That really depends on the god you are talking about.
When you start defining gods in human terms, which the vanity of humanity dictates will happen, then you begin to set up criterion that will make that god easy to dissect and prove that such a defined god does not exist. Intellectually, philosophically and theologically; one can easily prove a defined god does not exist. Start talking about undefined gods then I, like many others, have to claim agnosticism.
The reason one claims agnosticism when discussing proof of non-defined gods is because one cannot prove a negative. You cannot prove that something does not exist – only that it does. We will get into burden of proof in a bit. To be technically accurate, when proving a defined god does not exist, all you are doing is showing that the defined god cannot exist under those definitions; leaving a non-defined god in its stead.
What one has to look at is the likelihood of existence and not the absolute position of does or does not (in this respect agnosticism is the more appropriate position to take). How likely is it that said god exists? How likely is it that said god does not exist?
We can talk about possible gods and possibilities all day and get nowhere. We can talk hypothetical and “what if” until we are blue in the face. Until we start dealing in probability, facts, and raw data, we are accomplishing nothing. This is why the theist will never prove their gods exist – they cannot produce probability, facts, or raw data.
How does one prove a negative? How do you prove that Polka-dot unicorns do not exist? How do you prove that Leprechauns do not exist? Since you cannot prove a negative, it leaves you in the position of showing that the positive lacks merit, or the positive must prove that it exists. This is the burden of the theist – they have the positive so they are forced to find the proof; the burden of proof is on the theist.
Exceptional claims require exceptional proof. Theists make the exceptional claim that there is a god. That claim requires exceptional proof. Therefore, the burden of proof is on the theist and not the atheist.
Let us try an analogy to discuss the burden of proof:
Bert is a property owner and Ernie is a tenant. Ernie leaves the apartment complex without paying the rent and Bert takes Ernie to court to collect monies due. Whose responsibility is it to prove to the court that Ernie actually lived in the apartment and owes Bert money? Who is responsible for providing proof of Ernie’s residency in that apartment? Bert, as the property owner, is required to prove that Ernie lived there, and therefore, owes Bert money for rent past due. Ernie has no burden in proving that he did not reside as a tenant – he is not making the positive claim.
Let us look at another analogy to help understand what an exceptional claim is.
If I tell you that I have a poodle at home, do you have any reason to doubt me? Not really, because poodles are a common occurrence and many people have them as pets. This is a non-exceptional claim. Another example of a non-exceptional claim would be for me to say, “My grass is green and the sun will rise tomorrow morning.” There is nothing exceptional about that statement.
If I told you that I had a levitating psychic poodle at home, what would you think? Would you have any reason to doubt me? You bet you would! I would have made the exceptional claim and I would have to prove that I had such a poodle at home. If you told me that I did not have such a poodle at home, and I demanded you prove that my poodle does not exist, would that make much sense? Of course, it would not. The burden of proof is on me, the one making the exceptional claim that I have a psychic and levitating poodle at home. It is not your task to prove me wrong.
Even in the court of law, prosecutors have the job of proving that the accused was there (existed) in the first place. The burden on the prosecutors is not to prove that the accused was not there (does not exist). The defense does not have to prove his client was not there either. The defense only has to state that the prosecution has not provided proof of such.
What are the methodologies in disproving gods or un-defining the defined gods?
The Christian God is a defined god. The definition of the Christian comes from his abilities, his activities, his past actions, and even his physical traits in the Bible. By breaking apart those definitions philosophically, logically, scientifically and rationally – we provide evidence against those definitions – and therefore against said defined god.
The events of September 11 2001 help to underscore this. It is said that God is omnipotent (all-powerful), omniscient (all knowing), omnipresent (all present) and omnibenevolent (all loving). If that is the case, as defined by the followers of that God, then that God is easy to pick apart simply using the example of the terrorist attack on September 11, 2001.
If God is all-knowing (omniscient) then he knew the attack was going to happen and he knew who was going to die and who was going to survive.
If God is all present (omnipresent) then he was there in the airplanes, in the World Trade Center, in the Pentagon, in Pennsylvania and on the ground.
If God is all-powerful (omnipotent) then he had the power to stop the attack from occurring or he could have saved everyone from death during the initial attacks or the falling debris.
If God is all-loving (omnibenevolent) then he must not perpetuate evil and must go out of his way to stop evil and he must do everything in his power to stop people from dying from anything other than a natural death (old age).
Because the attacks happened then we can safely say that God, based on the four criteria given by Christians, does not exist or at a minimum is not acceptable on the definitions attributed to it. The criteria for that god contradict each other.
How can he be omnibenevolent at the same time that he is omnipotent to stop the death of his loved ones? Does he not love everyone or was he impotent to stop it?
How can he be omniscient and omnipotent if he failed to stop the attack? Did he not know about it or was he impotent to stop it? Was he simply not there because he is not omnipresent?
Alternatively, perhaps the one true God is actually Allah. After all, Allah answered the prayers of the terrorists when they successfully flew their airplanes into their intended targets. I say this tongue-in-cheek, of course, but the Islamic faith has a better apologetic (I say better very loosely) stance because the prayers to Allah by the terrorists were answered; they completed their mission. The prayers of the Christians to Jesus went unanswered – unheard.
I cannot prove a god does not exist. I can only point to the inconsistencies of defined gods and reduce their likelihood of existence. In the end, this is rather moot, because the theist, the one claiming such a god exists, has the burden of proof in their court.
In the millennia since the evolution of religiosity, not a single theistic camp has proven that their god or gods exist. That says a lot about likelihood.