Saturday, April 11, 2015

The uselessness of ontological arguments

This is part of my series on debugging the ontological argument.

Previously, I rebutted the conceptual ontological argument (COA).  But I want to make one more point about its soundness and validity.

Soundness and Validity

In logical/deductive arguments, we have the concept of validity, and soundness.  An argument is valid if its conclusions follow from its premises.  An argument is sound if its conclusions follow from its premises, and the premises are true. Consider the following arguments:
Socrates is a man.
All men are mortal.
Therefore, Socrates is mortal
(Valid and sound)

Socrates is a snake.
All snakes have eight legs.
Therefore, Socrates has eight legs.
(Valid but not sound, and conclusion is false)

Socrates is a flying submarine.
All flying submarines are mortal
Therefore, Socrates is mortal.
(Valid but not sound, and conclusion is true)

Socrates is a talking plant.
All mortals are talking plants.
Therefore, Socrates is mortal.
(Neither sound nor valid, but the conclusion is true)
Note that if the argument is unsound, the conclusion can either be true or false. Soundness, however, always implies validity, and always implies that the conclusion is true.

Is the conceptual ontological argument sound?

So what about the COA?

The COA takes a single premise, that "God is conceivable".  From there it concludes that God exists in the real world.  The objection I raised before is that the proof works only if we take a particular definition of "God is conceivable."  Namely, if we conceive of an object, we can call it God only if the object exists in the real world.  This makes it rather difficult to verify that God is conceivable!

But I would say that the COA is valid, and it's only the soundness I question.

Now suppose for a moment that God really does exist.  We know that all things that exist are also conceivable.  So you'd have to conclude that the premise is true, and COA is sound.  If God exists, then the COA is sound.  Equivalently: if the COA is unsound, then God does not exist.

As an opponent of ontological arguments, people often think my role is to argue that ontological arguments are unsound.  However, if I did successfully argue that COA is unsound, I would not just refute the COA, I would be disproving God entirely!  While I am unapologetically atheist, such a conclusion remains outside the scope of this series.

I do not wish to argue that ontological arguments are unsound, instead I wish to argue that they are "useless".

Useful arguments

My concept of "usefulness" is my own idea, but it's inspired by something written by Chris Hallquist.  He says:
An argument can be sound and still not be any good. Imagine arguing with someone who believes that the Sun orbits the Earth rather than the other way around. Now imagine giving them the following argument: “Premise: the Earth orbits the Sun. Conclusion: the Earth orbits the Sun.” If the premise of this argument is true, the conclusion must be true, and the premise is true. Thus the argument is sound. 

Yet you couldn’t blame anyone for not being persuaded by that argument.
With that in mind, I say that an argument is useful if its conclusions are more difficult to demonstrate directly than its premises are.

Note that usefulness is not a logical concept.  Within the formal logic, there is no notion of "direct demonstration" and no notion of "difficult".  Usefulness is a pragmatic concept.  Consider the following sound but useless arguments:
The Earth orbits the sun.
Therefore, the Earth orbits the sun.

If Mars is a giant egg, then the moon is made of cheese.1
The moon is not made of cheese.
Therefore, Mars is not a giant egg.

All four cards in my hand are aces.
Therefore, at least one card in my hand is an ace.2
Since I do not believe in gods, I also believe that the COA is unsound.  However, even if you disagree on this point, you must agree that the COA is useless.

It is only possible to demonstrate that "God is conceivable" if you first demonstrate that God exists.  Since the conclusion of the argument is that God exists, that means that the premise is at least as hard to demonstrate as the conclusion.

This is an important point moving forward, because I will argue that all the remaining ontological arguments in this series fail by being useless.3


1. This premise is true if we're using the material conditional.  The material conditional will appear much later in this series, but for now I refer you to Google.

2. The idea here is that proving that all four cards in my hand are aces is at least as hard as proving that at least one is an ace.  Actually this argument isn't sound because I'm not actually holding any cards right now, but please grant the hypothetical.

3. There's an interesting philosophical question: Even if all known ontological arguments fail, how can we be sure that we won't find one which succeeds?  In my opinion, to address this question, we need a good way to define "success".  We already have ontological arguments which succeed, in the sense of being sound.  For example, I define my keyboard as a keyboard that exists.  I can conceive of this keyboard (I'm typing with it!), therefore it exists.  The premise is correct, the reasoning is correct, and the conclusion is correct.  However, the argument still fails in the sense of being useless.