Debugging the ontological argument

I'm introducing a new series on the ontological arguments for the existence of God.  Ontological arguments are basically attempts to prove that God exists using pure reasoning alone.  For example:

God is defined to be the most perfect being.
It is more perfect for something to exist than to not exist.
Therefore, God exists.

However, this is just one ontological argument, and I will cover several more, culminating in Godel's ontological argument.

This is the masterpost for the series, containing a complete list of links, as well as an explanation of my purpose and perspective.

Outline of series:

• The definitional ontological argument
• Is existence a predicate? 
• These things do not exist
• The conceptual ontological argument
• Making sense of existence
• The uselessness of the ontological argument
• Interlude: Aesthetics in the ontological argument
• Plantinga's modal ontological argument
• Modal logic semantics
• Addressing the argument
• Gödel's ontological argument
• Gödel's workarounds to the ontological argument
• Consistency and the material conditional
• Gödel's positive predicates
• Improving on Gödel

Purpose:

The primary purpose is to talk about logic.  When we discuss apparent paradoxes, I find that many beautiful details about logic come out of the woodwork!

I also know there are lots of people out there who are just plain curious about the ontological argument, so my secondary purpose is to satisfy your curiosity.

I am not here to merely show that ontological arguments are wrong.  If I wanted to persuade people, I could simply assert the argument's absurdity--this is essentially the strategy adopted by Richard Dawkins in The God Delusion, for instance. The fact of the matter is that a vanishingly small number of people think ontological arguments are correct.  While I'm sure a few proponents will show up in the comments, most people look at ontological arguments and immediately find them absurd and unpersuasive.

My purpose here is to pinpoint errors in the ontological arguments.  I also call it debugging the argument, as if to go line by line in a computer program and find the missing semicolon. Although unlike debugging a computer program, I will not actually correct the errors, since ontological arguments are fundamentally unfixable.

There are definitely ways to refute ontological arguments without pinpointing the problems.  For example, an argument ad absurdum extrapolates the argument to reach an absurd conclusion:

Ted is defined to be the most excellent being.
It is more excellent for something to exist than to not exist.
Therefore, Ted exists.

But even if you accept the argument ad absurdum, that doesn't tell you what is wrong with the argument.  It's like executing a program and encountering an error--it tells you that there's a bug, but doesn't tell you where.  Thus, in this series, I will refer to, but not rely on argument ad absurdum.

Perspective:

I am a random person on the internet.  I am not here to explain historical refutations of the ontological argument, I am offering my own original vision.  For a more scholarly treatment, I recommend more formal resources such as Wikipedia or the Stanford Encyclopedia of Philosophy.

My perspective is more that of a mathematician than a philosopher.  Most ontological arguments can be framed in logical terms, and my writing will focus on these terms.  Some ontological arguments add rhetorical bells and whistles to the logic, and privately I view these ornaments as unhelpful at best and obscurantist at worst.

Expertise:

Unless you count my minor in math, my expertise here is basically self-taught. I taught myself philosophical concepts as necessary, sometimes consulting my boyfriend, who has a degree in philosophy.  Many years ago, I taught myself modal logic just so I could understand modal ontological arguments.  I wrote a bunch of blog posts about it (see references below), and argued endlessly with a few ontological argument proponents.

Basically, you shouldn't trust me based on my expertise, but based on my arguments and reasoning.

Comment Policy:

If you have comments that do not pertain to any specific post, please comment here on the masterpost.  I will not reply to all comments.  I do not promise to be polite.

Throughout this series I will use MathJax to render LaTeX equations.  This requires that you enable Javascript.  LaTeX will not work for comments, so in the comments I will adopt the following conventions:

E - existence quantifier
A - universal quantifier
~ - negation
^ - and
V - or
=> - implication (will be rendered as =>)
&lt;=&gt; - equivalence (will be rendered as <=>)
N - necessary
P - possible
-&gt; - entailment (will be rendered as ->)
|= - satisfaction relation

I encourage readers to adopt the same conventions to avoid confusion.

Complete list of old posts
This is all the stuff I've previously written on the ontological argument.  I'm afraid some of it is not very clear, and I may have changed my mind on some of the details.  This new series is intended to be my definitive word on the subject.

A simple ontological argument
A modal ontological argument
Godel's ontological argument
Godel's ontological argument, step by step
Modal ontological argument, revisited
Plantinga responds to me
An anecdote on obscurantism
Necessity isn't so necessary