By Max Andrews
ONTOLOGICAL ARGUMENT [1]
This is the ontological argument that advocates the existence of an essential, omniscient, omnipotent and morally perfect being:
The property of being maximally large is exemplified in some possible world.
The property of being maximally large is equivalent, by definition, to the property of being maximally excellent in all possible worlds.
The property of being maximally excellent implies the properties of omniscience, omnipotence, and moral perfection.
A universal property is one that is exemplified in all possible worlds or none.
Any property that is equivalent to a property held in all possible worlds is a universal property.
Therefore, there exists a being that is essentially omniscient, omnipotent, and morally perfect.
Now, this is a very technical argument... So, let's try to make some sense of this:
Defense of Premise 1. When I refer to a possible world I am referring only to a possible logical state of affairs. The first premise merely states that the property of being maximally large is logically possible – that is, that no contradiction obtains.
Defense of Premise 2. Premise 2 outlines the logical equivalence of maximum greatness with maximum excellence.
Defense of Premise 3. Premise three follows from the logical equivalence located in premise 2.
Defense of Premise 4. Premise 4 presents a disjunctive: either the universal property X is valid in all worlds (hence its universality) or it is necessarily a contradiction, and is impossible to obtain.
Defense of Premise 5. The fifth premise asserts the first disjunctive stated, which is simply that if a property holds in all possible worlds, then it is a universal property. Therefore, if a universal property holds in some possible world, then this universal property holds in all possible worlds. Logic does not vary across possible worlds.
Defense of the Conclusion. Therefore, if these universal properties hold in all possible worlds, they are valid in the actual world. This argument also does not "define" God to exist. Rather, it is an a priori argument that considers the mere possibility of a being with maximally great properties. This modal form of the argument shows that if a being with maximally great and maximally excellent properties is possible, then that being must exist.
Anselm's ontological argument
Anselm's argument can be formulated as follows:
God exists in the understanding.
God is a being.
If X exists only in the understanding and is a possible being, then X could have been greater.
Let us suppose that God only exists in the understanding.
God could have been greater (Dado 2, 4, 3).
God is a being of whom nothing greater is possible.
So a being for which no greater being is possible is therefore a being for which no greater being is possible.
Since 4 gives rise to a contradiction 4 must be false.
God exists not only in the understanding.
Therefore, God exists in reality.
Existence in reality is an aggrandizing property.
The argument is a reductio ad absurdum . To prove X assume ¬X. Show how ¬X leads to a patent contradiction or falsehood.
Gaunilo's objection
Gaunilo proposes the idea of a perfect island. “I can conceive of a perfect island so this perfect island must exist.” The problem with this is that the island could, in reality, always be better. How many palm trees? How big is the island? How good is the climate? Inevitably, when you start adding all the big properties together to form the island you get Anselm’s idea of God.
Plantinga's modal ontological argument
This is the formulation of Plantinga's Argument:
It is possible for a maximally great being (God) to exist.
If it is possible for a maximally great being to exist, then a maximally great being exists in some possible world.
If a maximally great being exists in some possible world, then it exists in all possible worlds.
