To: Christian M.
From: Geoffrey Klempner
Subject: Does Descartes succeed in proving that God exists?
Date: 3 July 2007 10:33

Dear Christian,

Thank you for your email of 24 June, with your University of London essay in response to the question, 'Does Descartes succeed in proving that God exists?'

In response to your question about further reading, I would suggest reading some of the 'Objections and Replies' because these are fascinating. Just dip in. There is no need to start at the beginning and read through to the end. The complete works of Descartes can be found in the Haldane and Ross edition, first published in paperback with an up to date translation by Cambridge University Press in 1967. You should be able to find an inexpensive copy on Amazon.

You have written a very good exam answer on Descartes' proofs of the existence of God. If I was an examiner I would be impressed. You explain yourself clearly and marshal your arguments effectively, showing that you have a good understanding of Descartes' arguments and the questions that might be raised against them.

This is an open-ended question, like the other questions that you will come across in an exam. There is no final agreement amongst philosophers or scholars on how these arguments should be evaluated. You will even find attempts to defend versions of the ontological argument today. I am going to suggest some issues that you had perhaps not thought of, not in the spirit of criticism but rather in order to give you more to think about - and perhaps some extra ammunition too.

The main problem with the argument from the idea of infinity is presenting it in a way which makes it even seem plausible. One can hardly claim success in evaluating the argument if one presents it in a way which makes it seem obviously fallacious and therefore easy to refute (I'm not necessarily saying that you've done this). Why does Descartes put so much faith in this argument? It can't just be the fact that it came to him as a 'clear and distinct idea'. What is the idea?

A possible approach is to consider our concept of infinity, as such. The series of natural numbers 0, 1, 2, 3... is held to be infinite. Do we understand what that means?

Mathematicians have a neat way of defining an 'infinite' set which seems to circumvent the problem of getting one's mind round infinity. A set has infinitely many members if there is a function which maps these members onto a proper subset. The set of natural numbers is infinite because there is a function, 'times 2' which puts the set of all natural numbers into a 1-1 correlation with the set of even numbers.

While that approach works for mathematics, it does not help at all when it comes to the question, e.g. whether as a matter of empirical (though unverifiable) fact, the universe is infinite, either in extent or in time. What does someone believe when they believe this? Is there, in fact, a coherent content or we merely mouthing nonsense when we use the word 'infinite' in this context?

In the philosophy of language, you will come across the influential view, developed by Hilary Putnam and Saul Kripke, that so-called 'natural kind' concepts gain their meaning from their extension - pointing out objects in the world and saying, 'the same kind as that'. The concept 'gold' requires the actual existence of gold, it is not something that merely comes out of our own heads. Though this is not a view advocated by Descartes, it looks like the kind of thing he is talking about when he raises the question of what would be sufficient to explain the occurrence or use of an idea.

I liked your use of the example of the butterfly effect, because it helps to raise the question of the source of concepts in a precise way. A butterfly lands on a window pane and sparks an idea in the mind of a novelist which leads eventually to a magnificent novel of fantasy and adventure. However, not all concepts arise 'from our own heads'. The concept 'Gold' is not the same as the invented concept 'heavy yellow metal'. If there were no gold, we logically could not have a concept of it.

I hope you can see the pertinence of this to the question of our concept of infinity and God. I would say that Descartes does not, although he thinks he does, have an 'idea' of God or actual (non-mathematical) infinity.

A philosopher who has a very high opinion of Descartes 'idea of infinity' argument is the continental thinker Emmanuel Levinas, who argues that this structure applies to the problem of self and other. I won't attempt to summarize Levinas's view but this is something you can look up for yourself.

In criticizing the ontological argument, you say, 'You can formally attach the predicate 'necessarily existing' to any idea (e.g. a green angel that necessarily exists) but this does not entail its ontological existence.'

If by 'formally attaching' you mean merely writing down the sentence then of course this has no consequences for existence.

However, if I say to you, 'I have a concept of a green angel that necessarily exists,' then you should challenge me to produce a PROOF that my concept has the consequence of necessary existence.

Consider mathematics again. There is at least one set, the null or empty set. Leaving aside the question of what exactly 'exists' means in logic or mathematics, here we have an example of necessary existence. If you can form the concept of the null set then there must be a null set in every possible world, including this one. If the null set necessarily exists then a fortiori the null set exists.

Similarly, Descartes hasn't just attached 'necessary existence' to his favourite pet idea. He is claiming that he HAS the idea of God as a being which, because of its perfection, must necessarily exist. That is the claim that one needs to attack.

All the best,

Geoffrey