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Gödel based his argument on an early argument of St. Anselm's. St. Anselm defined God as the greatest being in the universe. No greater being could be imagined. However, if God did not exist, then a greater being had to be possible to imagine - one which exists. Since it wasn't possible, by definition, to imagine a greater being than the greatest being imaginable, God had to exist.
Still hanging in there? Check this out.
God can either necessarily exist, or necessarily not exist. If God is an all-powerful being, and he exists, he necessarily exists in all possible worlds. If he doesn't exist, he necessarily doesn't exist in any possible worlds. It is not possible to say that God does not exist in any possible world. No matter how slim the chance is, God might exist. That means that God can't necessarily not exist. Since the choices are either God necessarily does exist, or necessarily doesn't, and we have eliminated the possibility that he necessarily doesn't, the only possibility left is that he necessarily does.
So...there you go. Science. Make sure you read the rest of the article.
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