Arguments for God, #1: The Ontological Argument

When I first heard the Ontological Argument, I thought it was the most obvious piece of sophistry I had ever heard. I assumed that nobody today believed in it. But I later learned that I was wrong: there are philosophers who still think this argument is okay. Anyway, even if you agree with me that the argument is obviously terrible, you might still find it interesting to talk about exactly what the mistake in it is.

The Ontological Argument

The traditional argument is something like this:

St. Anselm’s version:

1. God is defined as the being such that nothing greater than it can be conceived. (Premise/definition)

2. So nothing greater than God can be conceived. (From 1)

3. One can conceive of a god that exists. (Premise)

4. A god that exists is greater than one that doesn’t exist. (Premise)

5. Therefore, if God doesn’t exist, then something greater than God can be conceived. (From 3, 4)

6. Therefore, God exists. (From 2, 5)

Descartes’ version:

1'.   God is defined as a supremely perfect thing. (Premise/definition)

2'.   So God is supremely perfect. (From 1')

3'.   Any supremely perfect thing possesses all perfections. (Premise/definition)

4'.   Existence is a perfection. (Premise)

5'.   So God possesses existence. (From 1'-4')

6'.   So God exists. (From 5')

Whatever is wrong with one version is probably also wrong with the other.

Two Traditional Objections

The Pizza Objection

The first objection you think of is the reductio ad absurdum: if this argument works, you can also prove the existence of a perfect pizza. Just define a word, “Spizza”, to denote a supremely perfect pizza. Since existence is a perfection, Spizza must exist.

Descartes responded to this by saying that the concept SPIZZA (he used a different example) is different because it combines two distinct concepts: that of perfection, and that of pizza-hood. We can’t guarantee that there is anything having both of these attributes. But the concept GOD uses only one, simple concept, that of perfection. All other attributes of God follow from the concept of perfection.

I don’t buy that response; I think it’s irrelevant whether the concept is simple or complex since the logic of the Ontological Argument would seem to apply either way.

However, the reductio objection does not tell us what is wrong with the Ontological Argument. It just gives us a reason to think something is wrong with it. We should keep looking for what that is.

Existence Isn’t a Property

Another objection is that the fourth step in both versions of the argument is false. Existence isn’t a perfection, nor is it a great-making property, because existence is not an attribute of a thing at all.

Maybe a better way to put the problem is this: 4/4' states that a thing would have more of some attribute (“greatness”, “perfection”) if it existed than otherwise. This is conceptually confused, since it assumes that there can be nonexistent things. You take an existing thing over here, and then compare it to a non-existing thing over there . . . but that makes no sense. “Non-existent” doesn’t mean that you have a thing with a certain attribute; it means there is nothing there at all. So there is nothing to compare the existing thing to.

I think this objection is philosophically insightful. However, it appears that you could avoid any objection to step 4 by just explicitly building existence into the definition of “God”. E.g., define “God” to be “the all-powerful, existent creator of the universe”. Then you don’t need any step like 4, and you don’t have to argue about whether existence is implied by “perfection”, or “greatness”, or whatever.

Of course, this might make it more intuitively obvious that the argument is mere sophistry. Still, we haven’t said what exactly is wrong with it.

What’s Really Wrong

Descartes’ Version

Let’s focus on Descartes’ version for now. Step 2' does not follow from step 1'. Step 1' is a premise about the meaning of a word, the analysis of a concept, or something like that. For simplicity, call it a premise about the meaning of the word “God”. Such a premise can tell us what characteristics a thing must have in order for the word to apply to it. It can’t tell us whether the word applies to anything; for that, we would also need to know whether anything in fact has the needed characteristics.

So the correct inference would be:

1".  “God” is defined as “a supremely perfect thing”.

2".  Therefore, if “God” applies to anything, that thing is supremely perfect.

That would be valid. Equivalently, you could say, “If God exists, then God is supremely perfect”.

This is the same thing we would say about any other concept. For example, bachelors are defined to be unmarried men. It follows from this that if bachelors exist, then they are unmarried. Or: If “bachelor” applies to anyone, then that person is unmarried. But there’s no way of getting a completely unconditional statement (without the “if”).

This point might be concealed by the fact that we usually say “all bachelors are unmarried” follows from the definition of “bachelor”, and it doesn’t superficially look as though “all bachelors are unmarried” contains a clause like “if such-and-such exists . . .”. But there are two readings of “all bachelors are unmarried”:

• a. It can be read with “existential import”, as they say in logic. This is how it is treated in Aristotelian logic. On this reading, “All bachelors are unmarried” entails that there are bachelors. But, uncontroversially, “All bachelors are unmarried” would then not follow merely from the meaning of “bachelor”.

• b. It can be read without existential import, as in modern logic. On this reading, the statement really means, “If anything is a bachelor, then it is unmarried.” (In predicate logic: (x)(Bx --> Ux).)

Applying this point to God, we could consider two readings of “God is supremely perfect.”

• a. The reading with existential import. On this reading, “God is supremely perfect” does not follow from the meaning of “God”.

• b. The reading without existential import. On this reading, the statement would have to mean, “If anything is God, then that thing is supremely perfect.” (In predicate logic: (x)(Gx --> Px).)

Now you can see that the argument falls apart. The clause “if anything is God” will have to be carried all the way through the argument, whose conclusion will now read:

6".  If anything is God, then God exists.

And the atheist will have no problem with this. He’ll just deny that anything is God.

Anselm’s Version

The application to Anselm’s version of the argument is straightforward. For 2 to follow from 1, step 2 must be read as:

2*.  If anything is God, then nothing greater than that thing can be conceived.

And the conclusion will have to be:

6*. If anything is God, then God exists.

However, because of the “conceivability” operator in Anselm’s version, there is another possible reading. One could argue that step 2 will still follow if it is interpreted as:

2**.   It is impossible to conceive a scenario in which there is God and some other thing, and the other thing is greater than God.

That seems legitimate. But then, to avoid equivocation, step 5 would have to be given a parallel reading:

5**.   If God doesn’t exist, then it is possible to conceive a scenario in which there is God and some other thing, and the other thing is greater than God.

But now that’s false, and we have no reason to accept it. Remember that step 5 was supposed to be derived from:

3.    One can conceive of a god that exists.

4.    A god that exists is greater than one that doesn’t exist.

5** does not follow from those. What follows is that if God does not exist in the actual world, then you can imagine a world in which there is a god who would be greater in that world than God is in the actual world. In the actual world, let’s suppose, God’s degree of greatness is 0 because he doesn’t exist. You could imagine a world in which there’s a God with a nonzero degree of greatness. So in that sense, you could imagine something greater than God. But of course, you still cannot imagine a world in which Anselm’s God and some other god are both present, and the other one is greater.

Modal Version

Modal versions of the ontological argument are now more popular. They go something like this:

1. It's possible that there is a necessarily existing God.

2. If it's possible that it's necessary that P, then it's necessary that P. (Theorem of modal logic, specifically of S5)

3. Therefore, God exists necessarily.

I don't give much attention to this, because I think there is no difficulty figuring out the problem there -- #1 is just obviously false. (Note: Consider that [God doesn't exist] isn't contradictory, and if it isn't, then obviously it's false that it could be contradictory. The same applies to metaphysical impossibility.) I think it might seem plausible to some people, though, because of some confusion.

Anyway, I think #1 is as plausible as

1'. It's possible that there is a necessarily existing pizza.

from which you can prove that there is a necessary pizza.