I understand it this way. There are three terms describing two different concepts encased to two different verbs. 1. to know. 2. to believe. I am an agnostic atheist. I do not believe in the existence of God or Gods so I am an atheist. I lack belief. I disbelieve. I am an atheist I use them interchangeably and it is a choice I make in view of what I see as a lack of evidence. I do not know if there is or is not a God or Gods. I do not think we can know if there is or is not a god or gods. I am therefore an agnostic. An agnostic theist would be someone who agrees that he does not know there is a God, does not think we can know that there is, but believes that a God exists as a matter of choice. All you have to accept to understand this, is that the human mind can choose to believe or not believe in something even if there is no claim to know or even that it can be known. Post script. I am not in here to debate these concepts or definitions. You can agree or not. I don't care. I thought my restatement might be useful for clarity.