- God exists in the understanding but not in reality.
- Existence in reality is greater than existence in the understanding alone.
- God’s existence in reality is conceivable.
- If God did exist in reality, then he would be greater than he is (from 1. & 2.).
- It is conceivable that there be a being greater than God is (3 & 4).
- It is conceivable that there be a being greater than the being than which nothing greater can be conceived (5., by the definition of ‘God’).
- It is false that it is conceivable that there be a being greater than the being than which none greater can be conceived.
Since 6. and 7. contradict each other, we may conclude that
- It is false that God exists in the understanding but not in reality.
So if God exists in the understanding, he also exists in reality. 
Thus, step 1 is the proposition “to be reduced to absurdity.” Steps 2, 3, and 7 are premises in the argument of which step 2 poses the only real problem. That is, is it necessarily true that “existence in reality is greater than existence in the understanding alone?” What is
However, Plantinga reformulates the argument and remedies these inconsistencies. First, it is important to understand that “those who worship God do not think of him as a being that happens to be of surpassing excellence in this world but who in some other worlds is powerless or uninformed or of dubious moral character.” Thus, if P is a property of an individual, then it can be stated that, “P is a universal property if and only if P is instantiated in every world or no world.” Therefore, unlike
- The property has maximal greatness entails the property has maximal excellence in every possible world.
- Maximal excellence entails omniscience, omnipotence, and moral perfection.
- Maximal greatness is possibly exemplified.
Thus, if the property maximal greatness is possibly exemplified in any world, then it is necessarily follows that it is exemplified in all world by the mere definition of maximal greatness including or entails maximal excellence. Therefore, the ontological argument can be restated as follows:
- God exists in a conceivable world but not in reality.
- It is conceivable that God exists in a world W and as a perfect being has an essence E such that E is exemplified in W and E entails has maximal greatness in W.
- Maximal greatness necessarily exemplifies the property has maximal excellence in every possible world.
- Therefore, God’s essence entails has maximal excellence in every possible world.
- If world W had been actual, it would have been impossible that essence E fail to be exemplified given its necessary nature.
- Therefore, there exists a being that has maximal excellence in every world.
1. Define God: God is that than which no greater can be conceived.
2. It is greater to exist not only in the mind or in the imagination but also independently of the imagination (i.e. in reality) than to exist only in the imagination.
3. It is possible to conceive of that than which no greater can be conceived.
4. It is possible to conceive of God existing not only in the mind but also in reality.
5. If God exists only in the imagination but not in reality then (because of 2.) it is possible to conceive of a being greater than that than which no greater can be conceived.
6. Number 5 self-contradicts.
7. Therefore, the protasis of 5. must be false (i.e. God exist only in the imagination.)
8. Therefore, God exists not only in the mind but also in reality.
Plantinga’s ontological argument was much more cogent and convincing than his disappointing Free Will Defense. The argument definitely required at least a cursory knowledge of logic and valid syllogisms. All in all, it was an intellectually rigorous work, but well worth the read. The one point at which I believe an atheist or atheologian could respond is in questioning the premises. The reasoning is valid, but the axioms utilized to establish the validity of the conclusion would undoubtedly be attacked by contrary thinkers, albeit, it is an unjustified attack given the cogency of the argument.
I would recommend both of these arguments to be read by believers. The Free Will Defense can aid the Reformed thinker in flushing out his own beliefs about God’s sovereignty and the means by which free agents both act/move and are culpable for their actions. Plantinga’s ontological argument is a good example of right reason and logic applied to the things of God in a cogently conclusive manner.
However, I would not recommend the Free Will Defense to unbelievers or for any use in an apologetic discourse. As noted above, it is fraught with too many perils. However, if you can get an unbeliever to actually go through the ontological argument with you, I believe it can serve to show forth the rationality and coherence that is Christianity.