The point stands no matter how you write it - those two things are not equivalent. Case in point, an agnostic fits one of those, but not the other. An agnostic

The point stands no matter how you write it - those two things are not equivalent. Case in point, an agnostic fits one of those, but not the other. An agnostic does not believe in a god, but they also don't believe in "not god". If those two things are equivalent, then "not Belief(god)" and "not Belief(not god)" couldn't both be true (as they are for agnostics). The issue is not that you need to find a way to frame it as boolean logic, the issue is that we don't believe in boolean logic. Belief has more than two states. Of course, this is all a side track because the central point remains: believing there is no god does not require disregarding the possibility of being wrong any more than believing in anything does. It simply means you think it is the most reasonable belief given what you know at that time, as with any belief.