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- 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?

Active Discipleship- 2 Corinthians 9:7, 1 Corinthians 13:3, Moroni 7:6

Every man according as he purposeth in his heart, so let him give; not grudgingly, or of necessity: for God loveth a cheerful giver.

And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing.

For behold, God hath said a man being evil cannot do that which is good; for if he offereth a gift, or prayeth unto God, except he shall do it with real intent it profiteth him nothing.

COMMENTARY

Every man according as he purposeth in his heart, so let him give
At first glance, it may appear that this verse condones a more passive discipleship. If you do not feel the push to give yourself fully to the gospel, then don’t. Just invest to what degree you feel like. One might try to use this verse as justification to dabble with God and say that that was enough.
But that is a misreading of the passage. It does not say “according as he purposeth in his mind,” it says the “heart.” It has always been my mind that tries to rationalize effortless discipleship, but my heart has always yearned to give myself even more to God. I think many of us, if we are really honest with ourselves, have a heart that is more giving than we allow it to be. Not a one of us has a stingy heart…only a suppressed one.

Though I bestow my goods to feed the poor, and have not charity, it profiteth me nothing
For if he offereth a gift, except he shall do it with real intent it profiteth him nothing

And so long as we keep our hearts suppressed, then we will receive no benefit for whatever token efforts we make. God is not going to reward us for our begrudging discipleship. He is not going to pat us on the back for doing things devoid of any real heart. If He did, it would reinforce our passive lifestyle, and prove detrimental for our development. Thus it becomes all too easy to make a half-hearted effort at following God, receive no spiritual nourishment for it, and then say “see, there’s no benefit in this.” But even as we say this, our conscience knows we never really tried.
God is not content with us going through the motions like trained monkeys. He is a jealous God, and He wants our hearts. Real relationships require real investment, and God wants the realest relationship with us imaginable.

Active Discipleship- Zephaniah 1:12, Malachi 3:14

And it shall come to pass at that time, that I will search Jerusalem with candles, and punish the men that are settled on their lees: that say in their heart, The Lord will not do good, neither will he do evil.

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?

COMMENTARY

The men that are settled: that say in their heart, The Lord will not do good, neither do evil
It is vain to serve God: and what profit is it that we have kept his ordinance
The only reason why any of us do anything in this life is because we expect to gain something worthwhile by it. The easiest actions to take are those that are immediately pleasurable, such as eating, sleeping, and pursuing entertainment. But we can even learn to endure actions that are momentarily inconvenient if they provide later benefits, such as exercising, gaining an education, or working a job. Even selfless acts of service still benefit us for the warmth of conscience we gain by them.
Indeed, we can perform any action and overcome any obstacle, so long as we are properly motivated by the promise of goodness afterward. But if there is something for which we see no gain, then we will struggle immensely to invest in it. The root of complacency then, is the lack of desire, the inability to see any reward in the striving. These verses I have quoted describe those that do not see the profit in following God. I have been in that state myself, where life seems pretty fine just how it is, so why should I distress myself with the difficult work of spiritual progression? Why should I lay up treasures in an unseen heaven, when there is mortal pleasure to be had in the here and now?
An object at rest will stay at rest. This is our natural and default state, it is the entropy to which all of us would be consigned if God did not come and disrupt our lives. But He does disrupt, and tomorrow we will examine how he puts the desire in us that we all need to push forward.

The Nature of Sacrifice- Psalm 50:5, Exodus 24:8, Matthew 26:28

Gather my saints together unto me; those that have made a covenant with me by sacrifice.

And Moses took the blood, and sprinkled it on the people, and said, Behold the blood of the covenant, which the Lord hath made with you concerning all these words.

For this is my blood of the new testament, which is shed for many for the remission of sins.

COMMENTARY

Those that have made a covenant with me by sacrifice
Behold the blood of the covenant, which the Lord hath made with you
For this is my blood of the new testament
There are some passages of scripture that I read, and I feel like I understand their reasoning immediately. Then there are some that I read, but I frankly do not understand them. Instead I get the sense that I am teasing at ideas that are still beyond me. One such example of feeling out of my depth is when I consider the three verses that I shared above.
It seems that there is something about sacrifice being a necessary component of our covenants with God. I’m not entirely sure why these two are so connected, but I get a sense that they really are. The Law of Moses was a covenant instituted by regular animal sacrifice, and the Higher Law was a covenant instituted by the great sacrifice of Christ.
In Hebrews 9:15-22, Paul gives us a small treatise on covenants and sacrifices, in which he states that no testament is in force until after the death of its testator. Why, exactly, I do not know, but there it is even so.
I suppose that performing a sacrifice as part of entering into a covenant makes the experience far more impactful in the heart of the disciple. Also, making that sacrifice would be a representation of what the covenant life will surely require multiple times in the years that follow.
But still I think there are things here that I do not understand, and so my mind continues to turn these verses over. I hope my thinking-out-loud on them is helpful for you, it certainly has been useful for me.

The Nature of Sacrifice- Personal Example

In a previous study I examined the differences between sacrifice and consecration, and I talked about how I was afraid that God would ask me to sacrifice my love for writing, where in reality He only sought that I consecrate it for a greater good. Of course, there are other things which God has asked me to sacrifice, but I do not regret the loss of any of them.

Here is one example.

I didn’t play my first video game until my mid-teens, but once I tasted them I fell deeply in love. As soon as I got away to college, and had control of my days, I would play them non-stop, never mind what classes I was supposed to be attending. After a few years I was able to ease off the gas somewhat, but basically if I didn’t have to be doing something else, then games was where you would find me.

It wasn’t that I thought that video games deserved such a high priority in my life, I knew perfectly well that they were quite trivial in the eternal scheme of things. But at that point I needed them. At that point there were a lot of unhealthy habits and lingering wounds all around me. I wasn’t dealing with them, and video games were one of the only things that gave me a distraction from them all. I thought it was peace.

Interestingly, God never actually asked me to sacrifice video games, He just gave me real peace. He pushed me to address those underlying wounds and fears, and then soothed the resultant pains with His love. I didn’t need to hide from those hard parts of life anymore, because they were genuinely being healed.

Then, naturally, I started playing games so much less. I sacrificed them without even thinking about it. Now that the real world was finally a place that I could live without shame, I was much more interested in engaging with it. I became a better husband and father, and started spending genuine quality time with my family.

In fact most of the gaming I do now is social. I play a lot more board games and card games, because it is easier to include other people in them. Our family regularly works through puzzles and legos together. Many of the video games that I purchase now are specifically chosen for their cooperative elements, so that I can play them alongside of my wife and son.

That doesn’t mean that I don’t ever play single-person games during my me-time, but it is far less than before, often with a few months between sessions. More importantly, when I do play them, it is for the actual enjoyment of them, not to escape. I do not need them anymore you see. I do still have needs, but God has given me something far better to take care of them.

The Nature of Sacrifice- John 12:24, Matthew 16:25

Verily, verily, I say unto you, Except a corn of wheat fall into the ground and die, it abideth alone: but if it die, it bringeth forth much fruit.

For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it.

COMMENTARY

Except a corn of wheat die, it abideth alone
Whosoever will save his life shall lose it
Each one of us is given something at birth: a life to live. It is the greatest gift we possess, and it is ours to do with as we will. Understandably, we tend to put a lot of value in that life and guard it jealously. We avoid anything that we deem a danger to it, and prickle at the notion of someone else taking control of it. These instinctive tendencies of ours are good things, and they represent a healthy mentality.
But then, sometimes, the one that gave us that life asks us to give Him back a part of it. In some cases He even asks for all of it! And then those protective tendencies start to prove a hindrance. They naturally balk at the request. If we listen to them, and refuse our creator’s request, then we might be able to keep our life, but now it will be alone and empty.

But if it die, it bringeth forth much fruit
Whosoever will lose his life shall find it
If, however, we overcome the natural man, we might be able to give a completely bizarre and unnatural response, instead. We might agree to part with that which we have. In this case we take our precious life and hand it over, saying “it isn’t for me to choose anymore, God, you steer this thing where you want it to go.”
Make no mistake, it is a hard thing to do. Even Jesus hesitated at the prospect of it, and wondered if the cup could be taken from him. But, in the end, he settled on the mantra “not my will, but thine be done.” And because of it, he was resurrected, and the life he gave up was replaced by one that was better. So it will be for each of us as well. We have to be willing to part with the good things we have if we are to ever have space to receive the better.

The Nature of Sacrifice- 1 Corinthians 5:7, 1 Peter 2:5

Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us:

Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ.

COMMENTARY

Purge out therefore the old leaven, that ye may be a new lump
To offer up spiritual sacrifices, acceptable to God by Jesus Christ
Continuing the point from before, this new verse also speaks of how we are meant to change our old nature to align with Christ. And this change necessarily requires some sort of sacrifice. Quite simply we cannot put on a new piece of our Savior, until we have first made space for it by getting rid of something else. Thus, sacrifice.
This is why animal sacrifice was never sufficient to save souls, for it did not require any actual change. Those that came to the temple to only give up an animal missed the whole point of it. That offering was always meant to be coupled with one of these “spiritual sacrifices” that Peter mentions.

Even Christ our passover is sacrificed for us
When we see the sacrament prepared on the altar, we are witnessing what God is willing to offer to save us: the life of His son. But if we eat and drink, say “thank you,” and leave, then we, too, are missing the entire point. Because God’s offering was always meant to be matched with another…the “spiritual sacrifice” that we bring in return. The ancient Israelites never came to the altar empty handed, and neither should we.
Of course what we offer will not be on the same order of magnitude as what God has. That’s alright, it doesn’t have to be equal. But we should be offering something. Perhaps we could be giving up an old sin? Perhaps we could be making a new commitment for good? Just so long as it is something which states “I see what you have given up for me, God, and I will honor it by giving up my own inferior part, and taking the better one that you offer to replace it.”

All or Nothing- Summary

Half-hearted discipleship is a terrible limit on one’s soul, our own tepidness would forever hold us back from becoming the people we were meant to be. And I know this, because I have spent a great deal of time in this state! This study was absolutely meant for myself, a reminder for why I need to recommit myself body, mind, and soul every day. I’ve lately started a morning ritual where I reflect on the upcoming day, the temptations I am likely to face, and then make resolutions for how I will stand a little taller.

So much of it comes down to just living intentionally, not allowing myself to slip into autopilot mode. But to do that requires constant engagement, and I find that I cannot maintain it unless I am diving all in.

Anything that compromises me in one area, will tear down my defenses in all areas. I cannot try to be mostly good, I have to try to be all good. And though I will fail to be all good, just because I sincerely tried, the grace of Christ will come in to make up the rest.

Partial Commitment is No Commitment

God loves us and fights for us whether we are entirely devoted to Him, partially devoted, or even if we are not devoted at all. When He calls on us to be fully invested in His gospel, it isn’t because of His ego. It is for our own sakes. He knows that “all in” is the only way that discipleship can work for us. I spent years trying to live a double life, frantically filling my coffers with good deeds, to try and make up for the indulgent vices I was also doing on the side. It didn’t work, the vice robbed the coffers, and every good thing I tried to do felt hollow and insincere.
We know that Satan entices us to be full-blown sinners, but he is also perfectly content with part-time Christians. Both groups are left within his power. If we think that we are serving God and the world, in reality we only serve the world.
Lest it sound like I am demanding perfection, I wish to stress that our actions will inevitably be flawed, forever falling short of the ideal. But even if we never measure up to perfection in action, we can be perfect in picking ourselves back up again after each slip. Our commitment can still be complete, we can be invested in always trying once more. That is enough. That much God is able to work with.
Matthew 6:24- No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.
Luke 9:62- And Jesus said unto him, No man, having put his hand to the plough, and looking back, is fit for the kingdom of God.

The Gospel is as Valuable as You Make it

But what does it take to have a full commitment? Nothing less than the promise of all things. Only the assurance of every eternal happiness will compel a man to sacrifice all that he has. The question arises, then, do you believe that every happiness is offered within the gospel? Perhaps you don’t. Perhaps you only see it as able to offer some insights and some pleasantries, but not necessarily as the end-all-be-all ideology. If that is the case, then you will not be able to follow it wholeheartedly.
That doesn’t have to be the end of the story, though. One can work from this point forward. First and foremost is to accept that all things are promised by the gospel. Whether or not you think they can be delivered is another matter, but let there be no doubt that the gospel claims to be able to provide you with every eternal blessing.
Then the question is whether those promises of the gospel can be trusted or not. And to determine that, one only needs to test its various parts. Really lean into prayer and see whether you feel the presence of something eternal or not. Really dive into the scriptures and see if they are alive with an unseen Spirit. Really adhere to the commandments that you can and see whether you experience the promised change of heart. Test the gospel in enough areas, see it bear the fruit that is promised in each, and soon enough you’ll have faith in it all. But do your testing sincerely. Be all in each step that you take.
Luke 15:17-18- And when he came to himself, he said, How many hired servants of my father’s have bread enough and to spare, and I perish with hunger! I will arise and go to my father, and will say unto him: make me as one of thy hired servants.

Without the Gospel You Have Nothing

Who is willing to make such an experiment, to sincerely commit to something so demanding, and all on only a sliver of hope? Well, usually none of us until we are first broken and desperate. Most of us have to try and live without the gospel first, find ourselves in dire straits because of it, and only then become willing to try the things we had previously scorned.
But let’s back up a bit. At the outset, the world offers many things, and the pleasures it promises make it very easy for us to dismiss the gospel. Entertainment, recognition, diversion, stimulation…these are all pleasant things, and the first tastes of them are so intoxicating that we believe they will forever be enough. When you have enjoyment like this, what need is there for things like resurrection, grace, eternal life, and forgiveness? We are content without them.
In time, though, all the getting still leaves us wanting, the pleasures grow stale, some of them are even taken from us on a whim. Eventually we realize that the everything of the world means nothing to us anymore. And the spiritual things we considered to be nothing now mean everything. The soul grows desperate for the eternal, and one becomes willing to sacrifice everything of the world, just to obtain any of the grace that God is willing to measure out to them. And God, of course, is willing to measure out all of it.
John 6:68- Then Simon Peter answered him, Lord, to whom shall we go? thou hast the words of eternal life.
Matthew 13:45-46- Again, the kingdom of heaven is like unto a merchant man, seeking goodly pearls: Who, when he had found one pearl of great price, went and sold all that he had, and bought it.