This page should be a collaborative effort. I have neither the time nor the training to do it right. But it should be done; society needs it. It also happens to be highly amusing. Let's not reinvent the wheel: many (probably all) of these gods were refuted long ago--it would be better (and faster) to have the original refutations by, say Hume (?) or Socrates, than yours or mine. If you know just where to find them, drop me a line. If you think of any genuinely new gods to add to the list, send 'em along, but watch it: many gods have more than one aspect (tricksters!).
The existence of some gods can be disproven, e.g., the Moral Authority god. Such entities refute themselves because their definitions are self-contradictory. The classic example is Plato/Socrates's refutation of the god who is both omnipotent and good. The Metaphoric god isn't really a god, but rather a rhetorical device. But in most cases the existence of something isn't subject to proof or disproof.
Agnosticism is warranted when there is some reason to believe and some reason not to believe. The scale tips heavily in neither direction. It is false that an absence of evidence means we should be agnostic. If there is no evidence to support a claim, it must be disbelieved. The alternative is to believe an infinite number of (absurd) claims. The existence of omnipotent magenta elves (somewhere), push-me-pull-yous who arrived on the moon a minute ago (in some dimension), etc. must be believed if belief is allowed without evidence; a clinically paranoid worldview would be a logical worldview. More banter on this matter.
Tentatively, the answer is that a god must be a being, and that any proposed alternatives are really metaphoric gods (see below). That's the only axiom in this database. More particular definitions belong to the entries for the particular gods.
Here's a summary of Socrates's argument in the Euthyphro that I came across in an Internet newsgroup some years ago. Alas, I didn't preserve the author's name.
Leibniz offers his take on the Euthyphro in the Discourse on Metaphysics (1686). He discuses whether something can be wrong merely because god says so, and in the process proves the impossibility of being both omnipotent and good (praiseworthy): "So in saying that things are not good by any rule of goodness, but sheerly by the will of god, it seems to me that one destroys, without realizing it, all the love of god and all his glory. For why praise him for what he has done if he would be equally praiseworthy in doing exactly the contrary?" Done.
Divide all belief into thirds. 1) Active belief: "I believe that so-and-so exists." 2) Active disbelief: "I believe that such-and-such does not exist." 3) Non-belief: "I have no opinion on that." When is each kind of belief justified?
Our intuitions about religion are difficult to see clearly because they are heavily inherited, indoctrinated, and emotional. A less highly charged proposition than the existence of god will best clarify the nature of belief, disbelief, and non-belief. Consider the proposition that there are magenta elves. Should I believe, disbelieve, or be agnostic on that proposition?
I cannot prove that the proposition is false. I can search for magenta elves, but how do I know I searched in the right way, at the right times and places? Maybe the elves are the most elusive things in the universe. Maybe they are omniscient and omnipotent, and don't want to be found. I can't prove otherwise. Should I therefore believe in magenta elves?
I try and fail to verify the proposition. I pursue this elusive elf around the world. I meditate and talk to shamans. Nothing. No magenta elves. Others claiming to be Witnesses are unreliable. They provide no evidence. They disagree with each other over the definition of "elf"; they even kill each other over it, speaking poorly for their commitment to reason. Some of them (mostly boys) don't distinguish between magenta and purple. Understanding is simpler without the elf. In short, there is virtually zero evidence but, still, there is no disproof (there is never disproof). So should I actively disbelieve?
Alternatively, suppose I have some reason to believe the proposition could be true. Once I whirled around, and saw a flash of something purplish. Another time, I could have sworn I saw a pointy, tufted, magenta ear . Others report similar experiences. But, nothing conclusive. And, the glimpses always happen during highly caffeinated all-nighters. Once it happened while writing an epistemology term-paper using the idea of an elusive magenta elf to make a point.... So I have some grounds to think the proposition is false, but some to think it is true. Should I be agnostic on it?
Finally, consider this scenario. I turn, and there, standing squarely before me, is a small magenta elf. (It looks me in the eye. It speaks in my mind. I am to deliver its message to Humankind, and appoint myself special status as Messiah....) It appears before others, it appears on MTV. Should I actively believe?
You, being clever, have no doubt answered these questions correctly. But it's my Web page, and I am going to pronounce my opinions. Agnosticism is warranted when there is some reason to believe, balanced by some reason not to believe. The scale tips heavily in neither direction. It is false that an absence of evidence means we should be agnostic. If there is no evidence to support a claim, it must be disbelieved. The alternative is to believe an infinite number of (absurd) claims. The existence of omnipotent magenta elves (somewhere), pink extraterrestials in violet spaceships (somewhere), push-me-pull-yous who arrived on the moon a minute ago (in some dimension), etc. must be believed if belief is allowed without evidence; a clinically paranoid worldview would be a logical worldview. Positive belief requires a preponderance of evidence and/or reason. Done.