Of course you can! If you’re happy that the case for there being no God is proven to your satisfaction, then you B(¬G). I don’t believe that I’ve ever said otherwise!
But that is nothing to do with the OP. The OP states that ¬B(G) = B(¬G). I hope that I’ve convinced you otherwise.
pan
I said that the difference between them was merely one of degree, and that appears to be borne out by your descriptions of your own “beliefometer”.
There is no evidence for “not Santa Claus”, you are merely “happy” with the explanation that people made him up.
You are simply less “happy” about applying the same explanation to God, and so are not yet able to contend B(¬G), as I do.
Many thanks for you patience, kabbes. I put my head above the parapet expecting to be intellectually pelted with tomatoes, only to find I am treated with tolerance and gentle humour.
Well, you said, “the difference between absence of belief and belief (or between absence of belief and belief-not) is as arbitrary as the difference between 50% and >50% (or <50%), is it not?”, which isn’t quite the same thing. As I’ve been saying, you’re measuring a fundamentally different probability (P(D|¬G) vs. P(D|G)) and not merely looking at two probabilities on the same scale.
But I don’t want to rehash - I think this is coming to a natural conclusion.
Well, I think that there is evidence for ¬SC AND for ¬G. It’s just that I find the evidence for ¬SC satisfactory enough to accept it, whereas I don’t (for argument’s sake) find the evidence for ¬G satisfactory enough to accept it. Now that’s a matter of degree.
Oh tish tosh. If you approach a discussion in good faith and with patience, I would be less of a person if I didn’t do the same. And it’s easier for me, 'cos -I- was right 
pan
No evidence for “Not-Claus”?
He supposedly travels around the world giving presents to worthy girls and boys, and yet I have never heard of parents finding gifts under the tree that cannot be accounted for. Is there an Anti-Claus thqt follows him and steals the presents back, or what?
You cannot prove a negative of this nature.
You cannot provide absolute proof that he does not take the bought presents and replace them with identical elf-manufactured ones. Such a scenario is not logically impossible.
All you can do is provide an alternative explanation which any reasonable person would accept as proof “beyond reasonable doubt”, and adjust the needle of their belief-o-meter to well into the B(¬SC) zone.
Yes. Quite. Nobody mentioned absolute proof – only pursuasive evidence. Where has this “absolute proof” notion come from?
pan
That was merely my paraphrasing of “absence of evidence is not evidence of absence”.
Ah, well. There can be evidence of absence without it being incontrovertable proof.
Anyway, you can’t fool me: there ain’t no sanity clause.
pan
Can you give an example of something which is not mere absence of evidence for Santa, nor reasoning based on this absence (no-one’s ever seen him, all presents are accounted for, etc.), but is actual verifiable evidence that Santa does not exist?
But, point taken, we all agree that one cannot prove a negative, right? And, if I may be allowed to repeat myself, this is exactly why the equating of belief and not belief of the OP is incorrect. Qualitively, not believing in something (because of an absence of evidence) is different to believing something (presumably based on some evidence).
Indeed, TGU, but do you agree with kabbes that belief in not-Santa is justified despite no evidence of not-Santa?
I am still contending that ¬B(SC), while it is different to B(¬SC), is only different in that it is a slight nudge of the belief-o-meter needle.
Not quite proving a negative. If Santa Claus exists, then by definition he leaves presents in people’s houses. It’s what he does. If he doesn’t do this, then he isn’t Santa Claus by definition of Santa Claus.
The lack of presents, therefore, is positive evidence that there is no Santa Claus. At least - that’s my take on it.
Remember too that we are looking at P(D|SC), in other words the probability of the data given that Santa Claus exists. If Santa Claus exists, then what is the probability that there will be no presents left by him? Pretty damn low, is the answer. Certainly low enough for me to reject the Santa Claus hypothesis. This kind of hypothesis-rejection is what statistical testing is all about.
Aside from that, I note that I can trace the invention of the Santa Claus myth back to its origins. This is further evidence that Santa Claus is a made-up figure rather than a real one.
pan
But there are presents! You are merely providing an alternative hypothesis - that the parents bought them - for which there is evidence (receipts, security camera footage etc.). You have not presented evidence for the non-existence of Santa.
Similarly, I assume you would not argue that the theory of evolution provides evidence for the nonexistence of God?
An interesting concept but, as you imply, the term ‘Bright’ (even though used as a noun) would suggest that those that do believe are ‘Dim’…
‘Rationalist’ was a good term, but seems to me to denote a certain form of radical A***ism…
We need a new word…
Really. 
Sentient
It really has nothing to do with being a negative, but rather with the size of the set. It is merely impractical (but not necessarily impossible) to prove that there is no one pushing Christmas presents down chimneys. The set is the union of all homes for all time frames. It is the same difficulty were you to want to prove that ALL homes are visited in such a manner by someone. If you would accept (and could implement) a forced-compliance poll, you could prove either one.
Yes, “belief in not-Santa is justified”, or maybe not, oh I dunno.
But I was thinking, “What do I want for breakfast?”, and I thought I didn’t want anything – not that I didn’t want breakfast, but that my desires towards a particular configuration were neutral. Particularly, I didn’t want a sausage sandwich*, but then I didn’t not want one either.
It is the same thing with some beliefs – I don’t believe in God, and I don’t believe in not-God. However, one has to eat, so I did indeed have a sausage sandwich, if I had to take a position on the God/not-God dichotomy I would say I believe in not-God.
I hope this clarifies my position.
*(Cumberland style) vegetarian sausages, in toasted bread with ketchup
Not-God: It’s not just for breakfast anymore. 
Observe: Breakfast with the Simpsons
Anyway, my breakfast is starting to repeat on me…