Magic Man
Reaper of Conversation
I find all those formulations to be largely synonymous in everyday language; I would use them interchangably.
I don't think everyday language is the right basis here, though. We're trying to be accurate. For example, in everyday speech, I rarely use the word "whom", but when I write and I'm trying to be accurate, I use it when appropriate.
Those sentences are not synonymous. Saying "I don't believe God exists" isn't the same as saying "I believe God doesn't exist". The difference between them generally isn't important in everyday speech, but it becomes important in discussions like this.
I have a hard time, actually, keeping it straight in the atheist definition debate which implies belief and which doesn't, since they all really mean the same thing to me. Two of those formulations imply lack of belief; two imply presence of a negative belief.
As you say, the difference is one implies lack of belief while the other implies presence of a negative belief. When you say "I don't believe...", it's the same as saying "I don't hold the belief...". Basically when "don't" comes before "believe", it indicates the lack of a belief, not necessarily the presence of a different belief.
If the options are mutually exclusive, (ie, Kilgore can either be wearing a blue shirt, or he can not be wearing a blue shirt; there is no other option), and you don't believe he is wearing a blue shirt, by default, you also believe that he is not wearing a blue shirt.
That's not true. I don't believe he's wearing a blue shirt. I also don't believe he's not wearing a blue shirt. I don't know what color shirt he's wearing or even whether he's wearing a shirt at all.