atheism is disbelief, disbelief is belief, theism

Ah, but there IS an in-between. Unlike your hat, I hold that the dragon claim is false, based on my belief that dragons do not exist. Now, both of these are beliefs on my part. Let us reexamine your previous hat scenario in detail... So, the TRUTH is a dichotomy, which mean that one must be true and that both cannot be true. The two possible truths here are: (A) You are wearing a hat -or- (B) You are not wearing a hat Firstly, note that belief is not reliant on truth, and that it is fully possible for one to believe that something is true when it is in fact, false in reality. Now, in order for me to believe either (A) or (B), I would have to believe that the claim was true. In both of these cases, I would be making a positive claim, or assertion, in which case, I would possess belief. If these were the only two options, you would be right. However, though the *truth* may be a dichotomy, one's *belief* is not. Let us take a closer look a statement (A). We know that I could say (1) "I believe you are wearing a hat" which would be a positive claim. However, the opposite thing I can say is (2) "I do not believe that you are wearing a hat", which is a rejection of that claim, and therefore, a *disbelief*. Both sides of this argument have their own, sub-argument, each of which is a dichotomy. One side is the claim (or belief), and the other is the rejection of that claim (lack of belief). So, in this situation, we have two options among two dichotomies: (A)(1) "I believe that you are wearing a hat" (A)(2) "I do not believe that you are wearing a hat" (B)(1) "I believe that you are not wearing a hat" (B)(2) "I do not believe that you are not wearing a hat" If the wording of the above seems confusing (especially (B)(2) !), simply use the word, "convinced", instead: (A)(1) "I am convinced that you are wearing a hat" --(belief) (A)(2) "I am not convinced that you are wearing a hat" --(not a belief) (B)(1) "I am convinced that you are not wearing a hat" --(belief) (B)(2) "I am not convinced that you are not wearing a hat" --(not a belief) Moving on, since both of the sub-arguments of (A) and (B) are dichotomies (they are since one either accepts the claim or rejects it, and cannot do both), any individual must have a position in each of them. There are four possible combinations of positions, here (I am going to drop the parenthesis for clarity): #1 - A1 / B1 #2 - A1 / B2 #3 - A2 / B1 #4 - A2 / B2 Let us now assign the corresponding statements to each of there groups: #1 - A1 / B1 - This stance is inherently contradictory and is a paradox, so it is impossible (unless you are insane). "I believe that you are wearing a hat" "I believe that you are not wearing a hat" #2 - A1 / B2 - The second statement is redundant, since the first implies that you lack belief that he isn't wearing a hat. "I believe that you are wearing a hat" "I do not believe that you are not wearing a hat" #3 - A2 / B1 - This is the same as above; the first statement is redundant by the second. "I do not believe that you are wearing a hat" "I believe that you are not wearing a hat" #4 - A2 / B2 - Note that THIS stance does not hold ANY positive belief. "I do not believe that you are wearing a hat" "I do not believe that you are not wearing a hat" So, regarding your original statement, I reside in stance #4, in that I hold NO BELIEF that you are, or are not, wearing a hat.