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#159 Does the Ontological Argument Beg the Question?

May 03, 2010

Dear Dr. Craig,

As I Christian, I would first like to thank you for your work! It is extremely refreshing to see such a solid defense of Christianity in our pluralistic, secular world. My question is about Platinga's modal ontological argument which you use. Plantinga defines a maximally excellent being as a being with the properties of omnipotence, omniscience, etc. and a maximally great being as one which exists in all possible worlds. Now, if we let G be the proposition "A maximally excellent being exists", Plantinga's argument reduces as follows in modal logic. For readers unfamiliar with modal operators, "◊" means "it is possible that" and "□" means it is necessary that."

1. ◊□G [Premise]
2. ◊□G → □G [S5 axiom]
3. □G [1, 2]
4. □G → G [S5 axiom]
5. G [3, 4]

(1) ["It is possible that it is necessary that a maximally excellent being exists"]
seems modest enough. However, upon doing research into the argument, I found that the entailment runs the other way. In other words:

□G → ◊□G is true also because of the S5 axiom. So, this implies that ◊□G ↔ □G. Because (1) and (3) are logically equivalent, the argument reduces to:

1. □G [Premise]
2. □G → G [S5 axiom]
3. G [1, 2]

But this carries no force at all since no one will accept the first premise unless they accept the conclusion! Once it is clear that "possibly necessary" is the same thing as "necessary," the argument loses its force, for there seems to be no way to convince the atheist that God exists necessarily. In fact, he would object to such a notion since there is no logical contradiction in saying "God does not exist."

I really like the modal ontological argument, but it is because of this objection I now find it untenable. Is there any way to resolve this problem?

Thank you and God bless,


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Dr. craig’s response


The question of whether we have independent warrant for believing the first premiss of the ontological argument is certainly the crucial question facing the argument’s proponent. That premiss states that it’s possible that a maximally great being exists, where “maximal greatness” is understood to be the property of having maximal excellence in every possible world. The question, then, is whether maximal greatness is possibly exemplified.

PB, I think I can resolve your problem with the argument. First, your reconstruction of the argument is wrong. This is evident because you wind up with the contingent conclusion (5): "A maximally excellent being exists." But the ontological argument intends to show that a maximally great being exists, one whose existence is necessary. You should have stopped the reconstruction of the argument with step (3): □G.

Second, you confuse necessity de re with necessity de dicto. Necessity de re is the necessity of a thing (res); necessity de dicto is the necessity of a statement (dictum). The first premiss of the ontological argument asserts that a certain statement is possible, namely, the statement that a maximally great being exists or that maximal greatness is exemplified. It is not the statement, "It is possible that it is necessary that a maximally excellent being exists." That statement involves the iteration of two modalities de dicto. If we let G be the proposition "A maximally great being exists," the first premiss should be symbolized: ◊G.

Third, you confuse logical equivalence with synonymity. To say that “Possibly, a maximally great being exists” is, indeed, logically equivalent to saying that “Possibly, it is necessary that a maximally excellent being exists.” But these statements do not mean the same thing. It is the meaning of a statement that is relevant to its epistemic status for us, not its logical entailments. A statement may seem true to us even though we are quite unaware of its logical implications. It is therefore a mistake to say that "’possibly necessary’ is the same thing as ‘necessary,’" if by “is” you mean “means.” So it is a mistake as well to think that because ◊□G ↔ □G, the first premiss of the argument “reduces” to □G. It’s not a matter of reduction but deduction! The whole point of the ontological argument is to show that in asserting the possibility of the existence of a maximally great being one has committed oneself to its actual existence. The nature of a deductive argument is that the conclusion is implicit, stashed away, as it were, in the premises, waiting to be made explicit by means of the logical rules of inference. One typically believes that ◊□G without first believing that □G; at least one needn’t first believe that □G and then on that basis infer that ◊□G. One’s modal intuitions may support the belief that ◊□G, and then one may realize that that is logically equivalent to and so entails that □G, and so one comes to believe that a maximally great being exists.

In a nutshell: the logical equivalence of the conclusion of the ontological argument to its first premiss just shows that it’s a valid deductive argument, not that it’s question–begging.

As for the atheist’s retort that it’s not self-contradictory to say, “God does not exist,” this is irrelevant because the argument is framed in terms of broadly logical possibility/necessity, not narrowly or strictly logical possibility/necessity. There’s no contradiction in asserting “The Prime Minister is a prime number,” but that hardly shows that such a statement is possibly true in the relevant sense (that there is a possible world in which that statement is true). The atheist has to maintain that the idea of maximal greatness is broadly logically incoherent, like the idea of a married bachelor. But the idea of maximal greatness seems perfectly coherent and therefore possible—which entails that maximal greatness is exemplified!

- William Lane Craig