COMMENSAL ISSUE 96

Note : This was posted on the Meta list, which was discussing a book The Loom of God: Mathematical Tapestries at the Edge of Time (Plenum; 1997) by Clifford Pickover wherein he made this quotation from Wang, Hao (1987) Reflections on Kurt Gödel, MIT Press: Mass, (page 195). See Clifford Pickover’s Web Site http://sprott.physics.wisc.edu/pickover/home.htm.

The above theorem by Kurt Gödel has been discussed at length on the Meta Discussion Group, which is sponsored by the John Templeton Foundation. Meta postings are protected by the note below, which appears on all postings, and a selection of such postings follows by way of commentary.

Any thoughts anyone ?

Theo

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Daniel J. Berger (Assoc. Prof. of Chemistry, Bluffton College, Ohio, USA) : Gödel’s proof is a version of St. Anselm's ontological argument: "God = supreme perfection; existence is a necessary aspect of perfection; therefore God exists." I can't imagine that Prof. Pickover isn't aware of that, yet I don't see a nickel's worth of difference between Anselm and Gödel. I respond emotively to this argument; I think Anselm was trying to reduce real, mystical experience to formal logic. Nevertheless, I believe the ontological argument is generally agreed to be the weakest of the classic formal arguments for God's existence.

George A. Sargeant : I've heard of Gödel’s proof before, but this is the first time I've ever seen it. In all honesty, it looks like a rehashed version of the ontological argument. It isn't clear whether the terms "positive" and "negative" refer to numbers or to good and evil. If the latter is the case, we could just as easily assume that being God-like is a negative property.

John Brink (Prof. of Biochemistry Emeritus, Clark University, Worcester, Massachusetts, USA) : When I read Larry Pickover’s presentation of Gödel’s "proof" of God’s existence I felt that there had to be a premise (axiom) that is dependant on one’s definition of God which may or may not be true yet logically and mathematically provable. Gödel’s 2nd axiom seems to contain the limited statement that a positive property is the only property that God can have and leads to his definition that "something is God-like only if it possesses all positive properties". If this is so then it places a restriction on God since any negative properties could not be considered a part of God’s universality and hence his proof is merely a derivation of a premise that has partial meaning. It reminds me of the Andrew Wiles’ proof of Fermat’s last theorem that was widely heralded several years ago but was found to be incomplete until Wiles subsequently proved the Shimura-Tamiyama conjecture which verified the theorem. We can only prove God’s existence if we know all the parameters that define God and if we did then we would be God and have no need to prove our own existence. What Gödel seems to have proven is that God is immanent without inclusion of the transcendent component of His universality.

Stan Tenen : I find Gödel’s "Mathematical Proof of God" to be unsatisfying, unsophisticated, and futile. It seems to me only wordplay to try to create a "proof of God". Far more useful would be a definition of God. Definitions are not subject to religious prejudices, and if they are consistent with reality, they can be very powerful analytic tools. I am proposing that the Abrahamic discovery was not that there is a God, but rather that "Atman and Brahman are One". The idea is that there is a transform relationship between the Great Singularity of consciousness in meditation, and the All-There-Is Wholeness of the universe. The idea is to define the Inner Single God and the Outer Whole God as one and the same. This is the equivalent of proposing that consciousness and physicality are also one and the same. They are complementary, like wave and particle. (G. Spencer Brown's definition of primary distinction, in his "Laws of Form," does this job in a modern topological context.) There's no need for a Gödelian tour-de-force. An appropriate definition does the job much better. Even though the definition is an abstraction, as it turns out it leads to meaningful discovery of the Transcendent as a bonus.

V. V. Raman : It was once alleged that in Catherine of Russia's court in the 18th century, during on argument with the French philosopher Diderot on the existence or otherwise of God, the mathematician Euler said something to the effect that [a + bⁿ]/c = d, therefore God exists, and that, unable to decipher the sophisticated symbolism of the eminent mathematician, the non-plused atheist Diderot left the court in embarrassment and humiliation. Historians of science have established that this was merely a story. In any event, that scene has been repeated in different variations by many people (scientists / mathematicians) since, but with more seriousness than Euler. Riemann tried to establish divine matters through mathematics, as did Gödel. And Tippler, in his provocative book quoted by Prof. Pickover, proved to the satisfaction of most who could not fathom his learned quotations from world-scriptures and technical physics that the soul’s immortality had finally been established beyond a reasonable doubt. What he illustrated in fact was the immortality of the debate and the obsession to PROVE God’s existence. The statement: "Were theologians to succeed in their attempt to strictly separate science and religion, they would kill religion," is equivalent to the declaration that if a person forgets his / her spouse’s birthday, that would end their marriage. This may be true in some cases, but cannot be formulated as a general proposition. The future of religions lies, in my view, not in hanging on to the coat-tails of empirical science for proof, respect, and recognition, but in appreciating the value and significance of trans-rational experiences and insights in matters spiritual, and in conceding the fallibility and finitude of the human mind when confronting the Infinite. Also, to say that "Theology simply must become a branch of physics if it is to survive," is as profoundly truthful as the statement that music must become a branch of Fourier analysis if it is to survive. Such statements arise from the blind veneration of reason in every dimension of human experience. Thus, the Proofs of God carefully elaborated by the likes of Spinoza, Tippler, and Gödel may be interesting for a handful of thinkers acquainted with logic, mathematics, cosmology or quantum physics, but they really become laughing stock in the reckoning of those who have experienced God through love or Nature, scripture or compassion, and above all through the faith that resonates in the heart. I am all for reason and rationality, but when one waves at me axioms and theorems, Heisenberg and quantum electrodynamics to convince me that Moses received the commandments from the Almighty out there in the Middle East, that Brahma is the one who made the universe, that Jesus was indeed the Son of God, or that the Archangel Gabriel spoke in Arabic to the Prophet, I am amused, if not uncomfortable. The aesthetic beauty and spiritual grandeur of mathematics are like the soul-uplifting magnificence of Art, Music, and Poetry. To contrive proofs of God through them is like using the piano to prove a Euclidean proposition.