Does this modal ontological argument prove the existence of God?

Question

What are some objections to this form of the argument? It seems like the only premise that can be disputed is premise 1, but nobody has successfully disproven the possibility of a maximally great being.

1. It's possible that a maximally great being exists. In other words, a maximally great being exists in some possible world.
2. If a maximally great being exists in some possible world, it exists in every possible world.
3. If a maximally great being exists in every possible world, then it exists in the actual world
4. Therefore, a maximally great being exists in the actual world.

Support for premise 2: A maximally great being wouldn't be maximally great if it only existed in some possible world. To be maximally great it has to exist in every possible world.

Answer 1

I understand your argument as follows:

1. A maximally great being possibly exists.
2. If a maximally great being possibly exists then it necessarily exists.
3. If a maximally great being necessarily exists then it actually exists
4. Therefore, a maximally great being actually exists.

Here is a reconstruction using modal logic:

1. ◊∃xGx
2. ◊∃xGx → □∃xGx
3. □∃xGx → ∃xGx
4. Therefore, ∃xGx

As written, the argument is valid; the conclusion does follow. Now for the premises.

Premise 3 is a logical truth, no problem there.

Premise 1, I take it, would be justified by claiming that a maximally great being is conceivable, and that it is therefore possible. That does seem plausible, but it is controversial whether conceivability entails possibility.

Premise 2 needs further support. You're assuming that if a maximally great being possibly exists then it necessarily exists, but you provide no justification for that. Possibility usually does not entail necessity, so you need some argumentation for this premise.

Finally, David Lewis provides a very good analysis of Anselm's modal ontological argument (which is somewhat similar to yours) in his paper Anselm and Actuality.

Answer 2

The proof does not work, I think. Your problems are premises 1 and 2.

My main problem is with premise 1: it is possible for a maximally great being to exist. Why should we accept this?

There is the tempting notion, mentioned in Eliran's (considerably better) answer, that anything we can imagine must be possible; but there is a great deal to be said about the nature of possibility and the rational mind before we can accept this. And even if it were true, the principle can surely only applied to determinate ideas, not simply names. For instance I can talk a fair amount about a circular square, but there is no true picture of such a thing in my mind. The same could be said of a world without time. Perhaps the same is true of a maximally-great being. At the very least I do not have such a picture.

We want some additional explanation for premise 2. We must show that necessary existence is greater than contingent existence. Now intuitively this is easy, in that it seems to be true, but we probably want to say that greatness comes from predicates, and it's not clear that necessity is a predicate.

To recap:

1. We don't know that intelligibility implies possibility

And

2. We don't know that "maximally-great being" is a truly intelligible concept

So

3. We don't know that it is possible for a maximally-great being to exist.

What's more,

4. We don't know that necessity is a predicate

Which means

5. We don't know it is greater to exist necessarily than contingently

Therefore

6. The proof fails.

Answer 3

The proof fails in the very first step. You try to justify this step in your initial explanation, but let's just put this explanation as part of the proof.

1. Nobody has successfully disproven the possibility of a maximally great being.
2. It's possible that a maximally great being exists.

You are basically fallaciously playing with the word "possible" here. What you've proven is that it's "possible" in the sense that "we do not know whether or not a maximally great being exists" i.e. the possibility is derived from uncertainty. However, you then try to jump to

3. In other words, a maximally great being exists in some possible world.

which requires you to establish a different meaning of possible--specifically, "in the set of all possible worlds, there is at least one in which a maximally great being exists." In this case, the possibility is derived from nonzero probability.

If your incorrect line of reasoning was valid, we could literally prove any mystery/uncertainty of the universe with it.

Answer 4

In a "round-about way" you are saying the same thing (using circular logic).
Let me rephrase:
1. It is possible that God Exists, (an assumption)
4. Therefore, God exists. (an unfounded assertion).
In other words, just because something is possible, does not necessarily make it so!

Answer 5

Breaking an informal argument into explicit steps is only half the battle; you also have to define your terms. In particular, this will often reveal that an "obvious" assumption is anything but . . .

. . . as it does in this case. You've edited to stipulate that statement (2) is justified by the definition of "maximally great being," so is implied by statement (1). OK, that's fine, but that depends on what you mean by "maximally great being." Whether or not the possibility of a maximally great being is plausible (let alone true) depends on what that phrase means precisely, and that's something you haven't even tried to do.

So you can indeed make (2) justified by choosing a sufficiently strong meaning for "maximally great being," but then that makes (1) extremely objectionable: given that maximal greatness now quantifies over all possible worlds, why on earth should such a thing be possible at all? ("Given any thing, I can imagine a better thing . . .")

And "nobody has successfully disproven the possibility of a maximally great being" is not a justification for (1) being a "reasonable" assumption at all. Nobody has yet disproved the possibility of a counterexample to the Riemann hypothesis; is that a reasonable assumption to make?

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OK fine, a comment on the last sentence: in mathematics people do prove "conditional" results, e.g. "If the Riemann hypothesis is false, then [something]." However, the hypothesis is part of the result: we do not claim to have proved [something]! So you can perfectly reasonably claim the conditional result "If the existence of a maximally great being is possible, then there is a maximally great being," but (a) that's not much of a surprise, and (b) you'll still need to define "maximally great being."

Answer 6

I assume your argument here is based on Plantinga's work. If so, a key thing you are ignoring is the primary axiom on which the argument relies, 'Axiom S5'. The modal operator states something along the lines of:

If it is possible that something is necessarily true, it must (logically) therefore be necessarily true in at least one possible world. If something is necessarily true in at least one possible world, it (logically) must be necessarily true in all possible worlds.

To demonstrate this, you could use a basic math sum as an example. It is possible that 2 + 2 = 4 is necessarily true, which means that in at least one possible world, 2 + 2 = 4 is necessarily true. However, if 2 + 2 = 4 is necessarily true in at least one possible world, it must also be necessary in all possible worlds.

To counter this axiom, with this example, you would have to argue why a world in which 2 + 2 does not equal 4 is a logically tenable possibility. This is fruitless though, because at this point you're arguing against a predefined set of terms, that are almost universally uncontroversial. The same can be said of Plantingas ontological argument and his concept of maximal greatness. The only way you might squeeze out of Axiom S5 as having these implications is if you, like James Garson, argue that necessary and possibility don't mean what Plantinga intends.

When the effect of this axiom is taken into account, the modal ontological argument can no longer be said to be begging the question, or circular reasoning. It simply demonstrates that if it is possible that the existence of a god-like being is necessarily true in one possible world, it's existence is simply necessary (in all possible worlds, of which ours is one).

Depending on your conclusions about the internal consistency of the definition of maximal greatness, this argument succeeds in proving that a maximally great being is either necessary (and thus god exists), or impossible (and thus god does not exist).

The problem with unicorns and pizza, and other silly replacements of maximal greatness is that there is nothing intrinsically "great" about any of them, especially in the sense that Plantinga means.

I'd strongly encourage you too study his argument more closely.

Answer 7

A better formation of the argument would go as follows:

Premise 1: "Either God exists or God does not exist."

Premise 2: "If God exists, then it is necessary that God exists."

Premise 3: "If God does not exist, then it is impossible that God exists."

Preliminary Conclusion: "Either it is necessary that God exists or it is impossible that God exists."

Premise 4: "It is impossible that God exists if and only if the concept of God is self-contradictory."

Premise 5: "The concept of God is not self-contradictory."

Preliminary Conclusion: "It is not impossible that God exists."

Final Conclusion: "It is necessary that God exists."

Notes: Premises 2 and 3 are supportable by logical arguments of their own. The arguments can be stated or not stated. Premise 5 needs to be proved. I hope this helps!

Answer 8

TL,DR: you must define your terms before using them.

Long version:

Just what does "maximally great" mean ? (Or even "great", in a theological context, for that matter...) As long as this concept of maximal greatness is not rigorously defined, any proposition derived from it is tainted and suspicious.

It follows from the vagueness of the premise 1 that premise 2 is meaningless as well. "Maximally" introduces the idea of a limit to greatness, without specifying what or where this limit is. Why should the aptitude of existing in multiple worlds (for whatever that means, again...) be within the limits of maximal greatness ? It might be impossible to exist in many worlds, why not? We have never observed a maximally great being or multiple worlds, therefore we can't possibly know. In all fairness premise 2 can't be granted as fact.