WLC7: When an Ontological Argument Simply Isn't

In earlier articles, I looked at William Lane Craig’s debating style (in Debatable Theism) and the logic in his “logical” arguments (in The Logic of an Apologist). In the latter, I said that I would address the content of Craig’s arguments, please check that article if you are not already familiar with the logical forms.  This article addresses what I have numbered as Craig’s Seventh Argument (although it is really Alvin Plantinga’s argument reworded) – note that it wasn’t claimed by Craig as being a knock-down argument but as “providing some prima facie warrant for thinking that it is possible that (God) exists”.  First a quick recap:

 

Craig’s Seventh Argument – Plantinga’s Ontological Argument (Reworded)

(defended during a Book Fair starting at 07:57 and on Craig's website)

1. It is possible that a maximally great being exists.
2. If it is 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. If a maximally great being exists in the actual world, then a maximally great being exists.
6. Therefore, a maximally great being exists.

This is a straightforward polysyllogism:

1. Premise 1 - If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
2. Premise 2 - If a maximally great being exists in some possible world, then it exists in every possible world.
3. Premise 3 - If a maximally great being exists in every possible world, then it exists in the actual world.
4. Premise 4 - If a maximally great being exists in the actual world, then a maximally great being exists.
5. Assertion – It is possible that a maximally great being exists.
6. Conclusion – Therefore, a maximally great being exists.

The major problem with this argument is highlighted by simply placing the Assertion directly above the Conclusion.  This should not affect the argument, for example:

1. Premise 1 - If an animal is a standard cat, then that animal is a mammal.
2. Premise 2 - If an animal is a mammal, then that animal has a brain.
3. Premise 3 - If an animal has a brain, then that animal has neurons.
4. Premise 4 - If an animal has neurons, then that animal (while alive) has electrical activity in its body.
5. Assertion – Tiddles is a standard cat.
6. Conclusion – Therefore, Tiddles (while alive) has electrical activity in his body.

You can put the Assertion wherever you like.  Another problem with the argument is that its structure can be used, with only relatively minor changes to prove the non-existence of a maximally great being:

1. It is possible that a maximally great being does not exist.
2. If it is possible that a maximally great being does not exist, then there exists a possible world in which a maximally great being does not exist.
3. If there is a possible world in which a maximally great being does not exist, then it does not exist in every possible world.
4. If a maximally great being does not exist in every possible world, then it is not a maximally great being.
5. Therefore, there are no maximally great beings.

Note that this argument is a bit shorter, because the negative argument only needs one example of sub-maximal greatness, whereas the positive argument needs to go from some possible world, to every possible world, then to the actual world.  The ramification, however, is that the negative argument does permit a sub-maximally great being.  This leads us to:

1. It is possible that a sub-maximally great being exists.
2. If it is possible that a sub-maximally great being exists, then (by virtue of being sub-maximally great) the sub-maximally great being doesn’t have to exist in every possible world.
3. If a sub-maximally great being doesn’t have to exist in every possible world, then it doesn’t have to exist in the actual world.
4. If a sub-maximally great being doesn’t have to exist in the actual world, then a sub-maximally great being doesn’t have to exist.
5. Therefore, a sub-maximally great being doesn’t have to exist.

On first reading, premise 2 seems to be a bit of a leap, despite the clarification that I inserted.  My reasoning is analogous to premise 4 of the previous argument regarding a maximally great being: if a maximally great being exists, it must exist in every possible world, because otherwise there is potential for a greater being which is equally great across more worlds (ie in every possible world).  However, if a being is sub-maximally great, then this requirement is removed - even if a sub-maximally great being exists, it (unlike a maximally great being) doesn't have to exist in every possible world.

So, if we accept this form of argumentation, we are left with a sub-maximally great being which doesn’t need to exist.  OK, if you want to believe in something like that, fine.  Note that Craig actually argues against a sub-maximally great being (here, although he calls it a quasi-maximally great being):

 

Any intuition for thinking a quasi-maximally great being to be possible also warrants belief in the possibility of a maximally great being; indeed, the way we came to form the idea of the former was by diminution of the idea of the latter. But our intuition of the possibility of a maximally great being, once we understand its implications, tends to undermine our intuition of the possibility of a quasi-maximally great being. We begin to suspect that despite appearances, it’s not really possible after all.

 

I prefer another version of the ontological argument which I call the “Argument for the Existence of William Lane Craig from Maximal Stupidity” argument:

1. It is possible that a maximally stupid being called William Lane Craig exists.
   (This is just a premise; I’m not saying it’s true that there is a maximally stupid being called William Lane Craig, merely that it is possible.  However, now that I have raised this possibility, the onus is on a-”WLC-is-stupid”-ists to prove that it is not possible that there is a maximally stupid being called William Lane Craig.)
2. If it is possible that a maximally stupid being called William Lane Craig exists, then he exists in some possible world.
   (You can’t be maximally stupid if you don’t exist.)
3. If a maximally stupid being called William Lane Craig exists in some possible world, then he exists in every possible world.
   (You can’t be maximally stupid if you only exist in one world, since someone else might be slightly less stupid but existent in two worlds thus reaching a higher level of cumulative stupidity.)
4. If a maximally stupid being called William Lane Craig exists in every possible world, then he exists in the actual world.
   (Well, yeah, so long as the actual world is possible, which seems pretty plausible to me.)
5. If a maximally stupid being called William Lane Craig exists in the actual world, then a maximally stupid being called William Lane Craig exists.
   (I’m not sure that this line is strictly necessary, but it helps confuse the issue, especially for the monumentally stupid.)
6. Therefore, a maximally stupid being called William Lane Craig exists.

Some might wish to argue that this proves that the argument merely shows that Plantinga’s ontological argument (reworded) is of a valid form (so long as we were all able to agree that William Lane Craig exists and is monumentally stupid).  These people should try replacing “stupid being” with “beautiful transvestite”.  Not even atheists believe that William Lane Craig is a beautiful transvestite, let alone maximally beautiful.  This argument would just provide some prima facie warrant for thinking that it is possible that William Lane Craig is maximally stupid. 

Craig argues against some parodies of this argument (here again), since they refer to “concoctions (which) are impossible, contrast to the apparently coherent idea of a maximally great being”.  I agree, “a necessarily existent lion” or “an unsurpassingly great island” are impossible.  However, a maximally stupid being is a coherent idea.  We can imagine a being whose thoughts and actions are generally informed and driven by stupidity.  Then we can imagine another being that is slightly more consistently driven by stupidity, and so on until we reach a being whose every thought and action is informed by stupidity.  If we are thinking of an infinite number of worlds (which could be taken to be an unstated assumption in Plantinga’s ontological argument, it's not though, Plantinga uses a different trick - see below), then there is no reason to think that there should not be an infinite number of these beings, whose every thought and action is informed by stupidity.  If there is an infinite number of these beings, they will take an infinite array of names, such that any name you could think of would be applicable to at least one, or an infinite number of them.  Therefore, at least one of them will exist, in some possible world.  Therefore, it is an absolutely coherent idea that it is possible that there is a maximally stupid being called William Lane Craig.  We then just run the argument, as above, and find that there is such a being and that being exists in our world.

 

William Lane Craig may be comforted by the fact that the argument is not temporally limited.  That means that the argument works now, tomorrow, yesterday, one million years ago, one million years in the future, in fact, from the beginning to the end of time – and beyond, if necessary.  Accordingly, we will always have and always have had some sort of being called William Lane Craig.

 

The problem with Craig’s argument against parodies is that he compares things (impossible concoctions) to ideas (the apparently coherent idea of a maximally great being).  By doing so he conflates Plantinga’s ontological argument with Anselm’s.  Anselm’s argument centres on the assertion that a being which exists only as a concept in the mind is less great than a being which exists in reality: “And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone.”  Plantinga’s argument says nothing about ideas, or concepts or things which exist in the mind.

We can all acknowledge the existence of the idea of the existence of a maximally great being (or at least a God), irrespectively of whether we agree that it is a “coherent idea”, or even an “apparently coherent idea”.  If we believe in the idea of the existence of a maximally great being, then that belief will entail a secondary belief that that idea of the existence refers to an actual existence of the maximally great being, rather than the existence of the concept of the maximally great being.  This is just another statement about belief, a totally non-controversial, tautological one.  If one believes in the existence of God, then one believes that God actually exists.

 

So we come to the crux of the argument.  Anselm is basically arguing that if one has extreme beliefs then they must be true.  Plantinga (as reworded) seems to be arguing that if something is possible then it must be true.  He argues this explicitly in line 2: “if it is possible that a maximally great being exists, then a maximally great being exists in some possible world”.  In his actual argument, Plantinga relies on some fancy footwork while deploying Axiom S5.  This axiom states that, in modal logic, ◊p→◊□p meaning “if it is possible that p is true, then it is necessary that it is possible that p is true” (modal operators are underlined as one chunk where possible – the single, but split operator “if … then” is shown in bold).  The meaning of this axiom is: if something is possibly true, then that something is possibly true in all worlds.  Plantinga’s sleight of hand involves invoking a dual to claim that ◊□p→□p which, in strong logic terms, means “if it is possible that it is necessary that p is true, then it is necessary that p is true”.  Compare these in consecutive lines:

 

if it is possible that p is true, then it is necessary that it is possible that p is true (◊p→◊□p)

if it is possible that it is necessary that p is true, then it is necessary that p is true (◊□p→□p)

 

You can easily hide this sleight of hand by using modal logic operators (explained below), but in plain text and in the strong sense, ◊□p→□p is clearly not true in any real sense.  You can make it sound true by slightly rewording it using the following chain:

 

(◊□p→□p)

if it is possible that it is necessary that p is true, then it is necessary that p is true

If it is possible that something is true in all worlds, then it is true in some world

If it is possible that something maximal is true across all worlds, then it must be true in some world

If it is possible that something maximal is true across all worlds, then it must be true in some possible world

If it is possible that something maximal exists across all worlds, then it must exist in some possible world

If it is possible that something maximal exists, then it must exist in some possible world

If it is possible that something maximally great exists, then it must exist in some possible world

If it is possible some being that is maximally great exists, then it must exist in some possible world

If it is possible that a maximally great being exists, then a maximally great being exists in some possible world (which is premise 2 of Craig's version of the ontological argument)

So where is precisely Plantinga’s sleight of hand?  He doesn’t use the chain described above, he goes via the weak (Kripke) semantic logic meaning of ◊□p→□p, where the meaning of ◊ changes from it is possible that to in some possible world it is true that and □ changes from it is necessary that to in all possible worlds it is true that.  Then he takes advantage of the ambiguity, illustrated thus:

weak logic – if in some possible world it is true that in all possible worlds it is true that p is true, then in all possible worlds it is true that p is true (This is valid)

undefined logic – (◊□p→□p)

strong logic – if it is possible that it is necessary that p is true, then it is necessary that p is true (This is not valid)

But that’s not all.  Plantinga, together with Craig, uses ambiguity again, by conflating the interpretation of “some possible world” in weak semantic logic, as used to investigate the validity of a logical argument, with a mundane interpretation of “some possible world” that could considered to be actual rather than figurative.  This second sleight of hand is what Craig uses.  So this is where the two tricks are hidden:

1. Premise 1 - If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
   (a statement which can be derived through a chain of thought as above, or possibly by just not understanding Kripke semantic logic – involves a figurative possible world)
   
   
2. Premise 2 - If a maximally great being exists in some possible world, then it exists in every possible world.
   (replaces a figurative possible world with a possible actual world)
   
   
3. Premise 3 - If a maximally great being exists in every possible world, then it exists in the actual world.
4. Premise 4 - If a maximally great being exists in the actual world, then a maximally great being exists.
5. Assertion – It is possible that a maximally great being exists.
6. Conclusion – Therefore, a maximally great being exists.

It seems that we have proved, once and for all, that two wrongs do not necessarily make a right.  (← For the more obtuse among us, this is a joke.)

--------------------------

If there is anyone out there who remains unconvinced that the Ontological Argument is faulty, then the following proof is especially for you:

Let’s say that G means "an omnipotent, omniscient, omnibeneficent God exists" and g means "a sub-maximally great being exists".

◊g
This means: It is possible that a sub-maximally great being exists

◊g→◊◊~G
This means: If it is possible that a sub-maximally great being exists, then it is possible that in some possible world there is not an omnipotent, omniscient, omnibeneficent God (if there were such a god in all worlds, this God would be a maximally great being)

◊◊P↔◊P
This means: If it is possible that something is possible, it’s possible, so

◊g→◊~G
This means: If it is possible that a sub-maximally great being exists, then it is possible that there is not an omnipotent, omniscient, omnibeneficent God

◊P↔~□~P
This means: If it is possible that something is true, it cannot be necessary that it is not true, so

◊g→~□~~G
This means: If it is possible that a sub-maximally great being exists, then it is not necessary that there is not not an omnipotent, omniscient, omnibeneficent God

P↔~~P
This means: Something being true is equivalent to something being not false (or not not true), so

◊g→~□G
This means: If it is possible that a sub-maximally great being exists, then in no possible world it is true that there is an omnipotent, omniscient, omnibeneficent God.

We now finish off Craig-style:

The Christian God is omnipotent, omniscient and omnibeneficent.  But we have shown above that in no possible world it is true that there is an omnipotent, omniscient, omnibeneficent God.

If in no possible world is it true that there is an omnipotent, omniscient, omnibeneficent God, then there is no omnipotent, omniscient, omnibeneficent God in any world.

If there is no omnipotent, omniscient, omnibeneficent God in any world, then there is no omnipotent, omniscient, omnibeneficent God in this world.

If there is no omnipotent, omniscient, omnibeneficent God in this world, then there is no omnipotent, omniscient, omnibeneficent God.

Therefore, the Christian God does not exist.