I would classify your first definition as nontheism, which is technically agnostic atheism, yes. And of course the most popular form of atheism.
The second is textbook agnostic atheism, except I think somewhere in there is the bridge between the lay person identifying themselves as an agnostic or an atheist. This is also what questioners become when they turn to the internet to settle their beliefs, and it's kind of annoying. I speak from some experience with youtube atheists, among which there are few really stimulating philosophers.
Rather rare, and downright rational for Anslem's God. But I wouldn't say it's the belief that gods are impossible, that's just the mechanism we use to get to it. Gnostic atheism is just the belief that god's don't exist.
The second is textbook agnostic atheism, except I think somewhere in there is the bridge between the lay person identifying themselves as an agnostic or an atheist. This is also what questioners become when they turn to the internet to settle their beliefs, and it's kind of annoying. I speak from some experience with youtube atheists, among which there are few really stimulating philosophers.
Rather rare, and downright rational for Anslem's God. But I wouldn't say it's the belief that gods are impossible, that's just the mechanism we use to get to it. Gnostic atheism is just the belief that god's don't exist.
