That said, there really isn't much to defend when it comes to mere unbelief. Once one notices that he has no reason to believe a particular proposition, then, given that we want to minimize such unjustified beliefs, we ought to give it up. The interesting question, then, is whether or not we can find a reason to think that God exists, and that is where the theist has a striking burden of proof.
Calvinist blogger Brian Knapp of choosinghats.com recently posted his own complaint to this situation. According to him, while we might not have a burden of proof defending unbelief in other gods, the Calvinist God is different, because it insists that we all know it exists (presumably this doctrine is based on his reading of Ro 1:18-25, and possibly other Biblical passages). He writes:
Now, if the God of the Bible was like any other god, they could get away with saying "no" and leave it at that---no burden of proof. However, the God of the Bible isn't like any other God. He claims that everyone knows he exists. He claims that he created the world. He claims that his existence is necessary for knowledge, ethics, aesthetics, etc. In short, he makes a bold claim about everyone's ability to reason, weigh evidence, draw conclusions, etc. He claims that none of those actions that we all do on a daily basis would be possible unless he existed as described in the Bible.
So that opens up an interesting challenge to the atheist. They aren't explicitly denying the existence of God when they say "I don't believe he exists", but they most definitely are *implicitly* denying his existence. Why is this? Well, it is because they are doing all these things that the God of the Bible claims ownership to, while at the same time they are saying "I don't believe he exists." They are relying upon all these basic beliefs that the God of the Bible claims *only* make sense if he exists.
To say they don't believe he exists is to say that it is *possible* to do these things (reason, weigh evidence, etc.) without him existing. But God says it is not possible to do them without him existing. Therefore (by implication) they are saying "This kind of God *does not* exist".
It isn't an explicitly positive claim that God does not exist, but is rather an implicitly positive claim. Either way, it is a positive claim, and therefore they own a burden of proof.
For Brian, the fact that we all believe God exists is corollary to something like an essential property of the Calvinist God. So to insist that we don't believe in his Calvinist doctrine is to deny the existence of his God; and this constitutes a positive claim in need of defense.
Now, before I address this, we may wish to make clear a certain distinction: for in one sense it is quite true that any self-professing atheist has his own sort of burden of proof with respect to the authenticity of his profession, insofar as a skeptic of genuine unbelief in God such as Brian might challenge him to defend it. This is not, however, the same as a defense of the negative atheist position itself. In other words, to challenge the accuracy of his self-identification as an unbeliever is not to challenge his justification for unbelief. The question of whether or not a person who declares himself negative atheist is justified in so doing is wholly separate from that of whether or not he ought to actually be an atheist, or other similar issues. So, maybe the Calvinist thinks this person is lying or self-deluded, and secretly believes in God despite insisting that he does not. Yet even if that's the case---indeed, even if we can prove it to be so---to the extent that we're interested in discussing the justification for negative atheism, we've made no progress.
Even so, Brian may be right to point out that in order to be consistent even a negative atheist must deny the existence of his highly specialized Calvinist conception of God (though even this is questionable). Yet the defense for disbelief he provides himself: our initial unbelief quite directly disproves the existence of the special Calvinist God which everyone knows exists. What additional proof does he require, the burden of which he thinks the atheist should shoulder? Now, he could always challenge our very unbelief, but that would, I think, move the conversation in a largely unproductive direction. We all trust our own ability to tell the difference between that which we do and do not believe. So for instance if I take myself not to believe one way or the other on the existence of a fifth moon of Pluto, that should be the end of the matter. It seems unlikely that any deeper self-reflection in that regard would be fruitful. Unless there is some outstanding reason to think ourselves in the throws of an unhappy delusion resulting in the subconscious repression of our belief in a fifth Plutonian moon, why should we consider the matter any further? I find myself in a similar situation with respect to my unbelief in God. It's possible that I'm just self-deluded, and that I really do believe in God, despite my second-order belief to the contrary. Yet we can say the same for any of our beliefs. Why afford this one special attention?
So while I appreciate Brian putting his finger on an interesting implication of Calvinist dogma, I must disagree that it has much bearing on the burden of proof had by negative atheists. Again, it seems like the most important issue is whether or not we have reasons to believe in God. It is certainly true that, as negative atheists, we should be responsible communicators and charitable interpreters, doing our best to understand and respond to the case for theism. However, in the end, the burden is on the theist to provide reasons for his belief.