Literally without theism . What is often described as atheism, the active disbelief in a god or gods, is more properly termed strong atheism . Zeus, for example, I imagine everyone is strongly atheistic about. Those of us who call ourselves atheists are typically strongly atheistic about nearly every popularized form of god, including the Christian, Islamic, and Jewish forms thereof. But they are not right because of a failing of the atheist's position.
Logical rules are only usable on concepts that are fairly well defined.
The concept of a deity is among the most nebulous and vague concepts that humans continue to talk about. Typically, once someone pins down some specifics about their favorite deity, it becomes a simple matter to show some inherent logical contradictions. If you don't think that logic is a good method for determining what to believe, make an attempt to convince me of that without using logic. No one has even bothered to try yet. I'm optimistic enough to think that we've moved mostly beyond the force stage, you're unlikely to convince me with emotion, and there just seems to be something odd in using logic to argue that logic isn't trustworthy.