"Disbelief in a proposition means that one does not believe it to be true. Not believing that something is true is not equivalent to believing that it is false."

The above is a quote from [here].

you can just use "!=" for "not-equal to"

If you have no concept of something, then you cannot believe it to be true, however you also cannot believe it to be false.

There's belief.
There's disbelief.

And there is something called unbelief. Unbelief is where you believe but struggle. You have doubts, etc.

Aight. Makes perfect sense now, thanks.

"I do not believe it is raining in France" does not commit me to " I believe it is sunny there right now."

Lets break this down;

Not believing that something is true = believing that it is false

If we can assume that in this equation "something" = "it" then we can reduce this to not true=false.

At this point we can introduce the liar's paradox into the argument. From Wikipedia here is the following description;

In philosophy and logic, the liar paradox, known to the ancients as the pseudomenon, encompasses paradoxical statements such as "This sentence is false." or "The next sentence is false. The previous sentence is true." These statements are paradoxical because there is no way to assign them a consistent classical binary truth value. If "This sentence is false" is true, then it is true and what it says is the case; but what it says is that it is false, hence it is false. On the other hand, if it is false, then what it says is not the case; thus, since it says that it is false, it must be true.

The problem of the liar paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules.

The simplest version of the paradox is the sentence:

This statement is false. (A)
If the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is false. Yet the sentence cannot be false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, the statement is both true and false.

However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is neither true nor false. This response to the paradox is, in effect, to reject the common beliefs about truth and falsity: the claim that every statement has to abide by the principle of bivalence, a concept related to the law of the excluded middle.

The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:

This statement is not true. (B)
If (B) is neither true nor false, then it must be not true. Since this is what (B) itself states, it means that (B) must be true and so one is led to another paradox.

Another reaction to the paradox of (A) is to posit, as Graham Priest has, that the statement follows paraconsistent logic and is both true and false. Nevertheless, even Priest's analysis is susceptible to the following version of the liar:

This statement is only false. (C)
If (C) is both true and false then it must be true. This means that (C) is only false, since that is what it says, but then it cannot be true, creating another paradox.

this question has nothing to do with the liar's paradox.

+1.

It is raining in France right now.

Do you believe this is true? Do you believe this is false?

Personally, I do not believe it is true, but I also do not believe it is false. I simply do not know one way or the other.

Maybe it is easier to see for the first time if you replace "believe" with "claim."

/thread...? please??

This is a very basic tenet of logic which people often misunderstand. Belief is holding the position that something is true. The statement "X is true" is what is called a truth statement, and is separate from the statement "X is not true", which is also a truth statement ("'X is not true' is true"). Not believing the first statement does not imply you must believe the second statement. However, if you do believe one of the two statements, you must necessarily believe that the other is not true, as per the second law of logical absolutes - the law of non contradiction: a truth statement cannot both be true and not true in the same sense at the same time.

The 'rain in France' example is a good one. Here is another:

I flip a coin, and do not show you the results. I then ask you if you believe that the coin came up heads (keep in mind I am not asking you to guess, I am asking you about your belief; I am asking if you are convinced that the coin came up heads). Logically, since you have no evidence that the coin came up heads and not tails, your answer will be no. However, that does not then mean that you must necessarily believe that the coin did not come up heads. Finally, if you do believe that the coin came up heads, you cannot believe that it did not come up heads.

lol, wut