Alvin Platinga's Ontological Argument

Platinga criticized Malcolm's argument because although it showed the necessary existence of the greatest possible being in some possible words, it did not successfully demonstrate that the greatest possible being exists in this actual world.

Platinga's response is in the form of a modal argument - modality refers to the necessity or contingency and possibility or impossibility of a statement. This can be analyzed in terms of possible worlds, which does not refer to another world  but a complete description of how things could be. For example, a necessary truth is one that is true in every possible world and an impossible truth is one that is false in every possible world.

His argument distinguishes between excellence (i.e. dependent on properties that are true in some possible worlds) and greatness (i.e. dependent on properties that are true in every possible world).

Platinga's Ontological Argument can be summarized as:
1 - There is possible world W which contains a being of maximal greatness.
2 - A being of maximal greatness would have maximal excellence in all possible worlds.
3 - A being is only of maximal excellence if it is omniscient, omnipotent and morally perfect.
4 - [According to Premise 3] An omniscient, omnipotent and morally perfect being exists in W.
5 - [According to Premise 4] In W the statement "There is no omniscient omnipotent and morally perfect being" is impossible.
6 - An impossible truth is one that is false in every possible world.
7 - Therefore, the statement "There is no omniscient omnipotent and morally perfect being" is impossible in every possible world, including the actual world.
8 - Therefore, it is necessarily true (true in every possible world) that an omniscient, omnipotent and morally perfect being exists.

The main criticism of this argument is that it is reversible, which means that the same logic can be used to demonstrate rationally that a being of 'no maximality' rather than 'maximal greatness' exists. This suggests the argument is not valid because the opposite conclusion can be reached using the same sound argument.
Additionally, there is the question of whether the Judeo-Christian God is truly demonstrated.

Norman Malcolm - A modern revival of The Ontological Argument

Malcolm's argument revived Anselm's 2nd Ontological Argument found in Proslogion 3, which posits that God exists necessarily. He believed that only a necessary being is worthy of religious devotion because a being that is limited in any way would not be consistent with the theistic idea of an omnipotent God or That Than Which Nothing Greater Can Be Conceived (TTWNGCBC).

He outlines four possibilities concerning the statement "God exists":
1) It is necessarily false (i.e. God cannot exist).
2) It is contingently false (i.e. God could exist but doesn't).
3) It is contingently true (i.e. God could exist and does).
4) It is necessarily true (i.e. God has to exist).

However, Malcolm implicitly defines God as immutable (i.e. he is unchangeable; he cannot and will not change), which means that God cannot come into existence nor cease to exist. As God is not limited or dependent on anything, he cannot change from the state of non-existence to existence or vice versa, and so his existence is either necessarily false or necessarily true. This translates that if God does not exist, his existence is impossible and if He does exist, his existence is necessary.

For Malcolm, regardless of how God is defined, the statement "God exists" cannot be impossible because it is not self-contradictory. A self-contradictory statement is not logically coherent, for example 'The square is round'. However, this does not apply in the same way to God because it is possible to imagine that God exists.

'The square is round' is a necessarily false statement because it is self-contradictory of the definition of a square.

Therefore, God's existence is not impossible and God necessarily exists.

Ontological Argument no. 2

The flaws in Anselm's first ontological argument are exposed in Gaunilo's reductio ad absurdum argument found in "On Behalf of the Fool" arguing the existence of 'the perfect island'. He stated that the fact that the greatest conceivable being can be defined does not mean it exists. This is because intentional existence (i.e. having an idea of a perfect island) does not imply formal existence (i.e. that the island really exists in reality).

Can you prove that anything exists simply by defining them as the 'greatest'?

Gaunilo's criticisms led to Anselm refining his original argument by defining the nature of God's existence. He dismissed the analogy of the perfect island because no example taken from the world is comparable to God as they have contingent existence (i.e. they can be thought to exist or not). Whereas, God cannot have contingent existence or he would not be TTWNGCBC, and therefore he has necessary existence (i.e. cannot be thought to not exist). He concludes that not only the fact that God exists, but that he exists necessarily.

The ontological argument is frustrating because it was not designed to convince non-believers of God's existence and therefore you have to believe in God in order to understand and agree that the argument is valid. This leaves many criticisms of the argument meaningless because it never intended to satisfy those who did not love and have faith in God.
Hmmm..