# Plantinga's Ontological Argument

## 3. Plantinga's Ontological Argument Restated

Analogies aside, what is specifically wrong with Plantinga's modal argument for the existence of God? Where is the mistake? The persuasiveness of Plantinga's argument rests on two key factors. Firstly, Plantinga very skilfully defined God's attributes in terms of possible worlds that were self-referential. Secondly, he capitalized on the intuitive notion that necessary truths are true in every possible world. His genius lay in his ability to weave inextricably these two components together so that his conclusion seemed to follow inexorably.

In order to untangle Plantinga's ontological argument and uncover its confusions, let me begin by stating his argument in a more structured fashion. The final version of Plantinga's [1975: 111–12] ontological argument can be put more clearly as follows:

- There is a possible world [
*W*] in which maximal greatness is instantiated. - Necessarily, a being is maximally great only if it has maximal excellence in every world.
- Necessarily, a being has maximal excellence in every world only if it has omniscience, omnipotence, and moral perfection in every world.

- If
*W*had been actual, then there would have existed a being that was omnipotent, omniscient, and morally perfect in every possible world.

- If
*W*had been actual, it would have been impossible that (33) 'There is no omnipotent, omniscient, and morally perfect being'.

- It is impossible that (33) 'There is no omnipotent, omniscient, and morally perfect being'.
- Necessarily, there is an omnipotent, omniscient, and morally perfect being.

Plantinga [1975: 111] claimed propositions (31′) and (33′) followed from his (29), (30) and (31). Conclusion (C1), he argued, followed from (33′) while (C2) followed from (C1). Note that the labels (31′), (33′), (C1) and (C2) did not form part of Plantinga's argument. I have added them here for clarity.

Was Plantinga right in thinking that this argument is valid? For Plantinga [1975: 109, 111], propositions (30) and (31) are true by definition. Both propositions (31′) and (33′) are indeed entailed by (29), (30) and (31). The leap from (33′) to (C1) relies on Plantinga's informally stated axiom of transworld impossibility; that what is impossible in at least one possible world is impossible in every possible world. Let's grant that if this axiom were included as an explicit premise in Plantinga's argument, the inference to (C1) would be valid. However, we would still need to conclude that Plantinga's argument was not sound. (Here, I take a 'sound' argument to be one that is both valid and contains true premises.) It remains unsound because its key premise (29) is false. Moreover, I will try to show that this premise is necessarily false.

This weakness in Plantinga's argument is fatal, as anything and everything follows from a contradictory premise. The subtle confusion in Plantinga's argument is camouflaged by the recursive nature of Plantinga's definitions of his key terms and also by their reflexive reference to possible worlds. As Plantinga's definition of 'maximal excellence' is doubly iterative, I will illustrate my counterargument using a simpler example.

Consider the following argument for the necessary existence of an invincible wizard.

- ⋄Qa

- Qa=
_{df}◻Ra

- ◻¬¬Ra
- ◻Ra

- There is a possible world [
*M*] in which exists an unbeatable sorcerer.

- By definition, an unbeatable sorcerer is an invincible wizard in every possible world.

- If possible world [
*M*] had been actual, then there would have existed an invincible wizard in every possible world.

- If possible world [
*M*] had been actual, then it would have been impossible that no invincible wizard exists.

- It is impossible that no invincible wizard exists.
- It is necessary that there exists an invincible wizard.

where

Qa = 'Entity a is an unbeatable sorcerer'

Ra = 'Entity a is an invincible wizard'

For ease of comparison, I have mirrored here the premise numbering with the numbering of the premises in Plantinga's argument above. Once again, let's grant that with the addition of the axiom of transworld impossibility (i.e., that what is impossible in at least one possible world is impossible in every possible world) the argument to conclusions (C1A) and (C2A) is valid.

My aim here is to show that (29A) is false, and necessarily so. Let's assume for the moment that (29A) true. If (29A) is true, by substitution using definition (31A), the following proposition is true:

- ⋄◻Ra

- There is a possible world [
*M*] in which exists an invincible wizard in every possible world.

If an invincible wizard exists in every possible world, then it's not possible for there to be a possible world in which an invincible wizard does not exist.

However, there is no self-contradiction expressed in the proposition:

- ¬Ra

- There is no invincible wizard.

Therefore, it is possible for there to be a possible world in which an invincible wizard does not exist. Therefore, it is impossible that an invincible wizard exists in every possible world.

Therefore, (29A′) is false. This falsity can be expressed formally as:

- ◻¬◻Ra

By substitution using definition (31A), it is impossible that there exists an unbeatable sorcerer. Expressed formally:

- ◻¬Qa

The existence of an unbeatable sorcerer is not only false, it is necessarily false. We can conclude, then, that premise (29A) is necessarily false. It is logically impossible that there is an unbeatable sorcerer in the sense defined here. Now, the structure of the above argument is essentially the same as that in Plantinga's ontological argument. By the same token, then, premise (29) in Plantinga's argument, that maximal greatness is possibly instantiated, is necessarily false.[1]

### Footnotes

- [1] Mackie [1982: 59] also argues specifically for the rational inadmissibility of this crucial premise on the grounds that other premises contradictory with this one are equally logically possible. His criticism here is independent of his other criticism of Plantinga's adoption of S
_{5}as the appropriate system of modal logic in which to express his ontological argument. Oppy [2016: §7] also rejects Plantinga's (29) along similar lines.