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.
None of which are convincing arguments for the existence of a god or gods. So I'll skip addressing the mathematical window dressing you've offered up. Don't get me wrong, however. It was all
very impressive looking.
... 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.
Again, I think Tolkien would have argued that he only resorted to calling them "elves" based on linguistic convenience. He wasn't trying to insist that they bore any resemblance to the faerie beings of known folklore. But as I've already said, the reference to elves seemed like a red herring anyway.
Indeed, to say that I don't in any single-celled mammals, I don't need to know any mammals or single-celled organisms.
I presume that when you say "that I don't in any single-celled mammals" you meant "I don't
believe in single-celled mammals."
I'll grant that one way to lack belief in any single-celled organisms would be to be totally ignorant of them. But if the non-believer in this case is offered evidence that single-celled organisms exist, it would seem to me that they've been afforded an opportunity.
Your basic understanding of a rather simple matter would be one issue.
And which rather simple matter would that be? Not the one that required all the flashy math and brackets, I hope?
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.
I'm fairly certain that you're talking down your nose to me without justification. You've certainly not demonstrated that the distinction is lost on me. You've merely asserted it.
Meanwhile, one who "doesn't believe" isn't making a positive assertion. One who "believes doesn't" is. One who "believes doesn't" has adopted the same burden of proof that one who "believes does" is obliged to shoulder.
If they want to convince anyone else, that is
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"
I don't believe that there are any spuds on this plate. I also believe that there are no spuds on the plate. The obvious difference with this example is that we have a concrete item to examine as evidence. So perhaps it isn't admissible?
...
I think most atheists are simply saying something akin to: "None of the theistic arguments that I've heard concerning the existence of a god or gods has convinced me." And they're not obliged to resort to intricate mathematical razzle dazzle.
Yet there certainly are atheists who claim
to know that a god or gods don't exist. It really depends upon the claims being made by the theist(s) in question. If someone claimed that their god was a circle with 359° ... then I'd feel confident in declaring that I know no such god exists. But typically, theistic claims aren't that specific.
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".
It sounds like you've erred there somewhere. When someone says "I don't believe any gods exist" they aren't looking at a set of things that they
already believe in and then denying that these
admittedly extant things lack "the property of being a god" (whatever
that happens to be).
Wouldn't it be better to say: "For me to believe that any possible entity/thing X exists (whether it has the property of being a god or not*), that entity/thing X would have to be demonstrated to actually exist?"
Who cares what X's properties are if you cannot demonstrate that it exists?
Apparently, one of the properties of every god throughout human history has been that none of them can be convincingly demonstrated to actually exist.
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".
Again, we're still waiting for a demonstration that 'X' exists. Then perhaps we can hash out its qualities. I don't see how rational people profit by debating the alleged properties of a possible entity that hasn't been demonstrated to exist.
In which case, you're little reference to which gods one doesn't believe in is completely unfounded and irrelevant.
Wow.
So you're saying that the entire history of religious conflict on this planet has been unfounded and irrelevant? Thanks. I think we might be making some progress here. May I quote that blurb freely any time a theist tries to argue that it's
crucially important regarding which god or gods we don't believe in?
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.
Feel free to correct me if I'm wrong here, but I think at this point you're reduced to semantic tap-dancing.
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.).
The reason that agnosticism isn't about belief is becasue it never was about belief. It was about knowing. O claiming to know. Or claiming to not know.
There is a distinction between knowledge and belief.
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.
Imagine if our courts were required to issued verdicts without knowing what those verdicts should be?
Every belief can be phrased as non-belief and vice versa.
So for instance, if I asserted that I believe 1 + 1 = 2, how would you phrase your non-belief of that equation?
Heath Ledger's Joker's quote (from The Dark Knight). Not a typo.
Sorry. I've managed to miss most of the Batman films that didn't involve Adam West.
Then you cannot believe the proposition "there is nothing in the box that is a cabbage" is true
I don't know what's in the box. I merely believe
what's been told to me about the contents of the box. All of my knowledge concerns what's going on outside the box.
meaning that you are making claim about the nature of contents of the box
Wrong. Simply and elegantly wrong. If I am told by a person outside the box that there's a cabbage in the box ... and that's enough to convince me that there's a cabbage in the box ... I'm am not simultaneously making knowledge claims about what is or isn't inside the box. All I'm saying when I say "I believe that there's a cabbage in the box" is "
I believe it when I'm told that there is a cabbage in the box." I have no way of knowing. I cannot possibly
know. To make knowledge claims based solely on personal testimony is absurd.
meaning that you claim to know something about the contents of the box.
Sorry. You've failed to demonstrate that the words 'belief' and 'knowledge' may be used interchangeably.
Every epistemic (belief) claim is a function of degree of subjective certainty regarding the truth of the claim.
Epistemology is concerned with knowledge, not mere belief. Correct? Beliefs don't need to be demonstrably true, correct?
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.
How so?
If someone claims to know that the world is flat, what sort of truth is underpinning that belief statement? And can we really declare that a belief in a flat earth somehow constitutes knowledge?
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.
Does it? If I say that I believe it's true that vanilla ice cream is the tastiest ice cream, what sort of
knowledge would we be dealing with? Please elaborate.
Perhaps because, in addition to the problem I referred to immediately above, you've conflated theism with non-theistic beliefs
'Example A' would be ... ?
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"
Atheism is simply not accepting the proposition that a given god or gods exist. Simple. The rest of your accusations are irrelevant. Feel free to come back with some more ornate mathematical gingerbread if you think that'll help.