One can't define or even deal with such definitions logically (in the standard sense), as truth-values are binary.
We're not talking about truth values, we're talking about belief. Belief is the acceptance of the claim as true, regardless of the truth value of the claim itself. It is quite logically simple to consider a person not accepting a claim as being true when they have not had the claim presented to them or are unable to process the claim - in much the same way as it is reasonable for a person to not accept the claim "sushi tastes delicious" without having tasted sushi.
However, extensions of logic to e.g., possible worlds or fuzzy logic allow us to deal formally and more flexibly with mental state predicates/epistemic claims. In fact, modal logic is an extension to classical logic (or extensions) which includes the addition of a modal operator that refers to/signifies epistemic modality.
Okee dokee.
Disbelief is not regularly defined or used to refer to an inability to accept that a proposition is true except insofar as "inability" refers to e.g., my "inability" to accept that creationism is true. I am actually capable of accepting that creationism is true in a way that e.g., rocks, infants, or those who have never heard of creationism are not.
In almost every definition I have encountered of disbelief, "inability" is a word regularly used.
"Not accepting" is an act.
Not necessarily. If you have not been presented with a claim, you are not in a position to accept it. You have no accepted the claim until such a time as the claim has been presented and you decide to accept it. Until then, it can be said that you do not accept it.
It requires that one evaluate a proposition, for otherwise it is not true one is "not accepting" it. I don't "not accept" propositions or positions that I am unaware of.
Yes you do, because that's the default position. You can't believe a proposition you have not been presented with, ergo the only position you can logically hold is that you do not accept the truth of that proposition. It's about an absence of the acceptance of the claim, not necessarily the rejecting of a claim after it has been presented.
It is quite literally to negate "holding".
No it isn't. NOT doing something is not the equivalent to doing its logical opposite. NOT doing something is merely the NOT doing of that particular thing. You can NOT hold a position while not holding a contrary position.
To "hold" or "have" a belief is to engage in a mental "action", and the negation of "holding" a belief is to engage in the opposite "action". It is to "hold" the negation of the proposition (to be true).
I agree. But to NOT hold or NOT HAVE a belief doesn't require any mental action, it merely requires not holding or having a particular belief.
Colloquially? Sure. And in that case I agree. But in that case it is senseless/meaningless to claim that anybody who hasn't evaluated some proposition/position X doesn't "hold X" the way that atheists don't hold that god exists. There are those who don't hold that god exists because they don't believe god exists, and those who don't hold god exists because they have no beliefs.
It's no less meaningless than asserting a null hypothesis, or stating a baby doesn't have a concept of good or evil, or that rocks are incapable of thought. It is merely a description of a mental state. Can it be applied to babies, amoebas and rocks? Sure, technically. I don't see how that diminishes in any way the function of the term or what it refers to. The fact that it is so broadly defined doesn't make it meaningless. If it were meaningless, I wouldn't be able to define it so concisely and you and I wouldn't be having this discussion.
To "not hold a belief" is quite literally (or logically) to hold that the belief is not true.
No it is not. To not hold a belief is to simply not hold a belief.
You are choosing to rely on colloquial definitions in one case and reject them in another: infants don't hold beliefs about god(s) because they neither disbelieve nor believe in god, while atheists DO hold beliefs about gods, which is the definition of atheism.
Wrong. Atheism is a lack of belief or disbelief in the existence of Gods. Atheists don't necessarily have to hold a position about Gods.
There are infinitely many things that any given person doesn't hold a belief regarding, yet we have no words for these "non-beliefs" in general because we don't define words or mental states in general in terms of "lacking" or not "having". Atheism is meaningful and is used as a word only because it refers to a position, not the lack thereof.
It has just as much meaning being defined as a lack of belief, which is what the word both literally and etymologically refers to, than it does referring to a more specific position. I have heard it argued that defining atheism so broadly makes it "meaningless", but I have never once heard sufficient justification for this argument and have never found it particularly compelling.
The general idea seems to be that "broad = bad" whereas "specific = good". I find this distinction unjustified and arbitrary, and I personally find the whole wrangling over the definition itself absurd. I define atheism in the broad sense because it's what makes the most sense to me considering both the definition and origin of the word, and for framing the debate correctly by identifying atheism as the null hypothesis. I only tend to end up debating the definition of the word when people insist that this broader definition is somehow "incorrect" or shouldn't be used for some arbitrarily defined reasons which are never sufficiently explained. It really shouldn't matter this much, and it's a constant source of irritation to me that people are so insistent that something so arbitrary as using a broader definition a word - provided you give that word clear and concise definition when debating it - can be a source of such lengthy diatribes.
I have no issue with anyone starting a debate about atheism and explaining that, for the sake of that debate, they are defining atheism as "the belief in the non-existence of God" rather than using my definition. I only have an issue when someone tells me that my definition of atheism is "wrong" or "inaccurate" based on some poorly defined criteria that assumes that a word is somehow less useful and functional if it can be applied more broadly, despite the fact that it has a very specific function and value.
