Kurt Goedels God existence proof

In the collected work of Kurt Goedel one finds a proof of Gods existence.
He never published it. But considered it to be a purely logical analysis. Even though he felt it still had some weaknesses.

-------------

It comes from theologian Anselm of Canterbury ideas:

It goes with our concept of God, that God is the most complete
being you can imagine. You can't imagine anything that is more complete
than God.
Completeness gives existence:
Therefore God must exist, because if he didn't exist, he would
lack this existence, and lacking existence would be incompleteness
for God.
If God didn't exist - you could imagine an even more complete
being - who would be very much like God, but with the added
ingredience of existence. But this would go against our concept
of God. Because you can't imagine something more complete complete
than God.

I.e. God exists.

-------------

George Boole in his "Laws of Thought" (1854) on such proofs,

mentions that a main motivation for him to develop this binary logic was to formalize & simplify the age-old logic of Aristoteles, as employed by Spinoza (17-th century phylosopher) and more recent Clarke for their God_existence 'proofs' -- And to check these proofs (editor: Boole himself was son of a clergyman/minister in Ireland).
His conclusion: those arguments were 'circular' (the result was in the premises;-) No surprise...

So what to make of it?

In Cranial Explorations one finds the idea that there is actually a 67 percent chance of existence.... :

So does He exist?
Stewen Unwin: God?

Q: Yes.
SDU: I don't know. Although my book does expand on this response.

Q: How so?
SDU: Well, most people write books on subjects they know. I did the opposite. My book is really about things I don't know about uncertainty.

Q: Uncertainty is seldom the stated position of participants in the debate about God's existence.
SDU: No, it isn't. We do tend to admire certainty in our society.

Yet, I think it was Bertrand Russell who said--- and this is probably a very mangled quote-- the problem with this world is that thoughtful, intelligent people are generally racked with doubt and uncertainty, while fools tend to be cocksure of themselves.

My position is that uncertainty has a crucial role in the way we believe in an about God.

But back to Anselm and Goedel:

In Anselm's Proslogion: One, Simple Proof Anselm supplements these arguments with an argument from God's necessity: First, Anselm, asserts, that the maximal being, if he does exist, cannot not exist either actually or in the mind. To this he adds a second premise, viz., that whatever can be thought to exist and does not exist could, if it were to exist, possibly not exist either in actuality or the mind. It follows from these premises and Anselm's second introductory premise, that God can be thought, that God does, indeed, exist.
Enters Goedel: 1970 ontological proof :
"Goedel showed his *1970 [Ontological Proof] to Dana Scott, and discussed it with him, in February 1970. Goedel was very concerned about his health at that time, feared that his death was near, and evidently wished to insure that this proof would not perish with him. Later in 1970, however, he apparently told Oskar Morgenstern that though he was 'satisfied' with the proof, he hesitated to publish it, for fear it would be thought "that he actually believes in God, whereas he is only engaged in a logical investigation (that is, in showing that such a proof with classical assumptions [completeness, etc.], correspondingly axiomatized, is possible)." Scott made notes on the proof and presented a version of the argument to his seminar on logical entailment at Princeton University in the fall of 1970. Through this presentation and the recollections and notes of those who attended the seminar, Goedel's ontological proof has become fairly widely known.

In ontological argument one finds a discussion on the validity of the argument:

"So that's it. The obvious question to ask is whether Goedel's proof is correct. I find myself agreeing with C. Anthony Anderson when he says the following: Consideration of the axioms, especially ... [Axiom G2], may tend to dampen one's confidence in ... [Axiom G3] and ... [Axiom G4] -- that is, if one harbors any real doubt about self-consistency. I don't say that the argument begs the questions of ... [God's possible existence]; the charge is too difficult to establish. but observe that one cannot just tell by scrutinizing a property what it entails; one might be surprised at a consequence.

To my way of thinking, this adds up to saying that Goedel's proof is really an argument, because the axioms (particularly those mentioned by Anderson) are not sufficiently self-evident to warrant calling the whole thing a proof.

Does that mean that we are back where we started? Far from it. Goedel's argument suggests an interesting via positiva (or via affirmativa) to understanding the idea of God. For example, it is interesting to compare the idea of a positive property in Gödel's sense with those aspects of this world that Calvin described as "the sparks of God's glory." According to Wordsworth this is

"A presence that disturbs me with the joy
Of elevated thoughts; a sense sublime
Of something far more deeply interfused,
Whose dwelling is the light of setting suns"

While nothing has been convincingly demonstrated, the argument may appeal to those who, like the philosopher Spinoza or the theologican Tillich, see God as in some sense the ideal aggregation of certain fundamental and essential aspects of being. It raises metaphysical questions about the determination of those essential aspects of being which must be present whenever something is said to exist. It raises the possibility of exploring the idea of God by a metaphysical enquiry into precisely those properties which may be determined to be positive.

Even if the argument is right in all its aspects, we still may not have a clear determination of what "pure attribution" is. It is possible that the God that will be proved to have necessary existence will be some blind equation that governs the quantum fluctuations of reality, or it is possible that the God that is proved to exist may be the Judeo-Christian God or the Tao of eastern mysticism. We simply do not know."

Back to homepage index

September 12th. 2007.

-Simon
Simon Laub.