Statements of total disbelief

The problem with a statement such as 'I do not believe anything' is that it is contradictory. If you really do not believe anything, you also do not believe the statement in which you just said exactly that. There is danger in adopting contradictions. The principle of explosion allows every possible other statement to become true. In other words, a naive statement of total disbelief is in fact, exactly the opposite of what it looks like. Valid statements of disbelief must allow for at least one exception. You could, for example, say: 'I do not believe anything except for this very statement'. That would almost work, if this statement did not suffer from infinite recursion.

Since a statement of complete disbelief must contain at least one correctly-chosen exception, it is paradoxically also a strong statement of belief, exactly in that one exception. Example: 'I do not believe in any gods except for the one true god'. Then, what about 'I do not believe in any unicorns except for the one true unicorn?' Here, it depends on the definition of unicorn. In terms of the lambda calculus, both statements will most likely turn out to be alpha-equivalent. Only the form of what you say, really matters.

Atheists also disbelieve in any gods, but they would probably want to use another exception to keep their total disbelief consistent. What alternative exception do atheists propose?