguments for these ideas.
In other words, I do not believe it makes much sense to demand that philosophy and religion adhere to falsifability; it's not applicable in many (if not most) cases.
And it is for those exact reasons that I, and people like me, simply do not believe in such religions or philosophies, and feel that it is irrational to do so.