I proposed for consideration a bit of dialog:
A: The law of noncontradiction (LNC) is a law of thought merely.
B: I dispute your claim. LNC is not a law of thought merely; it is also a law of extramental reality.
In this example, B disputes what A says by making a counter-claim, a counter-assertion. Both are asserting. It strikes me as foolish to ask who has the burden of proof (BOP). How decide such a question? I assume that in a dialectical situation like the above, if BOP considerations are relevant at all, then the BOP is on one side or the other, but not on both, and not on neither. But there is no non-arbitrary way to place the onus probandi on one side or the other. Therefore, BOP considerations are a useless detour. Why not go straight to the question and evaluate the arguments pro et contra?
Suppose you say that the BOP rests on the one who opposes the received or traditional view. Then the BOP would be on A. But if you say that the BOP rests on the one who makes the stronger claim, the more committal claim, then the BOP would be on B. I don't see how there could be a non-arbitrary assignment of BOP in a dialectical situation like this. Correlatively, I don't see how it could be non-arbitrarily claimed that there is a defeasible presumption (DP) in favor of A's assertion or of B's. So I suggest we drop the BOP talk!
Lukas Novak's response:
Concerning your dialogue: In my opinion, both A and B bear a burden of proof here. For that reason, it is an unlucky start of a dispute - because it is in fact the start of two disputes at once, and a dialectical confusion is likely to arise. In order that the dialogue be fruitful, B should not have put forward a negation of A's claim as his own claim, but simply refuse to accept A's claim until proved (this is the meaning of the rule Necessitas probandi incumbit ei qui dicit non ei qui negat - "negare" here has the technical meaning of "to refuse to concede until proved", according to the rules of disputation). If A failed to produce a proof, his case would fail. If he produced one, his case would succeed unless and until B attacked that proof, thus prompting another argument to "restore" the former one. And so on, until one of the parties failed to do their duty. Only if A was the one who so failed, would it be in place for B to state his opposite meaning as a claim, if he wishes, with the burden of proof incumbent on him
There are three, not two possible dialectical states of a proposition: (i) proved (ii) disproved (iii) neither. The "burden of proof" just means that the default state is (iii).
Perhaps our difference boils down to this: you think that a dispute is about truth or falsity of a proposition, whereas I think that it is about validity or invalidity of rational support of a proposition. Whereas from the former point of view the dialectical situation comes out as symmetric, in the latter view it is inherently asymmetric.
Reply to Novak
Part of our difference here may be due to a different understanding of 'dispute.' I think Lukas may be using it is a technical way similarly as he uses negare in a technical way. And perhaps these technical meanings are the same. When I used 'dispute' in the little dialog above I was using it to mean 'disagree with.' Lukas seems to be using it to mean 'refuse to concede until argument is provided.'
Lukas seems just to be assuming that the BOP rests on A who must "produce a proof" otherwise his "case would fail." I take that to mean that A is obliged to give an argument for the claim he has made. (In my book, an argument is not the same as a proof, although every proof is an argument.) But, by my lights, if so, then the same goes for B: he too must give an argument for his counterclaim. B cannot just cross his arms across his chest and say, "I don't have to give an argument for my assertion; it suffices for me to poke holes in your argument. The BOP is on you, not on me." This is precisely what I reject. Otherwise, there would be a presumption in favor of B's claim. But there isn't. And to insist that there is, is to beg a philosophical question.
I think Lukas is right when he says that, for me, the dialectical situation is symmetric, at least in the example given above, while for him it is asymmetric.
Lukas is also right when he says that, for me, the dispute (disagreement) is about the truth-value of a proposition: Is it true or is it false that LNC is a law of thought merely? He says that, for him, the disagreement is "about validity or invalidity of rational support of a proposition."
But this needs explaining. Validity and invalidity are technical concepts from formal logic. Our present topic, however, is not formal logic, but dialectics. Lukas seems to think that there are certain procedural rules that govern the conduct of a discussion, and that these rules induce certain rights and duties in the interlocutors. Thus, he who makes an assertion puts himself under a dialectical obligation to support his assertion with one or more arguments, while the one to whom the assertion is made is under no obligation to support the negation of the asserted proposition: he has the right to do no more than find fault with the arguments for the asserted proposition.
I am skeptical of this entire adversarial model which has its provenience in the court-room situation and makes perfect sense there, but seems to me not appropriate in philosophy which, by my lights, is not a matter of debate or disputation but one of dialogue in which the interlocutors are not out to prove propositions they antecedently accept and do not question, but who aim at arriving at the truth together, a truth that they do not claim to possess, but are seeking.
See also: Philosophy, Debate, and Dialog