There is often debate between believers and nonbelievers concerning the burden of proof on various issues (but particularly that of god's existence). I am not sure that everyone understands how the notion of burden of proof works logically. Most, especially believers, seem to think that it is a single standard that always rests upon one party or the other.
In fact, the logical burden of proof will both vary in the amount of proof required and shift from one party to the other depending on the circumstances.
Generally, however, both in logic and in law, we all recognize that the burden of proof with regard to a proposition is on the person advocating the proposition.
In the law, burdens of proof are usually defined by statute. As most people are aware, the standard for a criminal conviction (at least in the U.S.) is proof beyond a reasonable doubt, but in the case of a civil suit, the standard is merely proof by a preponderance of the evidence. While it is true that the interpretation of these standards can be a bit more subjective than we might like to admit, they do provide distinct standards that differ significantly.
A preponderance of the evidence simply means that one party's evidence is greater than the other party's. The "beyond a reasonable doubt" standard is clearly a much higher standard when compared to the preponderance standard. It skates close to the line separating practical certainty in the real world from solipsistic uncertainty.
Burdens of proof are also affected by presumptions. One of the reasons the criminal standard is so much more difficult to meet is because of the presumption of innocence. Our society has made a value judgment concerning the relative harm done by wrongfully convicting an innocent person. This harm has been judged to outweigh the harm done by failing to obtain a conviction in other cases.
Likewise, logically, the harm that could be caused by believing in things that have no factual basis should lead any logical person to demand a greater level of evidence when deciding whether to accept a proposition that shows distinct signs of having no factual basis. Or, as Carl Sagan phrased it: "Extraordinary claims require extraordinary evidence."
Furthermore, burdens of proof are divided into burdens of production and burdens of persuasion. The minimal burden a party can bear with regard to a proposition he advocates is the burden of production. That burden requires that the party produce some evidence that the proposition he advocates is true. The amount of evidence in that case doesn't necessarily have to be enough to persuade others, merely enough to justify a presumption that the proposition could be true.
When sufficient evidence has been produced to meet the burden of production, then and only then does the question of burden of persuasion arise. If a party with the burden of production has no evidence, then there is nothing to examine and the case, or contention, is dismissed out of hand because it is not worth wasting time over it. In such cases, it is conclusively presumed, and logically so, that for purposes of that particular inquiry the proposition is false. The opposing party in such cases has no burden of proof at all.
This, of course, is precisely the case with religion. Religion has never even met its burden of production much less its burden of persuasion.
The religious argue that the existence of the universe meets both the burden of production and the burden of persuasion, but, as I pointed out before, this is circular reasoning. The mere existence of a mystery tells us nothing about the answer to it. Unless, that is, one implicitly assumes that only one answer is possible. But such an assumption by itself needs to be proven as well. So far the religious haven't even proven that their "invisible magic man in the sky" theory deserves to be considered a possible explanation--much less the only possible explanation.
So, one of the things you can say to believers in this regard is:
"You haven't produced any evidence at all that your invisible magic man in the sky theory deserves even to be taken seriously as a possible explanation for existence--much less the only explanation. Until you do, let's just agree that no one even knows what the possible explanations for existence are."