It should also be noted that God is logically possible in all possible worlds unlike contingent beings like us. Humans are not logically possible in worlds without matter or worlds without planets or worlds without heavier elements. God who is said to be a necessary, self-existent and immaterial being is logically possible in all of these possible worlds.Gödel's proof is slightly more involved (please see the link labeled "impenetrable gobbledegook" to see what I mean), but for brevity, I will not elaborate here. I will note that it follows modal logic, which has been rather thoroughly debunked as being worthless for making serious existence claims. I'll direct you to this video by the blogger that goes by CounterApologist, a blog well worth checking out on its own. Granted, CounterApologist addresses Alvin Plantinga's ontological argument, not Gödel's, but a quick read of Gödel's makes it pretty clear where Plantinga got the idea. Plantinga removes most of the gobbledegook for us.
CounterApologist's video on the modal ontological argument:
I was asked this question a while ago on a thread on BookTalk.org, and so my response here will be an updated version of what I posted there. My original response there (to a slightly different, vastly less specific question) can be found here.
About Gödel's ontological argument, like all other ontological arguments, it has been thoroughly debunked (see the videoabove, for instance). Though I still think Richard Dawkins (following Hume, to be fair) did it with the best style when he pondered aloud how anyone could accept as valid a strong claim being made about the universe that fails to take into account a single datum from it, a criticism that applies to all a priori arguments. This, combined with CounterApologist's presentation, is more than enough to be getting on with in terms of realizing that this "proof" isn't really proving anything of substance.
Still, let's concede Gödel's ontological proof anyway and see what it gets us. Hint: it's not what the theists want it to prove.
First, since we've arrived at this notion from examining axioms put forth by Gödel, no comment on the fact that they look pretty ad hoc, we get an axiomatic conception of God. So what? Who needs an abstract concept that they call God (other than Plato, maybe), and who actually believes in such a God? What does such a God do (Cf. the title of my book)? This is the "philosopher's God," the Platonic God, and it is completely and purely abstraction. There is no need to set up a religion to worship an abstraction. Indeed, it seems quite silly to do so.
Now, since we've arrived at this notion of this God arising from examining axioms, the (abstract) concept of God that it extablishes is also subject to those axioms. That means if those axioms are bad or don't match reality, then there's a problem. Let's examine Gödel's axioms specifically.
The first of Gödel's axioms is that there is a meaningful "moral aesthetic" positive. So this God is inherently subjective, not to mention abstract, at least unless we accept, additionally and on no evidence (we call this question begging) the premise that there is an objective moral aesthetic that exists independently of the (subjective) minds of sentient beings. This puts us wading dangerously close to "God is an imaginary friend" here.
The rest of Gödel's axioms are pretty presumptive too. Axiom 2 depends on the rule of the excluded middle (wherein he defines his logical system, which may not actually represent reality, however useful it is); Axiom 3 implicitly assumes being "God-like" is a moral positive (which is a bald assertion teetering awfully near begging the question); Axiom 4 asserts that positive in any hypothetical world implies positive in all hypothetical worlds (i.e. that in every possible world, the definitions of moral aesthetic positives need to be meta-universal)--but why in the multiverse should we accept this at face value? and Axiom 5 assumes that what he's wanting to show is a "positive" property. Look how close we are now to begging the question with an ad hoc construction!
That fairly well damages the credibility of Gödel's ontological argument, but a further problem exists because it isn't the only ontological argument out there (surprisingly carrying the same amount of empirical weight: zero).
For instance, if we consider the vastly more famous and common ontological argument of St. Anselm, which we really shouldn't in general but since we're accepting at least one ontological argument, we might consider it, we have to conceive of God as "that than which nothing higher can exist." But Gödel's axiomatic God is subject to his axioms, so we can easily conceive in the mind a God that is higher, one that is limited by fewer axioms or none at all. So St. Anselm's construction would reject Gödel's construction, and only intellectual contortionism allows us to accept both at once--this barring the core problem with Anselm's ontological argument in the first place, which I cover in detail in Chapter 6 of God Doesn't; We Do: that there is no salient way to define "most high" in the first place.
What does this tell us? In essence, it shows that any attempt to lay out axioms to prove God exists subjects God to a definition created by those axioms. So, if we want to follow Gödel and define God as an arbitrary and abstract moral-aesthetic positive that if it exists in one possible world then it must exist in all possible worlds, then maybe his ontological proof proves that God exists. Who cares, though? And why should anyone care? Who prays to that God or goes to church to sing "his" praises? What has this God to do with Christianity or Islam or Hinduism or Paganism? It's even worse for connecting to religions than is Anselm's ontologically "proved" God that is defined as the Platonic ideal of that which is good.
The problem left by such an a priori argument is that impossible chasms of non sequitur have to be leaped to get from that particular definition to the ones that are actually used by people, notably the Gods of faiths like Christianity, Islam, Judaism, Hinduism, etc. If proofs like Gödel's above don't commit it on their own, the question begging begins in obscene amounts the very moment we try to extend these very weird definitions of God to other completely incompatible meanings of that word, an act completely necessary to the validity of any of the theistic religions that can even be conceived of.
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