General Incompleteness Principle
Gödel’s Incompleteness Theorem and Divine Revelation
The Incompleteness Theorem
In September 1930, on the third day of a symposium on the foundations of mathematics, young Kurt Gödel detonated his bombshell: the Incompleteness Theorem. Loosely, by proving that formal mathematics cannot prove everything - even within its own formal system - it reduced the modernist aspirations of 19th century mathematics to rubble.
Douglas Hofstadter explains this to non academic audiences in his book, “Gödel, Escher, Bach: an Eternal Golden Braid”. The original theorem addresses TNT - Typographical Number Theory. Each theorem of TNT, true or false, is a string of symbols. The idea of TNT was a set of rules for modifications to a known true theorem to create new true theorems. The thought was to thus, in principle, iterate through proofs for all true theorems of TNT.
Gödel assigned each symbol a number, and thus each theorem became a number - TNT theorems also apply to TNT theorems. Read Hofstadter’s book for the fascinating details illustrated with Bach music, Escher drawings, and Hofstadter dialogs between Achilles, Tortoise, and others.
For our purposes, formal systems of math cannot enumerate all true theorems. And yet, humans can produce true theorems unreachable within the formal system. As these are also numbers, these were dubbed “Supernatural Numbers” since they originate outside of the formal system.
The Incompleteness of Law
Just as formal systems of mathematics attempt to define true theorems, so formal systems of law attempt to define righteous behaviour. No finite set of rules can cover cases. Hard cases that come up become case law once decided. Jewish case law for the Law of Moses is the Midrash.
Because they were exiled in Babylon for 70 years, they paid special attention to the Sabbath, laying out concrete standards for “thou shalt not do any work”, like “how many steps?”. Is electricity a kind of “fire”? (“Thou shalt not kindle a fire on the Sabbath.”) Jesus performed miraculous healing with the repeatability and volume of a professional craftsman. Hence, they classified such unprecedented healing as “work”, and forbidden even though releasing an animal from a ditch was permitted.
Even if they had accepted the additional Sabbath case law laid down by
the Lord of the Sabbath - the rules would still be incomplete. This was
explicity stated by Jewish lawyers and Christ Himself.
Mark 12:28-34
Rabbi Paul puts it succinctly in Romans 13:8-10, “Love does no wrong to its neighbor. Therefore love is the fulfillment of the law.”
The Incompleteness of Revelation
Progressive Revelation
“To know what would have happened, child?” said Aslan. “No. Nobody is ever told that.” “Oh dear,” said Lucy. “But anyone can find out what will happen,” said Aslan, “if you are obedient now.” — “Prince Caspian” by C. S. Lewis
The Seed of the Woman. The Seed of Seth. The descendents of Abraham.
Of Isaac. Of Jacob. Of Judah and Tamar. Of David. The curse of
Jeconiah. Born of a Virgin.
“this grace was given me: to preach to the Gentiles the unsearchable riches of
Christ, and to illuminate for everyone the stewardship of this mystery, which
for ages past was kept hidden in God, who created all things.”
Ephesians 3:8-10
Obedience with Incomplete Revelation
We are rarely told much ahead of time what will happen as a result of our obedience. It is strictly, “Need to know”, and contingent on the obedience of ourself and others.
Ruth was not given a road map. But she submitted to the Law of Moses,
and followed the instruction to glean in the fields. “And she happened to come
to the part of the field belonging to Boaz.”
Ruth 2:2-3
“I will instruct you and keep you in the way that you should go. I will guide you with my eye. Do not be like the horse or mule, which have no understanding; they must be controlled with bit and bridle to make them come to you. Many are the sorrows of the wicked, but loving devotion surrounds him who trusts in the LORD.” Psalm 32:8-10 Psalm 32 to music
This instruction comes to us from the Holy Spirit: “But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.” John 14:26 ]
Pray before anything to be filled with the Spirit. Listen for the voice of the Spirit. When that still small voice speaks, do a quick inventory of Scripture to screen out whims of the flesh. Then obey immediately. These nudgings are time dependent. The greek “Kairos” means “the right time” vs “Chronos” which is the amount or passing of time.
Sometimes this instruction comes via dreams. Each of us is given a personal LLM “AI” which Freud called the “subconscious”. It compiles our memories into “gut feelings” about a decision or the AI videos we call “dreams”. These dreams most often reflect what we fed our minds before going to sleep. Whether this is a movie, or the Word of God, or our prayers on our bed. “On my bed, I remember you. I think of you through the watches of the night.” Psalm 63:6 But God can throw his own revelation in there. So test them against the Word of God.
Dreams in the Bible include Abraham, Jacob, Joseph, Pharoah, Nebuchadnezzar, Daniel, Joseph, the Magi.
Besides systematic study of the Word of God, it is often profitable to pray for guidance, and then randomly sample the Scripture. Traditionally, this is by flipping to a random page and putting a finger on the page with your eyes closed. This method is biased toward passages near the center of the printed edition. Read the context as well.
Today, you can go to an internet radio station like The KJV Bible. It takes 70 some hours to read through the entire Bible, so “tuning in” effectively gets you a random passage.
Once you have an instruction, don’t expect more until you are obedient to what you received. God spoke to Abram, but Abram heard nothing more while he delayed in Haran - until he finished obeying.
The Incompleteness of the Christian without Christ
“I am the vine and you are the branches. The one who remains in Me, and I in him, will bear much fruit. For apart from Me you can do nothing.” John 15:5
How do you abide?
Be obedient to what He has already instructed you. Study His Word. Sample His Word. Pray: make your requests known and then listen. Feed your mind with not only Scripture, but the preaching and writing of Godly men and women. Do NOT fill your mind with junk food. A more practical function of dreams is to reveal what your mind has been fed or is dwelling on.
The Incompleteness of the Christian without Trials
“Consider it pure joy, my brothers, when you encounter trials of many kinds, because you know that the testing of your faith develops perseverance. Allow perseverance to finish its work, so that you may be mature and complete, not lacking anything.” James 1:2-4
The Incompleteness of the Christian without the Church
“Let us not neglect meeting together, as some have made a habit, but let us encourage one another, and all the more as you see the Day approaching.” Hebrews 10:25
