The Way That Things Are- Gödel and the Incompleteness Theorem

Kurt Gödel was a logician and mathematician born in the early 20th century. He was a contemporary and friend of Albert Einstein’s, and as influential to the world of logic as Einstein was to the world of Physics.

Gödel’s most famous contribution were his Incompleteness Theorems, which proved that for any system there are truths which cannot be defined by the system itself. There are some things which are true, but which cannot be proven until you utilize outside sources.

Now this is a very crude example meant only as an illustration, but think of it this way: if we have a system called integer numbers (1, 2, 3, 4…) then there are patterns about those integers which do exist, but which we will never be able to discover with integers alone. We will have to add something else, perhaps fractions, in order to prove them. But now we have a new system, one of integers and fractions, and there are new patterns about this larger system which we will never be able to explain until we add something like irrational numbers, and so it goes on.

Now Gödel’s Incompleteness Theorem was related to logical and mathematical systems, but they raise a strong philosophical question as well. I have always been baffled that we humans are so arrogant as to believe that we could ever fully understand ourselves. It seems to me that we are much too close to the subject matter to ever find all of the objective truths locked within our souls. I find it far easier to accept that the only complete understanding of myself would have to come from a being that existed in a higher system than our own.

Thus when society decides that truth must be one thing, but God’s word declares that the truth is something else…it frankly is not difficult to for me to side with the unknowable omniscient. Indeed, the fact that God is unknowable gives his argument greater weight to me, not less. If God was comprehensible to me, then there’s no way He’d be great enough to comprehend all of me.

The Way That Things Are- 1 Corinthians 13:12, Ecclesiastes 1:11

For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.

There is no remembrance of former things; neither shall there be any remembrance of things that are to come with those that shall come after.

COMMENTARY

For now we see through a glass, darkly
There is no remembrance of former things
We are mortal beings, and are therefore constrained to a very limited and temporal perspective. We can recall moments in the past, and we can imagine events in the future, but the only reality we can perceive directly is the singular now. We can hear of ancient days, and we can predict future ones, but we can only fully understand that which is immediately before us. We conceive of broader perspectives but we do not hold them. We think of the infinite, but we do not know it. Inherent in our natures is that we will forever view reality only through a narrow slice, one deeply tinted by our personal biases and contexts. And given that our view is so very narrow and skewed, and given that it is so very filtered, is there really any chance that we will be able to perceive even that narrow slice as it really is?

Now I know in part; but then shall I know even as also I am known
But an infinite being, one that existed on a higher plane, would be able to take in the bigger picture all at once. A being of a higher dimension could perceive all of time and space, as easily as how I perceive all of a two-dimensional picture. This higher being would be entirely aware of the lower system’s laws, and would have a clear understanding of things as they really are. What’s more, this higher being, if He was benevolent, would be able to teach us all that was necessary for us to live in harmony with our bigger picture. Therefore God’s purpose in giving us directions is to enable us to live with a higher degree of foresight (His foresight) than we could have ever held on our own.
It is okay that we are limited now, for it is unavoidable. But it will not always be this way. One day we, too, shall know all. One day we will see the end from the beginning. One day we will understand that which is now impossible to comprehend.
We can either wait until that later day to be convinced of the truth, or we can start living faithfully now, and watch as the rest of the universe seems to magically fall into harmony with our steps. Really, though, it won’t be the universe falling into harmony with us, it will be us finally falling into harmony with the universe.

The Way That Things Are- Acts 26:9-10, 12-14, Proverbs 21:2

I verily thought with myself, that I ought to do many things contrary to the name of Jesus of Nazareth.
Which thing I also did in Jerusalem: and many of the saints did I shut up in prison, having received authority from the chief priests; and when they were put to death, I gave my voice against them.
Whereupon as I went to Damascus with authority and commission from the chief priests,
At midday, O king, I saw in the way a light from heaven, above the brightness of the sun, shining round about me and them which journeyed with me.
And when we were all fallen to the earth, I heard a voice speaking unto me, and saying in the Hebrew tongue, Saul, Saul, why persecutest thou me? it is hard for thee to kick against the pricks.

Every way of a man is right in his own eyes: but the Lord pondereth the hearts.

COMMENTARY

I verily thought with myself, that I ought to do many things contrary to the name of Jesus
Saul had convinced himself that the world ought to be a particular way. Having been thus convinced he felt very strongly about it. He was very energetic in his opinions, going to great lengths to enforce them upon the world. But no matter how hard he wanted the truth to be the way that he wanted it to be…it just wasn’t.

Why persecutest thou me? it is hard for thee to kick against the pricks
Every way of a man is right in his own eyes
As Saul came to learn, it frankly doesn’t matter how strongly we feel that the world should be a certain way. If it so happens that it isn’t that way then it just isn’t. All of us convince ourselves that what we believe is right in one way or another, and when the actual truths of the world do not align with our expectations we feel pierced, like an ox kicking against the pricks.
We often speak of our desire to “change the world.” Our choice of words here betrays our vain arrogance, because in truth we can do no such thing. We can change society and we can change physical constructs, but the world, nature, and the underlying systems that define the way things are? Never. The rules of heaven, of earth, and of the soul: these simply abide as they are. So yes, we may change society, but we often change it to be contrary to actual truth. And then we fight for what we want but we never get it, because the entire world seems set to frustrate us instead. We are kicking against the pricks and wonder why it hurts.

The Way That Things Are- It’s True, Isn’t It?

The following is quoted from Gordon B. Hinckley, who was speaking at a Conference in April 1973. He was speaking of a young naval officer that he once met, one who had recently converted to Christianity.

He was introduced to me just before he was to return to his native land. I said, "Your people are not Christians. You come from a land where Christians have had a difficult time. What will happen when you return home a Christian?" 
His face clouded, and he replied, "My family will be disappointed. I suppose they will cast me out. They will regard me as dead. As for my future and my career, I assume that all opportunity will be foreclosed against me."
I asked, "Are you willing to pay so great a price for the gospel?"
His dark eyes, moistened by tears, shone from his handsome brown face as he answered, "It's true, isn't it?"
Ashamed at having asked the question, I responded, "Yes, it's true."
To which he replied, "Then what else matters?"

Often the world criticizes the principles and commandments found in religion, stating that adherence to a strict moral code is outmoded, and that the gospel needs to get with the times. They focus primarily on the behaviors that religion calls for, but do not ask whether those behaviors are based upon true premises.
In my experience, the observances followed by most world religions are remarkably consistent with the claims of that gospel. For example, Christianity teaches that each person is composed of an immortal spirit paired with a mortal body. It teaches that God created the first man and woman, and authored the institution of marriage between them. It teaches that we come to this earth life in order to gain a body, to learn to follow God’s will, all so that our perfected self can live with Him after the resurrection.
Now if all of these claims are true, then obviously there is an awesome responsibility related to birth, life, and the union we call marriage. If these premises are true, then it matters greatly how we deal with these subjects, and it is only logical that there would be laws to govern them.
If these claims are true, then doesn’t it make sense for there to be laws of chastity and sexual purity? Doesn’t it make sense for there to be safeguards that protect the sacred procreative power which binds an eternal soul to a mortal body? Doesn’t it make sense for marriage, and the definition of it, to be under the purview of the God who invented it? Doesn’t it make sense to master one’s appetites as necessary to pursue the true purpose of life?
If these claims are true, then what else matters? If these claims are true, then any argument that God’s laws are “outmoded” become hollow. If these claims are true, then these laws are simply the natural, logical extension of what is right.
Thus the only meaningful question is the one asked by that young sailor. Is it true, or not?

The Way That Things Are- 1 Corinthians 1:18-20, 25

For the preaching of the cross is to them that perish foolishness; but unto us which are saved it is the power of God.
For it is written, I will destroy the wisdom of the wise, and will bring to nothing the understanding of the prudent.
Where is the wise? where is the scribe? where is the disputer of this world? hath not God made foolish the wisdom of this world?
Because the foolishness of God is wiser than men; and the weakness of God is stronger than men.

COMMENTARY

For the preaching of the cross is to them that perish foolishness; but unto us which are saved it is the power of God
Those that discredit faith proclaim that to follow God is naive. And, if God did not exist, they would be right. For if God were not real, then none of the things promised in His name would be true. And if people believe in something which is false, then truly that is foolishness. Indeed, that is a very succinct definition for the word.

Because the foolishness of God is wiser than men
For the preaching of the cross unto us which are saved it is the power of God
But what becomes of this “foolishness of God,” if it so happens to be true? Is it naive to be a follower, if following these precepts actually redeems our hearts and heals our souls? Those of us which are saved attest that the preaching from the cross is not foolishness, but verifiable truth.
And what is the seeing of truth if not wisdom? This is a very succinct definition for that word as well. In the end, it does not matter how elaborate and complex a cynical statement is. If it is wrong, then it is foolish, no matter how intricate it might be. And it does not matter how simple and unvarnished a statement of faith is. So long as it is true, so long as it describes things as they really are, then it is wisdom.

The Way That Things Are- 1 Corinthians 2:6-8, 1 Nephi 8:27-28

Howbeit we speak wisdom among them that are perfect: yet not the wisdom of this world, nor of the princes of this world, that come to nought:
But we speak the wisdom of God in a mystery, even the hidden wisdom, which God ordained before the world unto our glory:
Which none of the princes of this world knew: for had they known it, they would not have crucified the Lord of glory.

And it was filled with people, both old and young, both male and female; and their manner of dress was exceedingly fine; and they were in the attitude of mocking and pointing their fingers towards those who had come at and were partaking of the fruit.
And after they had tasted of the fruit they were ashamed, because of those that were scoffing at them; and they fell away into forbidden paths and were lost.

COMMENTARY

But we speak the wisdom of God, even the hidden wisdom, which none of the princes of this world knew
As I said yesterday, truth does not need to be known to be true. That one does not understand something is not evidence against it. As a three-year-old I did not understand Algebra, Geometry, or Calculus, yet they still contained correct teachings.
Now imagine if I grew to adulthood, successfully gained an understanding of many other things, but still could not comprehend mathematics. Would the fact that I was capable of knowing many other things, but still not mathematics, be evidence at last that there was no truth in arithmetic? Still no.
To be intelligent beings, yet still have our blind spots of ignorance, is a fact of life.

And after they had tasted of the fruit they were ashamed, because of those that were scoffing at them
When our car has trouble we go to a mechanic, when we want to build a house we find a contractor, when we feel sick we seek guidance from a doctor. Wisely we have learned to rely on those who know when we ourselves are ignorant….except, it would seem, in one particular case.
For some inexplicable reason, we take the religious opinions of those that openly admit that they are not religious, and we take the moral guidance of those that are not moral. We give people credentials in the matters of the soul simply because they are popular or because we like them, not because they actually know.
There are those that actually know, there is even one who knows all. If we want to understand divine truth, we cannot hope to gain it through an ignorant source.

The Way That Things Are- John 18:37-38, Doctrine and Covenants 93:24, 30

Pilate therefore said unto him, Art thou a king then? Jesus answered, Thou sayest that I am a king. To this end was I born, and for this cause came I into the world, that I should bear witness unto the truth. Every one that is of the truth heareth my voice.
Pilate saith unto him, What is truth? And when he had said this, he went out again unto the Jews, and saith unto them, I find in him no fault at all.

And truth is knowledge of things as they are, and as they were, and as they are to come;
All truth is independent in that sphere in which God has placed it, to act for itself, as all intelligence also; otherwise there is no existence.

COMMENTARY

For this cause came I into the world, that I should bear witness unto the truth
Pilate saith unto him, What is truth?

During the trial of Jesus he had philosophical discussions with Pilate, in which he testified of his role as the bearer of truth. Pilate’s response shows a cynical mindset, one that questions what truth even is. Thus we see that a “meh” attitude towards the eternal verities is not a modern invention at all, it has been around for millennia!
For as far back as philosophy extends, the question of absolute truth has been debated. Are there things that are eternal and constant, or is everything shifting and impermanent? And if everything on earth is shifting and impermanent, can there still exist a higher realm where things are eternal and constant?

Truth is knowledge of things as they are, and as they were, and as they are to come
All truth is independent in that sphere in which God has placed it
I once heard a brother compare truth to a tool lost in the yard. If a family cannot find the tool, they might have all manner of opinions as to what became of it. The father doesn’t recall that the tool was ever actually owned. The mother knows that the tool was owned, she was the one who bought it for a specific project. The son who used the tool last knows that he must have been the one to lose it, and claims total ignorance of anything to do with the tool whatsoever! The sister hears all of these conflicting opinions and decides that there is just no definitive truth related to the tool.
But there is a truth. It is still sitting under the bush in the backyard, whether anyone knows that it is there or not. Because truth is not based upon opinion. It is simply “things as they are.” And so truth is independent, it does not have to be known or even accepted to exist. It just is.
Pilate didn’t know what the truth was. Not because the truth didn’t exist, but because he did not receive it. He delivered it up to the crucifixion instead. But even though he was ignorant, Jesus still was who he was, and the truth is what it is.

The Way That Things Are- Personal Example

I first thought of conducting this study after a recent experience with our newborn daughter in the hospital. She was still trying to get the hang of nursing, and it was a difficult task for her. She wanted to nurse, but she kept going about it the wrong way. She would bite, when she needed to suck. She would push away, when she need to pull in. She would lay idly, when she needed to work for it.

And through all this she became very frustrated. She needed nourishment, but she wanted it to come in particular ways, which ways were not in harmony with the ways of nature. At this point she had a choice. She could adapt to the way that things are, or she could try to force the world to work the way that she wanted.

Like most infants, she adapted. We are each born with a wonderful ability to recognize when we are being ineffective, and to learn from our mistakes. We feel resistance and we naturally align with the proper flow of things.

Imagine if my daughter had not done this though. What if she had thought to herself “biting, and pushing, and laying idly doesn’t give me the stream of nourishment I need…so therefore the stream of nourishment must simply not exist.” She could deny the existence of mother’s milk, she could even deny the existence of a loving mother. She could mistake the earnest efforts of that mother to correct her as being mean and punitive, refusing to meet her on her own terms.

Sadly, this sounds like a very familiar state of mind. Though we are born with the tendency to adapt and learn from our mistakes, as we get older we learn how to be more stubborn. We lean into our follies, even as they continually fail to provide us any gratification. And when our way does not work, we then deny that any right way exists at all. We claim that God must be a myth, or else He is a cruel being for not working the way that we want Him to work.

But the reality would remain what it was even so. If my daughter had chosen to deny milk, a mother, and parental love, all those elements would have existed even so. And if we choose to deny righteousness, God, and divine love, all those elements exist even so. They exist in the way that they do, and they are set in their nature. Thus it is up to us to adapt to their terms, not the other way around.

The Way That Things Are- Question

One of the fundamental claims of the gospel is that it teaches “truths.” There are those that view the gospel as nothing more than a suggested way to live life, or as a wishful description of how things ought to be. But the gospel does not state that it is either of those. Its clear and bold proclamation is that it defines things exactly the way that they are. It does not purport to be a way, it insists that it is the way.

Whether the gospel is effective depends entirely on whether that claim is true or not. We are told not to perform sinful actions, because those behaviors are inherently wrong. That is just the way that they are. And are they? If not, then the gospel has lied to us and has nothing of value to offer. If so, then we truly ought to abstain from them for our very own benefit.

My personal experience is that the gospel is correct in its claims, and if anyone wished to dispute my faith, they would have to illustrate why the truths proclaimed in the gospel are not actually truths.

With this study I would like to further establish how the gospel is bold in defining universal truths, and in dividing right from wrong. I wish to find examples that reinforce the notion that the gospel is the source of truth. I will also consider the folly of treating any of its precepts as mere “suggestions.”

In the meantime, I’d love to hear how you have come to view the gospel as a source of truth in your life. Have you ever had to overcome a tendency to view its teachings as recommendations? What truths of the gospel ring the most true to you? Did that faithful belief come naturally, or was it something you had to cultivate over time?

Active Discipleship- Summary

This has been a very good study for me. I find it very easy to slip back into a state of idle complacency, and every time I catch myself in it, I need to find a source of inspiration to push back into intentional discipleship. At those times I find that motivational words and stories go a long way to building up my resolve. Perhaps this study will be another good resource for me to reflect on in those moments.
Indeed, the more I think about it, all scripture is meant to motivate us towards a life of active discipleship in one way or another. Reading them, I find myself compelled to do the things I am otherwise hesitant to do. Keeping the commandments, reaching out to others, finding productive ways to improve myself…each of these sound like a chore when I am not drinking from God’s words.
Here are some of the principles that stood out to me the most from this study.

God Does Not Call Us to Live Passively

The example everywhere in the scriptures is of active men and women who would go and do. David fought Goliath where others remained idle. Esther spoke up to the king where others were afraid. Jesus healed the lepers that others refused to approach. Testimony is built by those who go out and look for it, not by those who sit and wait for it.
Each one of us wants to live a meaningful life as well, but we want it to come to us easily. We want to live passively, but still feel like we are adventurous. I have watched myself go through all sorts of mental gymnastics to try and accomplish just that. I try to convince myself that my sedentary life is actually one of purpose, that my small trials are epic giants, that my passive hobbies are my great calling.
But no matter how I try to spin it, a hollow life is still hollow and I know it. I have called mediocrity significant, but the words always tasted a lie. I only can have the active, adventurous, and meaningful life that God meant for me to live when I do that which I find hard to do.
2 Nephi 1:21, 23- Arise from the dust, my sons, and be men, and be determined in one mind and in one heart, united in all things, that ye may not come down into captivity;
Awake, my sons; put on the armor of righteousness. Shake off the chains with which ye are bound, and come forth out of obscurity, and arise from the dust.

The Conscience Distresses the Idle

What is the part of me that tastes the lie when I claim I am content with an idle life? That sense of in-authenticity cannot be explained by chemistry or biology, it something in my soul that discerns the truth from the error. It is something given by God.
When I feel the push to overcome my laziness and act, I know that it is divinity that is inspiring me. And therefore I know that I ignore those urges at my own peril. One of the greatest gifts God gives is to distress us when we are slothful. It may not feel like love to be made so agitated, but if He did not stir our hearts then we would live in a world without any heroes.
This isn’t to suggest that we must all become generals of armies or leaders of congregations. Not all of us are called to revolutionize the entire world. But we are all called to live a life that is meaningful, a life that blesses the world around us, a life that unveils the worth within us. Not every life calling that God gives is famous, but all of them are epic in their own way.
Romans 2:15- Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another;
John 14:12- Verily, verily, I say unto you, He that believeth on me, the works that I do shall he do also; and greater works than these shall he do; because I go unto my Father.

We Only Have Peace in Doing

Hard as it may seem to live the life of active discipleship, it is actually far harder to live that of idle discontent. Just as it is hard to bear one’s cross and live worthy of heaven, but far harder to spend an eternity in damnation. So God does not trouble us without cause. He does not ask us to do things that are not for our own good.
There is only one true peace, and that is from pushing further and further into the good. Any other philosophy is a lie, meant to seduce us into sleeping away our great potential. There is a reason why slothfulness is considered one of the deadly sins. It is not some silly misdemeanor that we can wink at. Yes, Satan tempts us to sin, but he also tempts us to just not do good. If he catches us on either point he has won.
Christ’s promise is that his burden is light, that his cross is easy to bear. It seems unfathomable , but that is the promise even so. We will never know the truth of it until we try it, and find the warmth of heart that makes all our burdens melt into joys.
Malachi 3:14- Ye have said, It is vain to serve God: and what profit is it that we have kept his ordinance, and that we have walked mournfully before the Lord of hosts?
John 14:27- Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid.