The question of the knowability of God and the belief of his existence are two distinctly different propositions:
p=”God exists” (ontology) vs p=”knowledge of God existing is possible” (epistemology)
By smashing together or juxtaposing terms like “agnostic” and “atheist” the intended usage of the phrase “agnostic atheist” is a vague mishmash of terminology, and quite ambiguously confusing as it can seemingly mean:
I believe God does not exist, and not asserting as knowledge. (atheism).
I believe God does not exist, and believe God’s existence is knowable. (atheism + soft agnosticism)
I believe God does not exist, and believe God’s existence is unknowable. (atheism + hard agnosticism)
I do not believe God exist, and not asserting as knowledge. (weak atheism)
I do not believe God exists, and believe God’s existence is knowable. (weak atheism + soft agnosticism)
I do not believe God exist, and believe God’s existence is unknowable. (weak atheism + hard agnosticism)
If used as an epistemic modifier you have:
~Kp ^ B~p (Does not know God exists and believes God does not exist) (strong atheism)
~Kp ^ ~Bp (Does know God exists and believes God does not exist) (weak atheism)
In the ~Kp ^ ~Bp case it seems superfluous to add in ~Kp as it is just making the same statement strong atheism is making.
In the ~Kp ^~Bp case it seems nonsensical and at best superfluous as if you do not believe God exist you have not met the sufficient conditions for knowledge (one being S believes p) and therefore merely holding to ~Bp would entail ~Kp as knowledge is a subset of belief. It to me however makes no sense to try to epistemically modify a “does not believe” position as again knowledge is a subset of belief, so it would require belief before any epistemic modifier is applied.
Taking “agnostic atheist” as two separate proposition seems to lead to even further confusion and ambiguity:
Agnostic atheist (Logically)*
~Bq ^ B~p
Bq ^ B~p
B~q ^ B~p
~Bq ^ ~Bp
Bq ^ ~Bp
B~q ^ ~Bp
The reason it’s “unknown” with ~Bp is that one can lack a belief because:
1) They can be agnostic and not have a position either way (~Bp ^ ~ B~p).
2) They can believe p is false (B~p) which entails they do not believe p (~Bp).
So it is ambiguous and unknown.
Leading into even more ambiguity, it could also mean:
“I do not believe nor disbelieve that I believe God exists” (Agnostic on being atheist?)
“I do not believe nor disbelieve that I do not believe that God exists” (Agnostic on lacking a belief?)
“I do not believe in God, and I don’t know if God exist” (At best this is superfluous as if you don’t believe in God you clearly don’t know if God exist, and at worse it is nonsensical as knowledge is a subset of belief)
“I believe God does not exist, and I don’t know if God exists” (Superfluous, same as just atheism)
Once again, I firmly believe people can use any terminology they wish to label themselves…but I am merely pointing out that such use of terminology is vague, imprecise and I believe epistemically misguided. The usage of the words “theist” and “atheist” are to convey ones ontological position on the existential nature of God, not to express any epistemological views on whether or not God’s existence is knowable or not. These are two different propositional questions in two different branches of philosophy…ontology vs epistemology. When one says that they are “agnostic” it normatively infers a state of indecision on the question of “Does God Exist?” or suspension of judgment on the proposition p=”God exists”. They are merely related in that when one suspends judgment on the ontology because of indecision, because agnosticism is also a normative epistemic principle as well as an epistemological proposition, it can be modified to mean the existence of God is knowable or may be knowable (soft agnosticism) or can not be known (hard agnosticism). While it is true it is not a direct answer to the ontological question, it is a response and it is a response with nuance. Nuance that is simply lost when people injudiciously use phrases like “agnostic atheist”.