The Ontological Argument II: Anselm

This is the second article in a series of posts addressing arguments for the existence of any god or gods.  See my first post here.


Anselm was an eleventh century Monk whose version of the ontological argument may well have been the first, and in my experience is the best known.  At this point, I must reiterate a point from my original post: I am not a physicist, not a philosopher, so my opinions here are more that of the educated layman.  I certainly welcome comment on what will follow.


As part of that 'educated layman' position, I have never read Anselm's actual writings.  So I'm going to quote wikipedia's summary of his reasoning.  However, this again follows what I have generally seen elsewhere when people have proffered an ontological proof of god.  The argument goes as follows:

1. Our understanding of God is a being than which no greater can be conceived.
2. The idea of God exists in the mind.
3. A being which exists both in the mind and in reality is greater than a being that exists only in the mind.
4. If God only exists in the mind, then we can conceive of a greater being—that which exists in reality.
5. We cannot be imagining something that is greater than God.
6. Therefore, God exists.

Let's break this down.

The first three points are premises, the fourth and fifth the actual argument, and the last point the conclusion.  This argument rests on a proof by contradiction.  We assume that god has some set of properties, and then show that if we further assume god does not exist, we get a contradiction.

So, where does this go wrong?

The big problem lies in the first premise.  This sounds like a fairly innocuous definition; for example, let's say that I replace the word 'God' with the word 'Squarble' wherever it appears in the above.  This does not change the logical structure, so if the argument is valid it proves the existence of something: the being-than-which-no-greater-can-be-conceived.

But does such a being actually exist?  Consider, by way of analogy, numbers.  What is the number, than which no greater can be conceived?  There is none; for any number you state, I can always construct a larger one.  Even answering infinity does not save you, thanks to the existence of transfinite numbers.  It is not clear if the first premise defines god as something that exists even conceptually.

To get around this, we would need to offer a more precise definition of the concept of greatness.  In particular, we need a definition which has an obvious upper limit, and agrees with the third premise above: something is greater if it exists than if it does not.  It is not obvious to me that such a definition exists.  Some alternative expressions of the ontological argument are more careful in their definitions, and I will address some specific cases in my next post.  I will then end by arguing why I think all such approaches are destined to fail; essentially, that they rely on equivocating between the idea of god, and god itself.