One sense of "burden of proof" seems to be a game-rule for a (non-Bayesian) adversarial debate game. It is intended to exclude arguments from ignorance, which if permitted would stall the game. The players are adversaries, not co-investigators. The player making a novel claim bears the burden of proof — rather than a person criticizing that claim — so that the players actually have to bring points to bear. Consider:
A: God loves frogs. They are, above all other animals, sacred to him.
B: I don't believe it.
A: But you can't prove that frogs aren't sacred!
B: Well of course not, it never occurred to me to consider as a possibility.
At this point the game would be stalled at zero points.
The burden-of-proof rule forbids A's last move. Since A started the game by making a positive claim — the special status of frogs — A has to provide some evidence for this claim. B can then rebut this evidence, and A can present new evidence, and then we have a game going:
A: God loves frogs. They are, above all other animals, sacred to him.
B: I don't believe it.
A: Well, the God Book says that God loves frogs.
B: But the God Book also says that chickens are a kind of flea, and modern taxonomy shows that's wrong. So the God Book isn't good evidence.
A: I found a frog once that had the word "God" encoded in the spots on its back in Morse code.
B: But the spots on frogs' backs are probably pretty random. How many frogs did you have to check?
A: Umm ... a few thousand. It was a sacred duty!
B: But it would be a lot more convincing if all frogs had that pattern, wouldn't it?
A: Well ... Frogs are sacred in Homestuck, which is the most financially successful webcomic of all time. Surely that's a sign of God's favor.
B: They're sacred to Prospitians, yes, but Dersites think they're blasphemous. Besides, if financial success was a sign of God's favor, we should all be worshiping Berkshire Hathaway, not frogs.
According to the rules of the game, B doesn't have to establish that God hates frogs. B just has to knock down each one of A's arguments. Then, since A has failed to establish any evidence that holds up, B is (so far) winning the game.
One sense of "burden of proof" seems to be a game-rule for a (non-Bayesian) adversarial debate game. It is intended to exclude arguments from ignorance, which if permitted would stall the game.
I like this framing, but "burden of proof" is also used in other contexts than arguments from ignorance. For example, two philosophers with opposing views on consciousness might plausibly get stuck in the following dialog:
A: If consciousness is reducible, then the Chinese room thinks, Mary can know red, zombies are impossible, etc.; all these ...
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