Veritas_Vincit, your objection to premise 1 seems to indicate you do not understand "possible worlds" semantics. https://en.wikipedia.org/wiki/Possible_world
The argument can be summed up as: If you think that it is broadly logically possible that God (the maximally great being most think of when you say God) exists then he does exist.
As Irrational said, it is important to understand the S5 modal logic that if something is even possibly necessary, it is actually necessary. (which would answer Kevin's question about the jump from 2 to 3.)
@Esquilax, one of your objections to maximally great being is that something "slightly more great" can be imagined makes no sense. What could be greater than an omnipotent, omniscient, morally perfect, and necessary being? If you could logically conceive of anything greater, then that would be God. Your parody about the greatest conceivable girlfriend illustrates nothing. 1) the qualities of such a person would be subjective and 2) there is nothing about such a person that would make her necessary.
To defeat the argument, you are left with showing why premise 1 is not true. This would require you to show that the concept of a maximally great being (God) is illogical.
The argument can be summed up as: If you think that it is broadly logically possible that God (the maximally great being most think of when you say God) exists then he does exist.
As Irrational said, it is important to understand the S5 modal logic that if something is even possibly necessary, it is actually necessary. (which would answer Kevin's question about the jump from 2 to 3.)
@Esquilax, one of your objections to maximally great being is that something "slightly more great" can be imagined makes no sense. What could be greater than an omnipotent, omniscient, morally perfect, and necessary being? If you could logically conceive of anything greater, then that would be God. Your parody about the greatest conceivable girlfriend illustrates nothing. 1) the qualities of such a person would be subjective and 2) there is nothing about such a person that would make her necessary.
To defeat the argument, you are left with showing why premise 1 is not true. This would require you to show that the concept of a maximally great being (God) is illogical.