We are going to learn some basic things such as the law of excluded middle and the English language laws of negation. We will learn the difference between 2 action sentences and 1 action sentences.
Lets start with the law of excluded middle(http://www.stanford.edu/~bobonich/glances%20ahead/IV.excluded.middle.html)(http://en.wikipedia.org/wiki/Law_of_excluded_middle)
The law is basically this, for every statement either the statement or the negation is true or in other words either a statement is true or false.. There is no middle ground. This is a rock can only have two possible truth values true or false. This is one of the foundational laws of logic and thought that we use. This applies to ignorant agnostics. You can either say that this statement is true or false:
I have the belief in god.
If the statement is true, you have the belief in god.
If the statement is false, you do not have the belief in god.
Also, this statement also has 2 truth values:
I have the belief that there is not god.
If the statement is true, you have the belief that there is no god.
If the statement is false, you do not have the belief that there is no god.
It is true, that if you do have the belief that god exists, you cannot have the belief that god does not exist and vice versa. This is one of the other basic laws of logic and thought called the law of non contradiction(or sometimes the law of contradiction)(http://en.wikipedia.org/wiki/Law_of_noncontradiction)(http://plato.stanford.edu/entries/contradiction/).
To put this into syllogism form:
If you possess the belief that no god exists, you must not believe god exists.
you possess the belief no god exists
Therefore you must not possess the belief that god exists.
This is a sound and valid syllogism (assuming premise 2 is true of you)
The reason premise 1 is true, is the law of non contradiction, a person cannot possess the belief that god both exists and does not exist.
The agnostic here will then turn around and try to affirm the consequent(http://en.wikipedia.org/wiki/Affirming_the_consequent)(http://www.fallacyfiles.org/afthecon.html) and make this syllogism:
If you possess the belief that no god exists, you must not believe god exists.
you do not believe god exists
Therefore you believe god does not exist.
Now we will move onto sentence structure. We have 2 different sentences to examine:
"I do not believe god exists" vs "I believe god does not exist"
Lets look at the first sentence.( diagram pointing out negations here: (http://tinypic.com/view.php?pic=35cq6xe&s=6)
in the first sentence the not negates the believe part. This means one does not believe this proposition: That god exists.
On the other hand the second sentence the not negates the exist. While the believe affirms that you have the positive attribute of belief in the nonexistence of god.
Before we go too far we should define belief:
a state or habit of mind in which trust or confidence is placed in some person or thing (http://www.merriam-webster.com/dictionary/belief)
In the first sentence you are not placing trusting confidence in the existence of god. in the second sentence you are placing trust or confidence in the nonexistence of god. These are completely different claims. Now we can see that the set of things that we do not believe and the set of things we believe not are not equal by this example:
My brother and I walk into a field full of grass. At this point, I do not place trust or confidence in the position that there is an even number of blades of grass in the field(Proposition E). I also do not believe there is not an even number of blades of grass in the field(Proposition NE). Why is this, I have not been presented enough logical evidence to believe either claim.
So we can safely put E into the set of things we do not believe. So now, the set things we do not believe looks like this:
(E).
With this said we cannot in turn put the proposition NE into the set of things we do believe so therefore the set of things we do believe remains:
().
It is now time for us to move on to the final part of this the fact that the sentences we are dealing with have 2 actions. The act of believing and the act of god existing. In this case the person as per the diagram must carefully exam which action the negation is being used for.
As per the diagram the sentence " I do not believe that god exists" negates the belief part. The second sentence " I believe no god exists" negates the existence. Strangely, this same rule of negation holds true under these two sentences: " I do not know that god exists" negates the know part where as the statement: " I know that god does not exist" negates the exist part. They are following the same rule.
Now the important part is to understand the question being asked is to understand the question being asked: The question is asking "Do you believe god exists" Not does god exist. We have already explored through the law of excluded middle that this proposition is either true or false:
I Believe god exists.
There are only 2 possible responses. The key word being believe, not "god exists".
