Okay, let's go with that.
"I dont believe your claim a desktop monitor exists"
"I believe there is no desktop monitor before you."
What's the difference? You didn't explain any distinction between the two statements.
In statement A, I am not making a positive claim. I am only making a statement of
disbelief of your claim about the existence of a computer monitor.
In statement B, I am making a positive claim. I'm am making a statement that I believe there is no monitor, in
direct contradiction to your claim.
With statement A, I remain open to the possibility of there actually being a computer monitor.
I can still be convinced, either way, that a monitor exits or it does not exist.
With statement B, I am closed to the possibility of computer monitor existence. I not only assert that the statement "a computer monitor" exists if false, but I also
make the claim there is no monitor.
Statement A is most analogous to 'soft/weak/negative' atheism (or 'agnostic atheism'). Statement B is most analogous to 'hard/strong/positive' atheism (or 'gnostic atheism').
It is when there's only two options.
Nope.
Even when dealing with a binary choice, its not an A or B option. Its an ['A' or 'Not-A'] and a ['B' or 'Not-B'] set of options. Each set deals with a separate horn of the binary choice dilemma - at least when responding to a claim.
For the coin toss, you could claim its heads. I can accept this claim (A), I can not accept this claim (Not-A), or I can reject it and make a counter claim of tails (B). The counter claim deals with a separate horn of the dilemma though.
Not accepting your claim of heads doesn't require me, in any way, to propose that the result of the coin toss is tails. There could be any number of reasons why I don't accept your claim. Until more or better information is available to me, there's no reason to move beyond non-acceptance.
There is a similarity with a criminal suit in a court of law. A person is either innocent or guilty of a crime. That's the binary. A or B.
However, when it comes to pleading and determining the outcome, the defendant doesn't plead 'guilty' or innocent' ('A' or 'B'), they plead 'guilty' or 'not guilty' ('A' or 'Not-A'). Similarly, the jury doesn't find 'guilty' or 'innocent', they find 'guilty' or 'not guilty' That's dealing with a single horn of the dilemma.
There's a key distinction to be made between the existence of a true binary and believing a claim concerning a binary (made by a third party).
The drivers license in my wallet is either expired or valid. If I claim that its valid, and you say you don't believe me,
are you arguing that it is expired?
Who on earth made up this imaginary "rule" you people continually spout?
I didn't "spout" an imaginary rule. And who are "you people"?
If you're referring to the basic laws of logic, I think Aristotle is generally credited with formally writing them down (although I suspect others preceded him, we just don't have their writings).
Creating more questions than you can answer is never helping.
I'm just trying to explain atheism to the best of my understanding and ability. I don't see where I created questions that are unanswerable. You didn't explain the questions I was creating.