One of the most mistaken aspects of reasoning in the Great Debate is over aspects of propositions, and namely, what denial is.
Example: “This is a square.”
We could deny this and mean a couple of things. First, we may lack sufficient reason to agree that “This is a square.” We may actually have sufficient reason to believe that it isn’t true that “This is a square”, though we may not know what else it actually is. Finally, we may actually know better. “This is really a rectangle.”
People usually mistakenly translate the denial of a proposition as the belief that its contradiction is true. So, mistakenly, denying “God exists” means one thinks “God does not exist”. This is not the case.
When denying “This is a square”, it’s clear that there’s no contradictory belief to hold. There’s no opposite to “square”. This implies denial applies to how the case is presented. In other words, “This is a square [is the case]”. Denial applies to this property of the proposition. Denial is then as follows:
Correct: [It is not true that] This is a square [is the case]
Incorrect: This is not a square [is the case].
Don’t see a difference?
If the proposition is “Steve’s T shirt is green” and I deny it, it’s not because I believe “My T shirt is not green.” It’s because I am not wearing a T shirt. Hence, denial is correctly “[It is not true that] Steve’s T shirt is green [is true]”. This shortens to simply “That’s not the case.” And consequently, I would deny the contradiction, “Steve’s T shirt is not green”.
The mistake happens honestly because of “negative facts”, contradiction, and “The Excluded Middle”. Folks mistake denial for contradiction. Above, with “This is a square”, insufficient reason and reason to doubt cause denial rather than contradiction. When two ideas cannot both be true at the same time, and cannot both be false, there’s a contradiction. With contradiction, something either is or isn’t. Either there is a God or isn’t, either it is a square or isn’t, either my T shirt is green or it isn’t. These have no “middle” ground. But as we see with my T shirt, denial isn’t contradiction though contradiction can cause denial.
So denying that “God exists” doesn’t mean a person believes “God does not exist”. It means they deny there’s reason to believe “God exists [is the case].” It happens that Atheists, Agnostics, and Theists alike, can all deny the proposition “God exists” yet have various beliefs about the existence of God.