The updated ontological argument for God’s existence

Still more from William Lane Craig on God in contemporary philosophy:

The ontological argument. Anselm’s famous argument has been reformulated and defended by Alvin Plantinga, Robert Maydole, Brian Leftow, and others. God, Anselm observes, is by definition the greatest being conceivable. If you could conceive of anything greater than God, then that would be God. Thus, God is the greatest conceivable being, a maximally great being. So what would such a being be like? He would be all-powerful, all-knowing, and all-good, and he would exist in every logically possible world. But then we can argue:

1. It is possible that a maximally great being (God) exists.
2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

3. If a maximally great being exists in some possible world, then it exists in every possible world.
4. If a maximally great being exists in every possible world, then it exists in the actual world.
5. Therefore, a maximally great being exists in the actual world.
6. Therefore, a maximally great being exists.
7. Therefore, God exists.

Now it might be a surprise to learn that steps 2–7 of this argument are relatively uncontroversial. Most philosophers would agree that if God’s existence is even possible, then he must exist. So the whole question is: Is God’s existence possible? The atheist has to maintain that it’s impossible that God exists. He has to say that the concept of God is incoherent, like the concept of a married bachelor or a round square. But the problem is that the concept of God just doesn’t appear to be incoherent in that way. The idea of a being which is all-powerful, allknowing, and all-good in every possible world seems perfectly coherent. And so long as God’s existence is even possible, it follows that God must exist.

This gets into highly technical philosophy, I suppose, but can anyone explain how it is that if God’s existence is possible, then God must exist?