Wow, you're wrong. In a nutshell, belief and knowledge are NOT the same thing.
I never said they were, did I? You are the one that wants to insist you know the answer while declaring that you don't. I suppose you think that makes you honest, but it just makes you silly.
To correct you, it is logically impossible to believe in something you don't believe in, because that is a contradiction (and violates the law of noncontradiction) and has nothing to do with being liar or crazy. It's not an option, logically.
Now you want to play like you know philosophy. This is going to be fun.
Tell me something, how does saying I am correct that it is impossible to believe in two opposite things at the same time prove I am wrong to say it is impossible to believe in two different things at the same time? If we assume that the universe is logical, which would be the only way the law of contradiction would apply, wouldn't anyone who claims to believe in the impossible be lying? If they actually believed it it, which is a possibility, wouldn't that prove they were crazy? Doesn't the law of the excluded middle prohibit any other explanation?
You simply don't have your epistemology at all correct. Knowledge and belief are two different categories, therefore, not mutually exclusive. Knowledge can be said to be justified true belief, and is therefore a sub-set of belief. Therefore, all knowledge is made of beliefs, but all beliefs are not necessarily knowledge, because they are not all true. I can believe that a square is a circle, but that would not be true simply because I believe it to be true, and is in fact demonstrably false because it is a logical contradiction.
I don't have anything wrong, you are trying to apply it to a logical universe that excludes belief and non belief at the same time while insisting that you have the power to do both and remain both sane and logical.
That said, lets see where we get if we apply epistemology to your claim. Since you have no justified true belief to apply, since you have no real evidence either way about the existence, or non existence, of God, we can ignore any arguments that use justified true belief as a basis.
Epistemology teaches us that all belief has to be based, at least in part, in truth. In other words, despite your assertion that knowledge and belief are separate, they are actually interdependent. Any belief we have has to be based, at least in part, in truth.
If we take your belief in a square being a circle, the fact that it is a logical contradiction is irrelevant here, all that matters to the matter of this being a belief is if any part of it is true.
I suggest you go back to your philosophy teacher and request a refund.
However, if I know something, I also believe it. It just happens to be a true belief, and therefore counts as knowledge. I know that I exist, because I also believe it, although many would argue this isn't truly knowable either, and I would agree. Descartes made this notion popular with "I think, therefore I am."
Almost.
The problem here is that you being correct that you knowing something means you believe it does not prove that your belief is actually valid unless it is based on truth. For instance, you probably know that English has three tenses. That belief is based in the knowledge imparted to you through many years of education. Unfortunately, that knowledge was based on the fact that teachers lied to you, there are 12 tenses in English.
Therefore, for something like god, because of its characteristics, many believe that it is not knowable whether one actually exists. Therefore, they are termed agnostic. However, just because one doesn't know god exists, doesn't mean they can't believe, as demonstrated above. Others think they have sufficient evidence to "know" that god exists, and are classified as gnostic theists. I do not believe in a god, but I also do NOT think it is possible to KNOW that no gods exist, because would be almost impossible to establish this empirically, given that I would need exhaustive knowledge of the entire universe in order to know this, because proving a negative is much more difficult.
The fact that many people believe something does not make it true. Even if it is true, that does not justify you using their belief to argue that your belief is true unless you know that it is.
Parsing agnosticism in an attempt to justify different levels of saying "I don't know" is stupid. If you don't know you don't know. Your lack of belief in the premise that God does not exist does not change the simple fact that you don't know.
People disagree on this, because the colloquial definition of agnosticism has come to mean something meaningless in addressing the question of belief.
I don't give a fuck.
I never said they were, did I? You are the one that wants to insist you know the answer while declaring that you don't. I suppose you think that makes you honest, but it just makes you silly.