So, although Burden of Proof is empirical canon at this point, it still is a rather unsatisfactory response to a question as legitimate as any: the question that asks how, if you can't prove that unicorns don't exist, do you know they don't exist? The traditional answer is that you can't, and I think we can all agree on this; however, I wish to expand on that answer.
I find a fundamental difference between absolute reality, that which exists as an absolute, and relevant reality, which I will call relevance for this thread. Relevant reality is that which is, as the name suggests, relevant. The difference between the two is that absolute reality exists absolutely, regardless of whether we can know that a given object in absolute reality exists or not. Relevance is a subset of absolute reality; relevance is everything that can be observed (See farther down), and therefore still contains existing things, but does not contain the unobservable but existent things that could exist in absolute reality, such as unicorns. Therefore, unicorns could exist, but aren't relevant because they are unobservable.
This is my reasoning for Observation=Relevance:
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Relevance can be defined as when something has an effect on another thing, and therefore is relevant to the thing it is having an effect on.
For something to be said to have an effect on something else, we must be able to observe that effect.
We can only observe things by the effect they have on us, even so minimal as by the photons it emits for our eyes or the indirect ways our instruments detect them.
Therefore, all things that can be observed (directly or indirectly) have an effect.
Therefore, all things that have an effect on something are relevant to that thing by way of that effect.
Therefore, all things that have an effect on us are relevant to us.
Therefore, all things we can observe are relevant to us by way of their effect on us.
Therefore, anything we cannot observe is not relevant to us because it has no effect on us due to being unobservable.
So when Johnny says that you can't prove that unicorns don't exist, he's right; but you can prove that they're irrelevant by way of their lack of evidence.
Because of this, I think that the Burden of Proof is not so much a requirement of proving the existence of something in reality, as it has been used, but is rather a necessity of proving something's relevance. It's all semantics, but it's interesting, and it gives you a smart response next time Johnny says his unicorn (or god, as probability would have it) can't be proved nonexistent. It's even more devastating, in my opinion, to be able to logically prove such silliness irrelevant, which is much more biting in its own way that nonexistence.
Do you guys agree that observation=relevance and burden of proof is better suited for relevance than reality? Input is welcome.