I was inspired to ponder the eight positions as a result of watching this series of videos by Aron Ra. He talks about belief and knowledge about god, but I think his presentation was incomplete, and this was the cause of some confusion in the Q&A session at the end.
"Does god exist?" I won't be trying to answer that question here. Instead I'm going to talk about answers. Whether we can answer the question is not the focus, but there are two classes of statement that should be addressed. They are the four positions on knowledge, and the four positions on belief.
I know god exists.
I know god does not exist.
I do not know that god exists.
I do not know that god does not exist.
Whether or not something can be known is the province of epistemology. Stating that something is known is that gnostic position. Stating that something is unknown is the agnostic position. I agree, for the moment, with the agnostic position that nothing can be known about god.
First, what is knowledge? Knowledge is distinct from belief in that we can all agree that a thing can be believed without being true. Many people pay good money for homeopathic potions, content in the belief that they are purchasing genuine cures. They are incorrect; they've purchased expensive water. They will be somewhat better hydrated, but they won't be taking medicine. For all that their belief in the efficacity of their nostrum is sincere, and for all that they believe they have evidence to that end, they are incorrect. Their certain belief does not rise to the level of knowledge.
The position of the strict agnostics, that nothing can be known about the existence of god, should be the default position, only abandoned in the face of evidence, or very good argument, to the contrary. Most theists, when pressed, will admit to agnosticism. "There's a reason it's called faith." Even the most ardent atheists will usually also admit to being agnostics.
So on the question of knowledge, the four positions are divided into two categories: gnoticism and agnosticism. I know, one way or the other, or I do not know, one way or the other. Regardless of what they believe, most people will admit to being agnostic.
I believe god exists.
I do not believe god exists.
I believe god does not exist.
I do not believe that god does not exist.
These four positions are divided into two categories: theism and atheism. The split is not the same as that of the gnostic/agnostic divide.
The two atheist positions are "I do not believe god exists." and "I believe that god does not exist." These are called weak and strong atheism respectively. The terms are not intended to be pejorative by definition, though they are sometimes used that way. Rather, weak atheism is so called because the statement is fundamentally negative on the part of the user.
The statement "I do not believe that god exists" places the negative aspect in the belief of the atheist. It is a responsive position. The theists posits that god exists and the atheist responds "I don't believe that". It's not a positive statement about the existence of god one way or another. This is in contrast with the strong position.
"I believe that god does not exist" is a positive, descriptive statement. It's a positive position on the part of the declarer about the existence or non-existence of god. Just as the theist is declarative when he says that he believes that god does exist.
Aron Ra, in his video, stated that the correct position is the weak position. I agree that it should be the default position and absent further argument or evidence, it cannot be abandoned. However, I disagree with him that there is no further argument or evidence. The various gods posited by theistic beliefs are all interventionist, with an impact on the world. Anything that alters the world can be tested by the scientific method. Further, supernatural hypotheses all necessarily suppose either that the deity is deceptive, acting to mask their intervention, or that the deity's intervention can be detected due to the violation of otherwise natural causality. As no evidence exists of supernatural intervention, the deity is deceptive, non-interventive or non-existent.
As for intervention, scientific studies have been performed on the efficacy of prayer. Not only did the studies find no positive benefit, it was determined that, when the patient is aware of the prayer, it has a negative placebo effect; they do worse. In this light, a deity is either non-intervening or non-existent.
We now come to the position that the non-intervening deity is functionally equivalent to the deist's position: the creator who then does nothing. However, our study of the cosmos gives us an alternative hypothesis for the origin of everything. We know the universe is closed, open, or flat; regardless, each one gives us an explanation for the existence of everything (the "problem" of why anything exists rather than nothing is usually advanced as a strong argument for a deity). There is no theory of the cosmos that cannot explain existence. The god hypothesis is superfluous. Worse, it's not even an explanation! The god proposed is even more inexplicable than the thing it's being proposed to explain! It takes the thorny problem of existence up to eleven!
The confusion I mentioned above was over the difference between the strong and weak atheist positions. Because Aron Ra hadn't clearly explicated the difference as the position of the negative. The querent queried, in essence, "Why do you believe their is no god?", mister Ra and, I believe, Matt Dillahunty, replied "I don't believe there is a god" The discussion went back and forth with the querent asking the same question and receiving, essentially, the same reply.
Next: Strong versus Weak Theists.