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Notes -
I'm having trouble understanding the idea that "the onus is on the person making the positive claim to provide sufficient evidence to prove their case". It looks obvious why this is a good idea, but it seems completely open to the rhetorical trick of putting the onus on the other party to prove you wrong even if your own case is unproven (perhaps because the question is a hard one and whoever is tasked with proving anything will have a hard time).
What got me thinking about this was an internet argument on immigration and crime. Half a century ago the status quo was restricted immigration and the onus would be on the person advocating for more to prove that it was a good thing, nowadays the status quo is liberal immigration and the onus is on the person advocating restrictions to prove that it is a bad thing. No scientifically relevant change has taken place, only a change in government policy, but one side can now quote a basic principle of science to bolster their case in an argument even if they know nothing more than the other party.
The due diligence question is obviously is this actually a fundamental aspect of science as stated or is it misrepresenting a more nuanced principle?
I googled "positive claim" and one of the first relevant things that came up was Burden of Proof, which speaks as if positive claim means existential qualifier, For example, "there exists a teapot orbiting the Sun somewhere in the solar system." It contrasts that with a negative claim, which asserts the non-existence of something. Certainly, it is easier to prove a positive claim than a negative one.
The issue you're talking about seems to be more like "null hypothesis," which is definitely just cultural consensus and is essentially a rhetorical trick, and not very rigorous. When I took statistics class in school, I never liked null hypothesis as a concept, as I noticed that it didn't seem mathematical to me (although it was intuitive).
Science is not immune to this at least according to Yudkowsky. I've read attempts to formalize what burden of proof ought to be, and the ones that seem aesthetic to me are just having proof "in proportion to how complex the hypothesis is," which is in line with Occam (buzzword dump). This has the added benefit of ignoring the order that evidence is encountered.
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