Jesus and Godel’s Theorem

“Religion” is an attempt to create or build a tower with a top, or to build a temple that is self-contained. The story of The Tower of Babel in Genesis 11 is the story of mankind’s attempt to create a world that is self-contained and does not need God. All ancient pagan temples were renewed attempts to complete the Tower of Babel.  These were termed “ziggurats,” and were viewed as connecting points, or umbilical cords between heaven and earth.  Heaven and earth were in the ancient pagan cosmology, part of one eternal entity.

The Temple in Israel was purposely built with a similarity to the ancient ziggurat, and as an answer to the ziggurat.  It was built on the top of a mountain, and was a “connecting” place to the God of Israel.  But the God of Israel was not encompassed or contained within it, nor was His liberty compromised by it, as were pagan gods by their temples.  Never-the-less, Israel was constantly tempted to believe that their temple was like the temples of the nations.  The destruction of Shiloh, the capture of the Ark in Samuel’s time (1 Samuel 4), and the destruction of Solomon’s Temple (2 Chronicles 36:15-21) contradicted Israel’s constant temptation to “religion”.  The theology of Steven Spielberg’s Raiders of the Lost Ark is quite accurate.  The Nazis, like Israel at Shiloh, believed that possession of the Ark entailed possession and control of Jehovah.  In this they were wrong.

Arend Theodoor van Leeuwen says that the destruction of Herod’s Temple in 70 A.D. was in principle the destruction of all temples.1 The last 20 centuries of Christian history have progressively undone one temple after another.  But, Christians themselves are tempted to new temples.  Byzantine was an attempt to recreate on a Christian basis, at least a partial “ontocratic” or self-contained church/state, to use van Leeuwen’s terminology.  The Roman Catholic Church has constantly been tempted in this way, and Protestant sectarianism is guilty in these ways as well.2
Hopefully, it is increasingly clear that there is no top to the towers of this world, as we saw demonstrated in the 20th century when we saw all of the great ideologies fall.  This opens the door to nihilisms, but also makes more clear than ever that it is only the Sovereign Triune God who is the I Am that I Am, and I Will Be that I Will Be.  Only He is self-contained.

The modern city, and indeed, the modern world as a “global village,” is a “tower without a top.”  Religion is done for.  Bonhoeffer glimpsed this possibility in what he termed a “religionless Christianity.3 The story of The Tower of Babel sets the theme for all of God’s redemptive work in history.  Fallen man’s idolatrous desire is to make for himself a self-contained world of complete adequacy.

When Carl Sagan says, “The Cosmos is all there is, or all there ever will,” he is stating the sentiments of the builders of the Tower of Babel.  For them, the upper emporium was the realm of the gods, but it was by human effort and construction, a reachable realm, and that was itself a part of one cosmos.  As one moved up the tower to the realm of the gods, one’s own being could also be “divinized”.  Man’s being was potentially divine, given the right techniques and methods, amongst which “tower construction” was foremost.4 But God frustrated them and left them off with an incomplete tower, a tower without a top.

II.

Gödel’s Proof was by all accounts one of the most spectacular intellectual feats of the 20th century.  I am not a mathematician, and I must rely on authority for my knowledge of it.  But one of its implications is indeed that “religion” of the sort that I have been describing, is not only dead, but an impossible dream.

Bertrand Russell and Alfred North Whitehead’s Principia Mathematica (1925-27) was a monumental attempt to completely ground mathematics in logic, and make these foundational disciplines wholly self-consistent, self-contained, and self-grounding.5 An unstated implication of Russell’s work (and I am not imputing a motive to Russell and Whitehead, I am pointing out an implication) is quite simply that if one can establish that logic and arithmetic are self-grounding, then God does not exist.  The existence of the creator God of the Bible (as opposed to pagan finite gods, and of Whitehead’s finite god of process theology) means that all things, and elements in the world are grounded in and upheld by God and can only find their completion and final consistency in Him.

He is the creator and sustainer of the whole universe, from the largest galaxies to the smallest quark, to a simple number.  If one could effectively demonstrate the complete self-consistency and self-containedness of so much as a single fly, then God’s existence would be overthrown.  To prove that logic and arithmetic are wholly self-complete and self-consistent, and need no grounding outside of themselves, was an ideal target and one that seemed feasible, and one that Russell and Whitehead pursued with Herculean effort.

Russell and Whitehead could never escape the consequence that logical and mathematical sets always generate their own internal contradictions.  This tendency seemed to be ubiquitous, and the thesis they set out to demonstrate (that logic and mathematics could ground themselves) could never be established.  This essentially broke Russell’s intellectual back.  After not succeeding, he never wrote another truly serious philosophical work, and became the intellectual world’s enfant terrible.  The very simple paradox of writing on one side of a card, “the statement on the other side of this card is true,” and on the other, “the statement on the other side of this card is false,” was irresolvable and is a very simple illustration of what was encountered in much more sophisticated and complex ways with all sets.  Kurt Gödel later (1931) demonstrated with a rigorous mathematical proof that this will always be the case, with all non-trivial sets.

Gödel was himself a believing Lutheran, and he later constructed his own proofs for God’s existence.  But it is fascinating that his most famous proof is itself a kind of mathematical reproduction of the old cosmological proof for God’s existence, which relies on the intuition that everything in the world, and the world itself, is contingent.  That is, it is not self-contained, but is ontologically dependent and relies on something other than itself for its own existence.  For Thomas Aquinas and others, this leads finally back to God as a first cause, and prime mover.

Now, Gödel said that every set will eventually generate its own contradictions that are not resolvable internally, but can only be resolved by moving up to the next set above it, and by introducing an assumption not inherent within that set.  The implications of Gödel’s Theorem for the possibility of a final Unified Theory that would explain everything are distinctly humbling.

The heavily mathematical nature of all modern cosmology may even spell its doom.6 The dream of fallen man for a self-contained and self-explaining cosmos is further away than ever.  But is there any “super set” that could resolve the contradictions of everything?  As a Christian, one can embrace the dogma that the Trinity is finally the only infinite, self-contained and entirely consistent “set”.  But the complete and final consistency of the Trinity is incomprehensible to the human intellect.  The Trinity must be bowed to, and cannot be controlled or contained.  There is no temple that we can build that will house Him.  And the simple final point needs to be made that the Trinity is not a part of the created order, but is the source of it.

If one gives sociological or historical application to this, all human and historical systems eventually become self-contradictory.   So for example, “it is not good that man should be alone.”  Aloneness is a contradiction to the self, and in the creation account could only be resolved with another self, the woman.  But married couples themselves are not self-contained, and for this reason the “bed and board” is at the center of marriage.  With the table, the meal becomes the foundation of hospitality and giving to those outside of the relationship, and the bed begets children.  Bed and board take the couple outside of themselves.

But families with children are not self-contained, and need schools, and neighborhood associations with clubs and other groupings to complete what the needs of both parents and children are.  And likewise, schools and other organizations are not sufficient unto themselves, but require authorities and structures above them to resolve contradictions that arise.  And up and up it goes, until finally one has reached the level of nations and world structures.  But it is clear that nations are not self-sufficient, that attempts at self-sufficiency have historically been one of the major sources of war.7) And now, it is apparent that an agency like the United Nations is not exactly contradiction free either.

It is patently obvious that the much touted need for “communication” as a panacea is illusory.  One can only communicate what one has, and if two parties are inherently contradictory, then “communication” can only enhance and highlight the contradiction that is there in the first place. This is exactly what the “vicious circle” is.  Forums like the United Nations often increase conflict rather than resolve it.  Vulgar reality shows in America like Jerry Springer find all of their impetus in making already conflicted couples “share” their conflicts before a national audience.  More often than not, it leads to a physical conflagration, which hugely entertains the audience.

A whole series of interlocking and self-contradictory systems that cannot find resolution can be aptly said to exist in a state of “hopelessness” and may exist in a state of war.  All that can happen is a reproduction of past contradictions, and these can be seen to be endlessly repetitive.  So, on a simple level, pastoral or psychological counseling constantly run into vicious circles.  If the wife could only give herself in the physical relationship, the husband would feel more accepted and could give the wife the love that she needs.  But if the husband could only give love to the wife, she might be more able to physically give herself.  And around and around it goes.

Both are sure the other is the responsible party, and neither has the resources to be different apart from the desired change in the other.  Or again, if a young man who is failing could only get an entry level job, it would begin to give him the confidence he needs to break out of a welfare mentality.  But, in order to get that job, he will have to have a certain level of confidence in the first place.  Most neurosis involves the “vicious circle” of this sort.  People need relationship and need to be able to depend on someone.

The greatest barrier to relationship is the fear of losing independence, and the other party also desperately fear being depended on.  All of these kinds of contradictions function at both the individual level and at the very highest and most complex corporate level.  A world forum like the United Nations is a mare’s nest of convoluted contradictions, and may be one of the places in the world least likely to promote peace and harmony.  At every level, self-generated contradictions in every system and institution are present, but increase in complexity increases the contradictions.

And from here, where does one go?

III.

What we have observed is an “odd rationality” that makes up the world. We have observed that the structure of rationality itself seems to have a kind of at incompleteness in the world, and every attempt to complete it destroys it. Completion is only found in the transcendent, outside of the world.

The creation is not self-contained, and can only find its completion in the Creator. The Christian story is the story of God Himself, in the second person of the Trinity, coming down into His own creation and taking upon Himself all of the contradictions of a cosmos gone mad. The One who came down is termed the “Logos” by John. “Logos” is the root word of the English word, “logic.”

One implication of Jesus being the “Logos” is that the completely self-consistent One came from the outside into history. The death of Jesus was that time when the Logos voluntarily took into Himself all of the contradictions of this world gone mad. His resurrection was in principle, the entire renewal and re-purposing of the world, with Him as the new, consistent head of creation. The first head of creation (Adam) plunged us into an impossible mad house. Jesus, being the Logos and the second person of the Trinity, reconnected the cosmos to the whole of the Trinity as its final end.

The Church is those who are “the called out ones” (“ecclesia” in the Greek). The Church is “a royal priesthood.” (1 Peter 2:9). A royal priest is a king / priest. A king rules and a priest is one who offers up sacrifice. And how do we rule and what do we sacrifice? Well, in the first place, we by faith partake of the sacrifice of Christ, which was the all sufficient sacrifice for all time and all places. But in partaking of it, we feast on its efficacy, and we have reproduced in us the same kind of life and death that He had. In the Lord’s Supper, we partake of His body which was broken on all of the contradictions of a world gone mad, and we drink His blood, which spilled in the violence of a world declaring self-sufficiency.

As each member partakes, the body is broken many times and the blood is spilt many times. But after partaking of His death, we are raised to new life, to supernatural life, to life that now finds its end in Him and in the Spirit and the Father. We find our true end as a people, even now at the beginning of resurrection life. The Church begins as broken and many, as a contradiction, but it ends as one, as a body that is reconstituted. The broken body of Christ now fills out His own resurrection in the resurrection and now supernatural unity of the Church. All of this happens by faith. We only see the barest outline of it.

But this is only the beginning. The Church is now called to be priest / king to the world. The sacrifice that we bring to the world is the sacrifice of praise. All of the brokenness of the world is to be brought to God by His people in praise and thanksgiving. As this is done, the healing power of God’s consistency is brought to a contradiction ridden world. We are told that even now, we are seated with Christ in the Heavenly places (Ephesians 2:6) which means that in a very mysterious way, we are even now co-rulers with Christ, who is seated at the right hand of the Father. The prayers, action, and speech of the church are the secret government of the world.

The Kingdom is here now. Christ is seated at the right hand of the Father, which means that He is now the king, but the manifestation is hidden. This is why virtually all of Jesus teaching about the Kingdom is in parables. The Kingdom is itself like a parable, it is comprehensible, but hidden. Over and over, Jesus says things like, “He who has ears to hear, let him hear, and he who eyes to see, let him see.”

On two occasions, God has allowed the world to come to almost a complete dead end in its own internal contradictions, as He let it go its own way. Those two times were the time immediately preceding the Flood, and the time that also coincided with the coming of Christ. By the time Jesus came, the pagan world had tried everything, had done everything that was humanly possible, and it had run out of gas. Augustus Caesar, the Caesar reigning when Jesus was born, was the final culmination point of the classical world.

After him, it was only the contradictions of an independent cosmos that could be manifest. Human decline was all that was left. At the very point of the beginning of the end, the final End and Purpose of all things was born to bring a new world. The Kingdom, which has its seed in the church, was born, and it has since that time, with all of her failings and weaknesses, continued to be the root and source of new life and of possible consistency.

Our calling is to learn to be ever more faithful priest / kings, because whether we are very aware of it or not, we are the bearers of the hope of the world. At every level, relationship and bonds break, and all attempts at communication become impossible.  Everything that is said, in a world without God, in all attempts to quell conflict, in fact only increase conflict.  But through worship and gratitude to the Living God, we enter into the perfect communion of the Father and the Son as they speak by the breath of the Holy Spirit.

God’s Breath becomes our Breath, and this Breath creates a new “fruit of lips” that brings the bonds of peace in a renewed language (Isaiah 57:18).  When Isaiah prophesies, “In that day there will be five cities in the land of Egypt which speak the language of Canaan and swear allegiance to the LORD of hosts” (Isaiah 19:18), he is promising that the language of vicious circles of all tower building people will end with the coming salvation of the Lord.  With the coming of the Lord into every set or level of reality, the outside factor that is not included within that set can be introduced, and consistency and peace can become realities.8

Richard Bledsoe is a Theopolis Fellow and works as a chaplain in Boulder, Colorado.

References   [ + ]

1. Arend Theodoor van Leeuwen, Christianity in World History (New York: Charles Scribner’s Sons, 1964) 417
2. Some Lutheran and Orthodox believers sincerely believe that their churches are “the one true church on earth.” Many Reformed people in practice believe the same thing of their own groups. Rome formally holds to this concerning herself, but I find it less vigorously applied.
3. I always have the feeling that Bonhoeffer has been illegitimately hijacked by liberal theologians. The whole corpus of his writing is remarkably evangelical, and on the basis of a few musings written under the most terrible duress while the whole world was falling apart, scores of liberal theologians have made him one of their own number. It seems to me that there are more fruitful and evangelical understandings of “religionless” than people like Harvey Cox have put forward.
4. It is also the case that the builders believed they could shut the Living God out, and that they could “outsmart” Him, and overcome Him. The text says that they used “tar” or “bitumen” in the construction (Genesis 11:3). These are waterproof mortars. They remember the flood, but can now rise above another one by means of a waterproof tower.
5. Alfred North Whitehead and Bertrand Russell, Principia Mathematica (Cambridge: Cambridge University Press, 1925-7) 3 vol.
6. Stanley Jaki, The Savior of Science (Grand Rapids: Eerdmans, 2000) 120-121
7. I remember many years ago finding Ludwig von Mises thesis in his book Omnipotent Government: the Rise of the Total State and Total War, to be immensely illuminating. With great lucidity, he showed how from a purely economic perspective, war was an inevitability under fascism, because the attempt of the state to become entirely self-sufficient (which he termed an autocracy) could only be off-set by the conquest of neighbors, when in fact the impossibilities of such self-sufficiency made themselves apparent. (New Haven: Yale University Press, 1944
8. The original idea for this article is traceable to a lecture I heard by my friend John Crighton, who was on Intervarsity Christian Fellowship Staff at Colorado University, in probably the summer of 1970 or 1971.