Baloney. "X" is merely a placeholder.
That's the entire point. This is simple (symbolic/formal/mathematical) logic. Or, alternatively, you could formulate it in set-theoretic terms, abstract algebras, modal logic, many-valued logics, etc. The result is always the same: negating the predicate (even a mental state predicate) is not only not equivalent to negating the argument/element of a relation/operator/function/etc. The difference with respect to a predicate like belief is that sentential/predicate calculi (classical formal logic) fails to be truth preserving here, which is why the most typical alternative is to use possible worlds semantics/modal logic. Personally, my familiarity with mathematics, empirical models, the cognitive sciences, etc., tends to make me more inclined to adopt e.g., belief functions (or their extensions into subjective or Bayesian frameworks) over and against non-classical logics, but the point is it doesn't matter. Whether I define the set X that contains all and only members with the properties of being deities/gods, some element god in a set of worlds W and a relation for a triple in modal logic, a belief function as below:
or any other method of treating mental state predicates or predicates involving "beliefs" in a consistent, truth-preserving, and logical way will consistently show that given any "blank space", variable, set, etc., that some person P doesn't believe in, we can make this hold true of all possible admissible variables or set members without defining each and everyone or even knowing these.
For example, consider the statement "I believe that there all real-valued multiples of 2 are even". I need not and
cannot define all of these (there are countably infinitely many), but I can prove the truth of the statement. Likewise, when I say "I don't believe Elves exist" it is absurd to require that I name e.g., every elf in Tolkien's work. Indeed, to say that I don't in any single-celled mammals, I don't need to know any mammals or single-celled organisms.
Are we now free to move along with our lives, or is there anything else regarding this (non-) issue that you'd like to hammer out?
Your basic understanding of a rather simple matter would be one issue.
And exactly how does one arrive at a belief like that?
It is utterly irrelevant. The issue is what statements about belief entail and imply. When you can't distinguish between "doesn't believe" and "believe doesn't", the issues involved evaluating rational beliefs, epistemology, etc., are much too sophisticated, nuanced, and subtle.
Are you saying that you simply define god(s) out of existence?
Of course not. I'm not even saying that the statement "I don't believe any gods exist" actually means that "I believe no gods exist" (as this is incorrect). I'm saying that the statement "I don't believe any gods exist" has the minimal interpretation that "for any possible entity/thing X that I believe in/believe exists, X doesn't have the property of being a god". A stronger interpretation (that equivalent with "I believe no gods exist") is "for any possible entity/thing X, I believe that X doesn't have the property of being a god".
That's a king-sized red herring if ever there was one.
It's so utterly basic and incredibly important it lies at the heart of linguistics, set theory, logic, category theory, and in no small way the sciences. It is the root of cognition itself.
Meanwhile, all anyone who wishes to make assertions one way or the other concerning the existence of elves really needs to know is that there's no evidence.
In which case, you're little reference to which gods one doesn't believe in is completely unfounded and irrelevant. After all, one possible way of describing the situation is that all "anyone who wishes to make assertions one way or the other concerning the existence of [gods]
really needs to know is that there's no evidence", and
not the names given to particular non-existent gods.
Again, agnosticism concerns what is known and atheism concerns what is believed.
Your idiomatic definitions aside, agnosticism was quite literally defined by a single person and adopted more widely as a needed term to describe a belief regarding god(s) that wasn't non-belief/atheism or belief (theism, polytheism, deism, etc.).
Are there not people out there seeking to prove that the Loch Ness Monster, Bigfoot, and God exist because ... while they believe it ... they don't know it?
Obviously.
If that's your chosen metaphor, I'm going to assume that it follows that theists are finding god guilty of existence and I am finding him not guilty of existence. That doesn't mean I feel God is innocent of existence, correct?
As soon as you move into the area of god's actual "verdict", you leave the metaphor entirely. The point is that one can render (and in the metaphor/example indeed MUST render) a verdict yet need not (and in this case can't) know what the actual verdict should be.
So you'd view "I don't believe" as a counter claim instead of a reaction to a claim?
Again, trivially and obviously so. Every belief can be phrased as non-belief and vice versa.
Heath Ledger's Joker's quote (from
The Dark Knight). Not a typo.
Seriously? Any belief claim is a claim to have knowledge?
Yes.
Being convinced, I believe that there is a cabbage in the box.
Then you cannot believe the proposition "there is nothing in the box that is a cabbage" is true, meaning that you are making claim about the nature of contents of the box, meaning that you claim to know something about the contents of the box. Every epistemic (belief) claim is a function of degree of subjective certainty regarding the truth of the claim.
Do I in fact possess any knowledge whatsoever regarding the actual contents of the box, or not?
I didn't say you did. You seem to have a difficulty with understanding the difference between an epistemic claim or belief and the truth of the statement that the belief/claim concerns. You can possess no knowledge about X proposition, but to say you believe that X is true is to
claim that you have knowledge about (the truth of) X.
And within those demarcations, we demarcate between those who believe any given proposition regarding the alleged qualities that the god or gods in question may or may not actually possess from those who aren't convinced that the god or gods in question possess these alleged qualities.
This is wrong, but I suspect you don't mean what you have implied and are just not used to the logical/formal linguistic issues with "any", so I'll refrain from commenting to give you a chance to look it over again.
That's the theistic quagmire as I see it from the atheistic side of the fence
Perhaps because, in addition to the problem I referred to immediately above, you've conflated theism with non-theistic beliefs, have failed to differentiate between the various demarcations among those who don't believe in any god(s) by incorrectly and inadequately shoehorning all such beliefs (which, as demonstrated above, you can't adequately evaluate/analyze) into the category "atheism", failing to deal with religious beliefs that involve no claims concerning gods, and finally failing to dealing with the quagmire that concepts in general have been shown to involve (especially since the work by Zadeh, by Rosch, by Lakoff, and by Langacker, although these and other pioneers make up a tiny amount of the work involved in the nature of categorization, conceptualization, fuzzy sets, etc.).