I have been surprised to find that some people doubt this principle. Onus probandi incumbit ei qui dicit, non ei qui negat - the burden of proof lies with the speaker, not with the one who negates. I cite Russell's Teapot and Hitchen's Razor. Occam's Razor provides context to the argument. I have seen no convincing argument against this principle.
The burden of proof falls on the one who makes the claim because, usually, they don't make this claim in a vacuum, without any goal in mind: they want other people to accept their claim and adjust their behavior accordingly.
- "I believe people who wear corduroy pants offend God and I want you to stop wearing those."
- "I think project X is a waste of resources and you should stop working on it."
Imagining a person making a claim without any specific goal, or without wanting other people to believe the claim is kind of difficult. It does not make sense; why make the claim in the first place? But if such a case were to exist, the burden of proof would not be an issue. "You believe the Earth is hollow, but don't care if I think the same and don't want me to do anything about it? Cool. You do you."
There is also the special case of claims with very small stakes, like "Hello, my name is Mike". The claimant clearly expects their vis-a-vis to adopt the behavior of calling him "Mike", but people rarely ask for ID to prove such a claim, because the stakes are very low.
If one wants people to change their behavior based on a claim, it's only fair that this person does the legwork to convince whoever they are addressing the claim to. In other words, the one who requires the change in behavior has to have people consent to this change. Otherwise the only option left to have them comply is force, i.e. potentially tyranny.
A decent argument could be made for this principle based on various moral theories, like the Golden Rule, Kant's Categorical Imperative, and Social Contract theory.
The "burden of proof" is the principle that if you have a good reason to believe what you believe, and you want me to believe what you believe, you ought to say your good reason to believe what you believe, and not rest your argument on the demand that your interlocutor explain why you shouldn't believe what you believe.
Saying, "You have the burden of proof, not me!" in place of an explanation of your good reason to believe what you believe... is resting your argument on the demand that your interlocutor explain why you shouldn't believe what you believe.
The burden of proof is merely the result of trying to figure out what beliefs we should start with and what should be proven from there.
It stops you from believing anything and everything without question, and being consistent in your reasons for believing things.
Consider the legal system: if someone is suspected of murder, we don't just throw them in prison unless they can prove they're innocent. The burden is on proving guilt.
There are justice-related reasons for this. But also, functionally speaking, it may be somewhere between difficult and impossible to prove innocence. How would you even be able to prove that at no point did you kill someone? You may need to account for every second of your time over days/months/decades. Whereas proving guilt merely needs to establish what happened at one particular moment in time.
And if 2 people are independently suspected of murdering a particular individual, do we just throw both in jail? They couldn't both have independently murdered the same person (putting aside from fringe cases where someone's heart stops, is restarted, and then stops again, although it's arguable whether the first case would then be murder). Concluding that they did so would be contradictory, and this could trivially be extended to 3 people, or 4, 5, 100, a million or 8 billion.
Similarly, if someone proposes the existence of some being, we shouldn't just accept that it exists without question. Proving non-existence is somewhere between difficult and impossible (combing every inch of the planet to prove that Bigfoot doesn't exist), and the existence of different beings may contradict one another. The burden should be on proving existence.
The idea of the burden of proof is almost universally accepted in some capacity (whether it's accepted by that name or not). It's pretty fundamental to how we learn things about reality. If you're in the forest, it wouldn't be smart to just eat random plants assuming they're safe to eat, but rather you should stick to ones you already know to be safe (if any) and look for proof that others are safe before eating them.
When people try to argue against it, they don't tend to argue against the principle as a whole (or they argue against a strawman of it), but rather they argue that a particular claim or set of claims shouldn't be subject to the burden of proof or that the burden of proof should be on the opposite claim. This is common in theistic discussion, where atheists ask for proof of God's existence, but are often instead asked to prove God's non-existence, or where theists say that God's existence doesn't need to be proven, that it's something that everyone already believes, or that it's a presupposition.
Maybe there's also some corner of philosophers who reject the idea of the burden of proof altogether (maybe those who don't believe in objective reality). Although I might challenge anyone who claims as much (unless they have almost zero autonomy), because I suspect you'd have a hard time surviving for more than a few days without that.
Note: "proof" in "burden of proof" doesn't mean a conclusive, 100% reliable and exhaustive mathematical or logical proof (which isn't possible for claims of reality in any case). It merely means sufficient evidence or other justification to warrant accepting a claim.
The burden of proof is the fundamental tenet of skepticism. It insists that there is a burden to prove, and that is not accepted by many people.
I have seen no convincing argument against this principle.
Yes you have, and it's called faith. Faith is a guiding principle for far more people currently and throughout history than doubt. And in fact, it can be extended beyond theological arguments. Philosophy explores this under the topic 'fideism'. From WP:
Fideism (/ˈfiːdeɪ.ɪzəm, ˈfaɪdiː-/) is a term used to name a standpoint or an epistemological theory which maintains that faith is independent of reason, or that reason and faith are hostile to each other and faith is superior at arriving at particular truths (see natural theology). The word fideism comes from fides, the Latin word for faith, and literally means "faith-ism".1 Philosophers have identified a number of different forms of fideism.2 Strict fideists hold that reason has no place in discovering theological truths, while moderate fideists hold that though some truth can be known by reason, faith stands above reason.
In my own upbringing, the chief argument of faith was presented as Jesus's exhortation to be as children and submit to the love of God.
And he said: “Truly I tell you, unless you change and become like little children, you will never enter the kingdom of heaven. Therefore, whoever takes the lowly position of this child is the greatest in the kingdom of heaven. And whoever welcomes one such child in my name welcomes me.” - Mathew 18:3-5
It is a call to humility to submit to the will of God, and is American as apple pie in the sense that fundamentalist Christian refugees populated the East Coast starting in the 17th century and continue to resist the call to reason. Prosperity theology in the US thrives on rejecting the skeptical burden of proof for better or worse.
That argument may not convince you, but the argument is alive and well and is accepted by billions of people.
Let us take an interesting example , suppose your neighbour claims he is your Dad ,then where does the burden of proof lies? On your neighbour ,or your mother ,or on you ,or your present Dad ? The situation is very tricky. Once a doubt in relationship has been created , you would like verify it yourself by asking your mother. It is also possible that your neighbour might like you to verify the claim by doing DNA testing. Burden of proof is a subjective prerogative. It depends on the situation.
The rule of onus probandi states that the burden of proof lies with the speaker, not with the one who negates, see the OP's question.
The three other principles mentioned in the OP’s question are characterized by wikipedia as follows:
"Russell's teapot is an analogy, formulated by the philosopher Bertrand Russell (1872–1970), to illustrate that the philosophic burden of proof lies upon a person making empirically unfalsifiable claims, rather than shifting the burden of disproof to others”, see https://en.wikipedia.org/wiki/Russell%27s_teapot
“Hitchens's razor is an epistemological razor that serves as a general rule for rejecting certain knowledge claims. It states "what can be asserted without evidence can also be dismissed without evidence."”, see https://en.wikipedia.org/wiki/Hitchens%27s_razor
“Occam's razor [...] is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements”, see https://en.wikipedia.org/wiki/Occam%27s_razor
All of the three principles are not laws of nature. They cannot be detected by research. Instead, they are principles of debate as @KristianBerry points out. Therefore they have to be negotiated.
The principles of Russell’s teapot and Hitchens’ razor do not imply that it is always the person, who makes a claim of existence (proponent), who has the burden of proof (rule of onus probandi), but not his opponent.
The rule of onus probandi breaks the symmetry between the proponent and the opponent, because it shifts the burden of proof to the proponent.
A fair debate should provide some argument, why to follow this rule, and should secure the agreement of the interlocutors to accept the rule of onus probandi.
An argument for accepting the rule of onus probandi in a debate between theism and atheism could be: The proponent can prove his claim of existence just by presenting the one entity. While the opponent in general cannot show the non-existence of the entity on all locations.
The asymmetry is between showing the existence on one location and showing the absence on all locations. The only chance of the opponent is to detect a logical contradiction in the argument of the proponent.
Hence, the evidence of logical inconsistency in the claim of the theist is one of the strongest arguments in the hand of the atheist. See Leibniz’ attempt to argue against the criticism uttered against the theistic position.
If there is agreement that the premisses of Occam razor are fullfilled, then it seems reasonable to prefer the more simple theory: Why make it complicated when you can make it simple?
I think burden of proof should be understood in a context of a claimant versus a skeptic. The claimant, taking initiative, says X is necessarily true. The skeptic says that X may possibly be true, but not-X may also possibly be true. The burden of proof is on the claimant to convert the skeptic from a position of uncertainty to one of certainty.
For example, take presumption of innocence in the U.S. legal system. The burden of proof is on the prosecution to convert a skeptical jury from uncertain of guilt to certain of guilt. The defense is not required to convince the jury of innocence. Nor, despite the term "presumption of innocence", is the jury expected to initially believe the accused is certainly innocent; the jury starts out uncertain.
I think "burden of proof" is more controversial and less applicable when it involves trying to change someone's mind from a "status quo" position of certainty to an opposite one. I.e. the claimant says X, and the skeptic currently believes not-X. You could argue the claimant has the burden of proof because she is trying to change the status quo, but you could argue that the skeptic is also claiming a position, not-X, which also requires proof. In this case there could be a lot of arguing over which stance is actually the "status quo" and who has the burden of proof.
It's useful to ask the question outside the realm of theology. We accept many things on the basis of trust: for example, the fact that a hydrogen atom has one proton and one electron, or the fact that Britain is an island, or the fact that vaccines confer immunity. We believe these things primarily because there is no reason to doubt the veracity of the claim, and we have confidence that the claim could be proved, or has been proved, even though we haven't seen the proof and might not understand it.
But if there is reason to doubt the claim, for example, because we don't trust the person making the claim, or because other people claim the opposite, then it's reasonable to argue that we shouldn't believe the claim unless the person making the claim can prove it to our satisfaction: at that point, the burden of proof falls on them.