I think the problem of strongly asserting nonexistence is purely a puzzle of logic or language. We lack terminology and language for something that is, informally, in between strict existence and non-existence, such as things that are proposed without evidence but taken seriously. I've been thinking about this since reading about things like faster-than-light travel, and the singularity.

Then the question is whether it's useful to assign a third category, or just to combine it with one of the original two categories. My own feeling is that strong versus weak atheism is not a useful distinction.