## Wednesday, May 13, 2015

### Aesthetics in the ontological argument

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

Let's take a little break from ontological arguments, and switch to math.  Consider the following proof.
Theorem: Given a square, opposite sides are parallel.
Proof:
By definition, a square is a rectangle with all equal sides
By definition, all the corners of a rectangle are right angles.
In the following figure of a rectangle, line AB and CD are cut by transversal BC.
By the consecutive interior angles theorem, AB and CD are parallel.

There's something very wrong with this proof.  Logically speaking, it's completely valid and sound, and I can't really think of a better way to prove the theorem it intends to prove.  But think about it:  Why are we only proving the theorem for squares?

The entire proof rests on the fact that squares are a special kind of rectangle. It's obvious that if we just replaced "square" with "rectangle", we could prove a more general theorem, and use fewer steps.  "Given a rectangle, its opposite sides are parallel."

This isn't an issue of logic.  It's an issue of aesthetics.  My mathematical training taught me to make the fewest assumptions necessary.  My training taught me to prove more general cases when I am able.

And that's why looking at the definitional ontological argument, I boggle.
$\text{God is defined to have all the perfections.}\tag{1a}\label{1a}$ $\text{Existence is a perfection.}\tag{1b}\label{1b}$ $\text{If something exists by definition, then it exists.}\tag{1c}\label{1c}$ $\text{Therefore, God exists.}\tag{1d}\label{1d}$
Earlier, we placed all our focus on the inference \ref{1c}, because that's the most questionable step.  But let's also take a moment to focus on the abysmal aesthetics of \ref{1a} and \ref{1b}.

The entire proof is based on the fact that God exists by definition.  Why, then, is it necessary to assume that God has all the perfections?  It is sufficient to assume that God just has one perfection--existence.1  If \ref{1c} were a correct inference, then we could prove a more general theorem, not just the theorem about God.

This is a problem for most ontological arguments.  They define God to have all the perfections, or to be the most supreme being imaginable.  In Alvin Plantinga's version, he goes so far as to define a "maximally great being" as omnipotent, omniscient, and morally perfect in every possible world.

Any decent mathematician would look at these words and say, "Why bother?"

Florid prose, or obscurantism?

I don't know what runs through the minds of philosophers who state ontological arguments with patently extraneous assumptions.  However, the florid definitions of God do serve a purpose, whether intentional or not.

The purpose is to prove only the special case of God, and draw attention away from the more general theorem.  Like with the theorem about squares, it's as if the mathematician wants you to only think about squares, and wants you to conveniently forget that the same theorem also holds for rectangles.

If people realized that the ontological argument works equally well for a large class of objects and not just God, then they might just realize that the ontological argument proves some things which are completely ridiculous.  For example, The Flying Spaghetti Monster is the most perfect cluster of noodles imaginable.  Therefore it exists.

I've made such reductio ad absurdum arguments before, and I find that ontological argument proponents dismiss them for various reasons.  For example, they would say the Flying Spaghetti Monster is inconceivable, or that it is conceptually inconsistent.

This is all missing the point.  When I look at the ontological arguments, it's clear that all the premises about God being the greatest and most perfect being are completely extraneous.  If ontological argument proponents truly think that the ontological argument only works to prove the existence of God and no other objects, then they clearly have some unstated premises.

In the next part of the series, I will be considering Plantinga's modal ontological argument.  However, the part of the argument where he talks about omnipotence and omniscience, that part will be dismissed and erased with contempt.

Maximization arguments

I should mention, for technical completeness, that sometimes the "florid" definition of God does some work after all, creating what I call the Maximization Ontological Argument.

In the Maximization Ontological Argument, God is specifically defined as the greatest thing that is conceivable.  Then it's asserted that a thing would be greater if it also exists.  I suppose this draws on the intuitive assumption that given any ordered set of things, there must be a maximum.  Of course, this assumption is just mathematically wrong (e.g. take the set of all integers, or the set of all irrational numbers less than one).

Even putting aside the fact that not all ordered sets have maximums, you can't simply assert things about a maximum on the basis that it would make it the maximum greater.  For example, consider the greatest even number less than 10.  Your first guess might be that the answer is 8, but consider that any number would be greater if you added 3 to it.  Therefore, 11 is the greatest even number less than 10.  I feel this argument is just flatly invalid, and doesn't really dignify in-depth discussion, so I'm going to move on.

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1. It's also worth noting that the extraneous assumption actively makes the proof weaker, because now we need the additional assumption that existence is a perfection.