The Ontological Argument: an assessment

This essay is © 1998 by Ed. Stoebenau. It is based on an older version that he sent me to host on my website some time in 1997. In moving it over to my new website, I have updated the formatting to correctly represent the logical notation that Ed. originally used. —C.J. 2006-08-02.

The ontological argument is unquestionably one of the most interesting arguments for the existence of God. Similar to all ontological arguments is that the concept of God entails that there exists in reality a being which corresponds to this definition, or more simply: God exists. Any perusal of the philosophical literature will show that the ontological argument is still very much debated in different forms. I will show that the ontological argument does not succeed in what it tries to do, namely, prove that God exists. I will consider the first form of Anselm’s original argument, Descartes’ argument, Hartshorne’s, and that of Plantinga.

Anselm first gave what has become known as the ontological argument in his Prosologion. He used the definition that God is that being than which no greater can be conceived. Using this, he gave a reductio ad absurdum, that if one claimed that this being did not exist, then there exists a being which is greater than the being which no greater can be conceived. A major assumption of Anselm’s was that whatever exists in both the mind and in reality is greater than that which exists only in the mind. However, it is tough to see why one should accept this premise as sound. Is five dollars actually being in my pocket greater than 100 dollars existing in my mind? Can we even make such a comparison? This does not seem likely. One cannot claim that an old worn down coin is greater than a hypothetical brand new one of the same date, just because it exists. Furthermore, the premise that if one denies the existence of God, that there is a being greater than the being which no greater can be conceived, presupposes the actual existence of that being, so the argument runs in a circle. Hence, Anselm’s original argument fails.

Descartes’ ontological argument is simpler than Anselm’s, but unfortunately is more question-begging also. His argument is:

  1. God contains all perfections.
  2. Existence is a perfection.
  3. Therefore, God contains existence (or God exists.)

The second premise is highly questionable at best. Generally, one would think that bringing something into in existence would cause an imperfection in the object; one does not see how at first why God would be any different. For example, if one thinks of a perfect hill (such as the one just outside of Buchanon VA), the conception of the hill would be more perfect than a hill in existence; hence bringing something into existence does not make it more perfect, and therefore existence is not a perfection. So Descartes argument also fails.

Hartshorne’s ontological argument is based on Anselm’s second argument and claims that God’s existence is logically necessary. Hartshorne’s argument is given here, where A means it is logically necessary that A, ~A means it is not the case that A, is strict implication, means or, and g means God exists:

  1. g → ▯g
  2. g ∨ ~▯g
  3. ~▯g → ▯(~▯g)
  4. g ∨ ▯(~▯g)
  5. ▯(~▯g) → ▯(~g)
  6. g ∨ ▯(~g)
  7. ~▯(~g)
  8. g
  9. gg
  10. g

This argument is valid. Furthermore, given an Anselmian conception of God, premises one and five are sound. Premise two is just the law of the excluded middle, and premise three is a law of the modal logic S5. Premise nine is obviously sound, so this leaves premise seven as the only premise to question. Premise seven says that it is logically possible that God exists. If you were to change it to:

7′. It is possible that God does not exist.

Then using premise one, and 7′, one gets this conclusion:

10′. God does not exist.

Therefore, one must have a good reason to prefer it is possible that God exists over it is possible that God does not exist. However, there does not seem to be. Therefore, with two premises of equal prior (epistemically) likeliness leading to opposite conclusions, I conclude that Hartshorne’s argument cannot succeed.

Alvin Plantinga’s ontological argument is similar to Hartshorne’s, and falls to the same attack. Plantinga’s argument is based on the semantics of possible worlds. For him, logically necessary existence means existing in all possible worlds, logically possible existence means existing in at least one possible world, and logically impossible existence means existing in no possible worlds. A modified version of Plantinga’s Argument follows:

  1. The proposition that a thing has maximal excellence if and only if it has maximal excellence in every possible world is necessarily true.
  2. The proposition that whatever has maximal excellence is omnipotent, omniscient, and morally perfect is necessarily true.
  3. There is a possible world in which the property of possessing maximal greatness is exemplified.
  4. Therefore, the property of possessing maximal greatness is exemplified in every possible world.
  5. Therefore, God exists.

Again, this argument can be critiqued similar in a way to Hartshorne’s, by using this premise:

3′. There is a possible world in which the property of possessing maximal greatness is not exemplified.

Combined with 1, we get:

4′. Therefore, the property of possessing maximal greatness is exemplified in no possible world.

From this, we can conclude that God does not exist. Since both 3 and 3′ are equally likely and lead to opposite conclusions, I conclude that Plantinga’s ontological argument does not succeed.

I have examined four ontological arguments. I have concluded that none of them succeed in what they try to do: proving God’s existence. They either rest on highly questionable premises, or on premises in which different premises equally likely lead to opposite conclusions. Therefore, if there is to be a proof for God’s existence, it lies elsewhere.

Other web sites:

For further reading:

  • Plantinga, Alvin: The Ontological Argument
  • Plantinga, Alvin: God, Freedom, and Evil
  • Plantinga, Alvin: The Nature of Necessity
  • Barnes, Jonathan: The Ontological Argument
  • Hick, John & McGill, Arthur C.: The Many-Faced Argument
  • Hartshorne, Charles: Anselm’s Discovery
  • Oppy, Graham: Ontological Arguments and Belief in God

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