Arguing about Ontology

 

1.  Introduction

In How to argue about gods, I stated my intention to construct a series on the arguments of natural theology.  This is the first post in that series, and it will cover the Ontological Argument, as defended by William Lane Craig.

Before we begin, I’d like you to have a good think about your answers to the following questions:

Q1.  Do you think it’s possible that God exists?

Q2.  Do you think it’s possible that God doesn’t exist?

Despite the simple language, there are a few terms (specifically, God and possible) whose precise meanings could potentially change your answers.  I’ll get to this shortly but, for the moment, it suffices to give your answers according to your intuitive understanding of the questions.  You might have answered Yes to both questions.  You might have answered Yes to one and No to the other; in this case, you probably already have your mind made up about the existence of God!  It seems obvious that there is only one prohibited pair of answers: you cannot logically answer No to both.

The first thing to note when discussing the Ontological Argument is that there are actually several very different ontological arguments, and I will most likely consider some or all of the others in future posts.  (For a very thorough discussion, see Graham Oppy’s books Ontological Arguments and Belief in God and Arguing About Gods.)  But the argument usually known as The Ontological Argument goes back to St Anselm of Canterbury, and I will be focusing on an adaptation of Anselm’s argument presented by William Lane Craig in this lecture and this debate.  (Craig very rarely defends this argument in public debates; I’ve only seen it in that one debate, against Victor Stenger.  This debate was also noteworthy for Craig’s decision not to defend the Fine Tuning Argument; this is a pity because Stenger, a noted physicist, has written extensively on the Fallacy of Fine Tuning, and it would have been interesting to see Craig pit himself against an expert in the field.)  Craig’s formulation of the argument is very similar to Alvin Plantinga’s, and the critiques I present here apply equally well to Plantinga.

2.  What does God mean?

Before outlining the argument, Craig defines a key term:

“God is, by definition, the greatest being conceivable.”

In an effort to help his audience grasp this concept, he adds:

“If you could conceive of anything greater than God, then that would be God”,

even though it makes precisely as much sense to say:

“A zillion is the largest number.  If there was a number larger than a zillion, then that would be a zillion.”

This makes me wonder if Craig truly understands the concept of Maximality, but I will speak more about this in a later post where I will also devote some attention to the troublesome notion of Greatness.  Craig then considers some of the consequences of such a definition.  To be the greatest conceivable being:

“God would therefore be all-powerful, all-knowing, all-good and would exist in every logically possible world.”

According to Craig, anything less could not be the greatest conceivable being, and this seems reasonable to me.  (Perhaps I would object that it is problematic for Craig to use “good” as a measure of greatness here since, for example, in his debate with Sam Harris, he states that “God’s own holy and loving nature provides the absolute standard against which all actions are measured”, so that to say “God is maximally good” is just to say “God’s nature is maximally like God’s nature”.  I won’t dwell on this issue here, though, as it is not central to my argument.)  Note that a maximally great being might have other properties; for example, it might enjoy watching basketball but not tennis.  But the properties listed above are among the essential ones.

It is very important to realise that many theists might believe in a God that would not conform to Craig’s definition.  For example, you might believe that the universe was created by a very powerful – but not all-powerful – creator; or you might believe that this being knows a lot – but not everything.  I will come back to this point a few times throughout the post.  Suffice it to say, even if I could successfully prove that there was no God, according to Craig’s definition, I may not have proved that your God doesn’t exist.

Now that we have Craig’s definition of God in mind, there is one more term we need to consider before we move on to the argument itself.  In the above quote, Craig mentions logically possible worlds.  If you are not familiar with this notion, the Wikipedia page on Modal Logic provides a brief but technical overview; the page on Logical Possibility is helpful too.  For this post, it is enough to understand a “logically possible world” to mean a non-contradictory state of affairs in some self-contained realm of existence.  An even simpler way to understand the concept would be “a way the world could have been”.  Such a world could be very much like ours, or very different, even to the point of having different physical laws; but it must not have any logical contradictions built into it.  (Some philosophers, the Modal Realists, think that all possible worlds have a real existence, just like ours does, with possible worlds being somewhat like causally isolated universes in a larger multiverse.)

It is now worth going back to questions Q1 and Q2 which, in Craig’s language, can be rephrased as follows:

Q1.  Do you think it’s logically possible that the greatest being conceivable exists?

Q2.  Do you think it’s logically possible that the greatest being conceivable doesn’t exist?

Why not pause again to consider your answers to these questions.  Have your answers changed from before?  From this point onwards, when I refer to Q1 or Q2, it will be these rephrased versions that I have in mind.

3.  Craig’s Ontological Argument

Now it’s time to delve into Craig’s formulation of the argument.  This is how he puts it:

1. It’s possible that a maximally great being (God) exists.
2. If it’s possible that a maximally great being exists, then a maximally great being exists in some possible world.
3. If a maximally great being exists in some possible world, then it exists in every possible world.
4. If a maximally great being exists in every possible world, then it exists in the actual world.
5. Therefore, a maximally great being exists in the actual world.
6. Therefore, a maximally great being exists.
7. Therefore, God exists.

(Note that Craig blurs the distinction between the terms “greatest being conceivable” and “maximally great being”.  Although there do appear to be some subtle differences, it will not be important to dwell on them here, so I will follow Craig and use the terms interchangeably myself.)

As you can see, the first premise amounts to a positive answer to Q1.  And Craig correctly assures us that Steps 2-7 are “relatively uncontroversial”.  (The trickiest part of the argument is Step 3, which involves an application of what is known as S5 Modal Logic.  A fairly informal justification of Step 3 might go something like this…  Suppose a maximally great being B exists in some possible world W.  Then, by the consequences of the definition of maximally great as noted above by Craig, it would be true for anyone living in W to say “B exists in every logically possible world”.  Hence, it is true to say that B exists in every possible world.)

So, as Craig notes, the whole argument hinges on the first premise, and he says:

“The whole question is Premise 1.  Is God’s existence possible?  Well, what do you think?  The atheist has to maintain that it’s impossible that God exists.  He has to say that the concept of God is logically incoherent, like the idea of a married bachelor, or a round square.  But the problem is that the concept of God just doesn’t appear to be incoherent in that way.  The idea of a being which is all-powerful, all-knowing and all-good in every logically possible world seems perfectly coherent.  Moreover, as we’ve seen, there are other arguments for God’s existence which at least suggest that it’s at least logically possible that God exists.  So I’ll simply leave it to you tonight.  Do you think that it’s possible that God exists?   If you do, then it follows logically that God does exist.”

(I’ll come back later to the question of whether it is logically coherent to speak of an all-powerful, all-knowing and all-good being that exists in every logically possible world.)  Given that Craig points out that the whole argument comes down to Premise 1, you’d think he’d give a pretty strong defense of that premise, wouldn’t you?  But instead, he simply asks the question “What do you think?”, and just leaves it up to his audience members to intuitively decide.  (I’ll show in later posts that Craig relies on the gut feelings of his audience in every single one of his arguments.)

Regardless of what you think about the first premise, if we grant the validity of S5 Modal Logic, the above argument serves as a proof of the following proposition:

Proposition 1.  A positive answer to Q1 would entail the existence of God.

4.  Equivocation

For the time being, I’ll leave the question of whether we should accept Premise 1 or not.  But it is important to consider this statement from the above quote:

“Moreover, as we’ve seen, there are other arguments for God’s existence which at least suggest that it’s at least logically possible that God exists.”

Here, amazingly, Craig is equivocating on the word “God”.  The other arguments Craig refers to are:

1. The cosmological argument,
2. The fine tuning argument,
3. The moral argument, and
4. The argument from the historicity of the resurrection of Jesus.

(I explain the idea of equivocation in Section 2 of How to argue about gods.)  I say that Craig is equivocating in this statement because these arguments do nothing to establish the existence of the greatest being conceivable.  Even if we grant the conclusion of these arguments (and I do not intend to imply that I think there is good reason to do so), we would believe that there exists a being that created the universe, set its parameters, decided what would be right and wrong, and arranged for Jesus to rise from the dead.  The astute reader will notice that these conclusions do not entail that such a being is the greatest being conceivable.  As I mentioned above, you might believe that the universe was created by a very powerful being, but not an all-powerful being; you might call this being God, but Craig would not, at least not according to his definition that we are working with.  In particular, when Craig asks the question

“Do you think it’s possible that God exists?”,

he is not asking the question

“Do you think it’s possible that the universe had a creator?”.

He is asking the question

“Do you think it’s possible that an all-powerful, all-knowing and all-good being exists in every logically possible world?“

(I won’t speculate here as to whether it was Craig’s intention for his audience to mistakenly confuse these questions.)  It may also be the case that Craig implicitly equivocates on the word “possible” when he asks

Do you think it’s possible that God exists?,

or at least hopes his audience will confuse logical possibility with the more everyday meaning of the word possible when considering their answer.  An untrained audience is very likely to mistakenly interpret this question as being the opposite of “Are you certain there is no God?“, and Craig would know this very well.  Again, I won’t speculate as to Craig’s intentions, as this really is a side issue.  But I do intend to devote a future post to the idea of swapping between meanings of the word possible in order to “prove” some rather remarkable (and demonstrably false) things.

5.  The Dual Ontological Argument

As I have already stressed, Craig’s Ontological Argument assumes a positive answer to Q1 as its first premise.  But what happens if we assume a positive answer to Q2 instead?  This is what happens:

1. It’s possible that a maximally great being (God) doesn’t exist.
2. If it’s possible that a maximally great being doesn’t exist, then a maximally great being doesn’t exist in some possible world.
3. If a maximally great being doesn’t exist in some possible world, then it doesn’t exist in any possible world.
4. If a maximally great being doesn’t exist in any possible world, then it doesn’t exist in the actual world.
5. Therefore, a maximally great being doesn’t exist in the actual world.
6. Therefore, a maximally great being doesn’t exist.
7. Therefore, God doesn’t exist.

Wow!  The exact same logic implies that God doesn’t exist!  Let’s call the above argument the Dual Ontological Argument.  Again, the trickiest step in this argument is Step 3, and this time I think it is worth giving its proper justification:

1. Suppose a maximally great being doesn’t exist in some possible world, W1.
2. Let W2 be any other possible world.
3. If a maximally great being exists in W2, then it would exist in every possible world (by Craig’s argument above).
4. In particular, if a maximally great being exists in W2, then it would exist in W1.
5. But this would contradict the assumption that a maximally great being doesn’t exist in W1.
6. Therefore, a maximally great being doesn’t exist in W2.
7. Therefore, a maximally great being doesn’t exist in any possible world.

With this justification in place, we see that Steps 2-7 of the Dual Ontological Argument are exactly as uncontroversial as Steps 2-7 of Craig’s Ontological Argument.  In what follows, I will paraphrase Craig’s words from above (but ignore his incorrect statement about the relevance of his other theistic arguments):

The whole question is Premise 1.  Well, what do you think?  The theist has to maintain that it’s impossible that God doesn’t exist.  He has to say that the very idea of there being no God is logically incoherent, like the idea of a married bachelor, or a round square.  But the problem is that the concept of there being no God just doesn’t appear to be incoherent in that way.  The idea that there is not a being that is all-powerful, all-knowing and all-good in every logically possible world seems perfectly coherent.  So I’ll simply leave it to you tonight.  Do you think that it’s possible that God doesn’t exist?  If you do, then it follows logically that God doesn’t exist.

It is important to remember that these words still refer to “God” as the maximally great being defined by Craig.  So the question

“Do you think it’s possible that God doesn’t exist?”

should not be confused with the question

“Do you think it’s possible that the universe didn’t have a creator?”.

You could quite well think that the universe had a creator, but not think that this creator was all-powerful, all-knowing and all-good in every logically possible world.

Again, whatever your opinion of the validity of its first premise, the Dual Ontological Argument certainly furnishes a proof of the following proposition:

Proposition 2.  A positive answer to Q2 would entail the non-existence of God.

6.  Does God exist?

So far, we have seen that, assuming the validity of S5 Modal Logic, it is possible to prove the following two propositions:

Proposition 1.  A positive answer to Q1 would entail the existence of God.

Proposition 2.  A positive answer to Q2 would entail the non-existence of God.

To me, the most interesting outcome of all this is that, since God cannot both exist and not exist at the same time, it is not possible for both Q1 and Q2 to have a positive answer!  And I have already noted that it is not possible for both Q1 and Q2 to have a negative answer.  So it follows that one, and only one, of Q1 and Q2 has a positive answer.  But which one?!

It is perhaps worth stating the questions again:

Q1.  Do you think it’s logically possible that the greatest being conceivable exists?

Q2.  Do you think it’s logically possible that the greatest being conceivable doesn’t exist?

Now, I don’t claim to know which of Q1 or Q2 has a positive answer.  But I do have a very strong leaning towards Q2, and I’ll attempt to argue my case shortly.  Note that, as I keep stressing, this doesn’t mean I believe the universe didn’t have a creator.  Although I don’t have a belief in a creator, I do not have enough information to form a reasonable belief that the universe doesn’t have one.  (For example, even if all the evidence pointed towards there being no creator, how could one rule out the possibility that the universe was created by an omni-shy being, who didn’t want anyone to know him, and therefore made it look like he didn’t exist?)  But I certainly don’t think it is obviously logically impossible, if the universe does have a creator, for that creator not to be maximally great.  As I have now said a few times, perhaps the universe has a very powerful creator, but not an all-powerful creator.

So let’s try and decide between Q1 and Q2.  Let’s first note what a positive answer to each question would entail:

Yes to Q1:  There exists a logically possible world in which there is an all-powerful, all-knowing and all-good being (which, by definition, must in fact exist in all logically possible worlds).

Yes to Q2:  There exists a logically possible world in which there is no all-powerful, all-knowing and all-good being (which, therefore, doesn’t exist in all possible worlds).

It should be noted that the Evidential Problem of Evil directly confronts the former situation.  A proper treatment of this argument will have to wait for another occasion but, roughly stated, it asserts that the sheer amount of gratuitous (human and animal) suffering we observe in the world is incompatible with the existence of an all-powerful, all-knowing and all-good being who, supposedly, would want to reduce the suffering, would know how to do so, and would be able to do so.  As such, anyone that deems this argument successful could not give a positive answer to Q1.  Many philosophers consider the argument insurmountable.

But let’s not dwell on the Evidential Problem of Evil because, as I said, now is not the time for a proper discussion of it.  Instead, let’s address Q2 directly.

Does there exist a logically possible world in which there is no all-powerful, all-knowing and all-good being?

I don’t see why not.  What about:

• a world in which there is simply nothing?
• or a world in which there exists nothing but a single grain of sand?
• or a world in which there is a single being incapable of creating anything?
• or a world in which there is an all-powerful, all-knowing, but completely evil being?
• or a world in which there are two beings, both of whom are always nasty to each other?
• or a world in which there is an infinite collection of beings, each more powerful, knowledgeable and good than the last?
• or a world with a universe created by a very powerful, very knowledgeable, very good being that is not, however, maximally great?

None of these worlds appear to me to be logically impossible, and none of the beings described in these worlds are maximally great.  All manner of other logically possible worlds could be described in which there does not exist an all-powerful, all-knowing and all-good being.

But these are just a few ideas off the top of my head that lead me to think that a positive answer can be more likely given to Q2 than Q1.  What must a theist do to justify a negative answer to Q2?  Well, as I have shown, if he would like to think that God exists, according to Craig’s definition, he must show that there is no logically possible world lacking an all-powerful, all-knowing and all-good being (and, further, that all logically possible worlds must have precisely the same maximally great being).  So not only must he show that each and every one of the worlds described above are logically impossible, he must in fact show that there are no logically possible worlds without such a being.

So it seems most likely to me that the answer to Q2 is Yes.  And this, as we have seen, entails that there is no maximally great being – in our world or in any other world.

7.  Conclusion

So what are we to make of all this?  If my arguments are deemed sound, does this settle the God Question once and for all?  I do not think so.

I believe that the problem with Craig’s Ontological Argument is that it requires too strong a definition of God.   In order to make the argument work, God must be assumed to be all-powerful, all-knowing, all-good and to exist in all logically possible worlds.  But, as we have seen, the very possibility of such a remarkable being not existing logically entails its non-existence.  And it seems quite obvious to me that there could be a logically possible world without such a being.

So, is there therefore no God?  Again, I don’t think I have answered this question.  But I think I have provided a strong case against the existence of an all-powerful, all-knowing, all-good being that exists in all logically possible worlds.  And this might not be your God.  It certainly isn’t the God of Christianity, despite what most Christians would say.

8.  Acknowledgement

I benefited from a discussion with Paul Almond during the preparation of this post.