1. The question this post raises is whether it is at all useful to speak of burden of proof (BOP) in dialectical situations in which there is no judge or tribunal to lay down and enforce rules of procedure. By a dialectical situation I mean a context in which orderly discussion occurs among two or more competent and sincere interlocutors who share the goal of arriving as best they can at the truth about some matter, or resolving some question in dispute. My main concern is with dialectical situations that are broadly philosophical. I suspect that in philosophical debates the notion of burden of proof is out of place and not usefully deployed. That is what I will now try to argue.
2. I will begin with the observation that the presumption of innocence (POI) in an Anglo-American court of law is never up for grabs in that arena. Thus the POI is not itself presumptively maintained and subject to defeat. If Jones is accused of a crime, the presumption of his innocence can of course be defeated, but that he must be presumed innocent until proven guilty is itself never questioned and of course never defeated. The POI is not itself a defeasible presumption. And if Rescher is right that there are no indefeasible presumptions, then the POI is not even a presumption. The POI is a rule of the 'game,' and constitutive of the 'game.' The POI in a court room situation is like a law of chess. The laws of chess, as constitutive of chess, cannot themselves be contested within a game of chess. The reason there is always a definite outcome in chess (win, lose, or draw) is precisely because of those nonnegotiable chess-constitutive laws.
As I pointed out earlier, defeasible presumption (DP) and burden of proof are correlative notions. The defeasible presumption that the accused is innocent until proven guilty places trhe onus probandi on the prosecution. Therefore, from the fact that the POI is not itself a defeasible presumption in a court of law, it follows that neither is the BOP. Where the initating BOP lies -- the BOP that remains in force and never shifts during the proceedings -- is never subject to debate. It lies on the state in a criminal case and on the plaintiff in a civil case.
3. But in philosophy matters are otherwise. For in philosophy everything is up for grabs, including the nature of philosophical inquiry and the rules of procedure. (This is why metaphilosophy is not 'outside of' philosophy but a branch of same.) And so where the BOP lies in a debate between, say, atheists and theists is itself a matter of debate and bitter contention. Each party seeks to put the BOP on the other, to 'bop' him if you will. The theist is inclined to say that there is a defeasible presumption in favor of the truth of theism; but of course few atheists will meekly submit to that pronunciamento. If the theist is right in his presumption, then he doesn't have to do anything except turn aside the atheist's objections: he is under no obligation to argue positively for thesism any more than the accused is under an obligation to prove his innocence.
4. Now we come to my tentative suggestion. There is no fact of the matter as to where the BOP lies in any dialectical context, legal, philosophical or any other: it is a matter of decision. This is because BOP is a procedural matter. If so, then there must be an adjudicator above the fray (i.e., a judge or arbiter who is not party to the dispute) who makes the decision as to where the BOP lies and has the power to enforce his decision. There must be an arbiter who lays down and enforces the rules of procedure. But in philosophy there neither is nor can be an above-the-fray adjudicator whose decisions are unquestionable and backed by the threat of violence.
For suppose I were to try to play the arbiter in a debate between a theist and an atheist. I give the following speech:
There is a presumption in favor of every existing institution, long-standing way of doing things, and well-entrenched and widespread way of belief. Now the consensus gentium is that God exists. And so I lay it down that there is a defeasible presumption in favor of theism and that the burden of proof lies squarely on the shoulders of the atheist. Theism is doxastically innocent until proven guilty. The theist need only rebut the atheist's objections; he needn't make a positive case for his side.
Not only would the atheist not accept this declaration, he would be justified in not accepting it, for reasons that are perhaps obvious. For my declaration is as much up for grabs as anything else in philosophy. And of course if I make an ad baculum move then I remove myself from philosophy's precincts altogether. In philosophy the appeal is to reason, never to the stick.
The situation in philosophy could be likened to the situation in a court of law in which the contending parties are the ones who decide on the rules of procedure, including BOP and DP rules. Such a trial could not be brought to a conclusion. That's the way it is in philosophy. Every procedural rule and methodological maxim is further fodder for philosophical Forschung. (Sorry, couldn't resist the alliteration.)
My tentative conclusion is as follows. In philosophy no good purpose is served by claims that the BOP lies on one side or the other of a dispute, or that there is a DP in favor of this thesis but not in favor of that one. For there is no fact of the matter as to where the BOP lies. BOP considerations are usefully deployed only in dialectical situations in which some authority presides over the debate and lays down the rules of procedure and has the power to punish those who violate them. Such an authority constitutes by his decision the 'fact' that the BOP lies on one side rather than on the other.
It follows from what I have said that if you disagree with me, then neither of us bears a burden of proving his metaphilosophical thesis. But this is paradoxical. For if you disagree with me, then presumably you think that BOP considerations are usefully deployed in philosophy, and that there is a fact of the matter as to where the BOP lies, and that therefore one of us must bear a probative burden.