Gödel’s Incompleteness Theorem: The Universe, Mathematics and God
80 years ago, Kurt Gödel toppled empires of mathematical philosophy with his famous Incompleteness Theorems.
 Kurt Gödel proved, ironically, that it's impossible to prove everything. And yes, he proved it. |
I’m every bit as interested in science, philosophy and engineering as I am in business. Gödel’s theorem has profound implications for every branch of knowledge.
The materialist view prevails in secular circles. Materialism states that the laws of physics and the universe we know are all that is. It sees the universe as a giant machine. It assumes that everything we experience is purely the result of blind cause and effect. It scoffs at the idea that there is any such thing as God or metaphysics.
This view was epitomized by “Logical Positivism” which was espoused by a group known as “The Vienna Circle” in Austria, led by Ludwig Wittgenstein. Logical Positivism says that anything that cannot be experimentally verified or mathematically proven is invalid.
The Logical Positivists were confident that very soon, all the loose ends of mathematics would be nailed down by a single unifying theory. The world would finally fully embrace reason and logic and leave the failures of religion behind.
Kurt Gödel was a member of the Vienna Circle and in 1931 proved that a single unifying theory was impossible. He proved that the goal of the Logical Positivists was unachievable. This was a devastating blow.
Gödel’s Incompleteness Theorem says that any system that is complex enough to express mathematics cannot prove, by itself, that everything it says is true. It will always rely on something outside the system that you have to assume is true but cannot prove.
You can then step outside the system and complete your proof, but in order to do that you will now have to invoke something else from the outside. So you keep expanding ever outward, invoking still more things that you cannot prove.
This was very disturbing to mathematicians, because mathematicians hate uncertainty.
Many people have raised the question of whether Gödel’s incompleteness theorem applies to the universe itself. If the universe is mathematical, then yes in fact it does.
Stated in Formal Language:
Gödel’s theorem says: “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”
The Church-Turing thesis says that a physical system can express elementary arithmetic just as a human can, and that the arithmetic of a Turing Machine (computer) is not provable within the system and is likewise subject to incompleteness.
Any physical system subjected to measurement is capable of expressing elementary arithmetic. (In other words, children can do math by counting their fingers, water flowing into a bucket does integration, and physical systems always give the right answer.)
Therefore the universe is capable of expressing elementary arithmetic and like both mathematics itself and a Turing machine, is incomplete.
Syllogism:
1. All non-trivial computational systems are incomplete
2. The universe is a non-trivial computational system
3. Therefore the universe is incomplete
Some time ago I posted an article about this: http://www.perrymarshall.com/articles/religion/godels-incompleteness-theorem/ and I was greatly interested in seeing if anyone would be able to poke a hole in my argument. (The article is a much more thorough explanation of Gödel than I am giving you here.)
Nearly everyone agrees that math is incomplete. The idea that the universe is also incomplete apparently makes some people very uncomfortable. If the universe cannot explain itself then there has to be some kind of higher power at work.
The debate essentially comes down to this:
- If the universe is illogical and inconsistent then it is possible for it to be complete.
- If the universe is logical and consistent then it is incomplete.
- If the universe is incomplete, then it depends on something on the outside.
In other words, if the laws of mathematics and logic apply to the universe, then the universe has to have a metaphysical source. Atheism can only be true if the universe is irrational.
(By the way, my experience from conversing with literally thousands of atheists via email and on my various blogs is this: When you get down to the core emotional center of why they don’t believe in God, it’s often because they feel deep down that the universe is irrational. They’re immensely disappointed that the world is full of evil and suffering. Because of this, they reject the idea of God.)
You cannot prove that the universe is mathematical. But belief that the universe is mathematical is the #1 assumption of modern science. Toss out that assumption and the whole philosophical framework of western civilization crumbles.
In the history of science, you will find that belief in a God who created an orderly mathematical universe was one of the foundations of scientific discovery.
If you visit the world’s largest atheist website, Infidels, on the home page you will find the following statement:
“Naturalism is the hypothesis that the natural world is a closed system, which means that nothing that is not part of the natural world affects it.”
If you know Gödel’s theorem, you know that all logical systems must rely on something outside the system. So according to Gödel’s Incompleteness theorem, the Infidels cannot be correct. If the universe is logical, it has an outside cause.
Thus atheism violates the laws of reason and logic.
The Incompleteness of the universe isn’t formal proof that God exists. But… it IS proof that in order to construct a rational, scientific model of the universe, belief in God is not just 100% logical… it’s necessary.
Practically speaking, all knowledge we have about anything is incomplete. There are always some things you’re certain of, some things you’re somewhat sure of, and some things you cannot prove at all. Human knowledge is always enlarging the circle of what is known, but every question that we answer just provokes more questions. In real human experience, the quest to enlarge that circle never stops.
And I would submit to you that this is the essence of faith, as actually practiced by thinking, reasoning people.
Many people assume that religious faith is some mystical imaginary idea that is embraced purely on the basis of emotion or intuition. That it has nothing to do with facts, reason or logic.
This is completely untrue – at least in in the Judeo-Christian tradition. No one is asking you to believe without evidence or rational reason. Belief in God, in Jesus, and even the afterlife is based on historical events, logical propositions, and reasonable arguments.
Science itself originated from theology. Science assumed then, and assumes now, that the universe is rational. That the universe operates according to fixed, discoverable laws. Even science itself is a very practical outworking of faith in the reliability and consistency of the natural order.
The practice of faith is in many ways living out a hypothesis: That if you follow the teachings and embrace the Spirit, you will have an excellent opportunity to experience success in your work and your family. And that you will be rewarded in your search for meaning and pursuit of the deepest questions.
Perry Marshall
P.S.: If this intrigues you, make sure you read my more extended article, Gödel’s Incompleteness Theorem: The #1 Mathematical Discovery of the 20th Century
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Not always have we understood everything we see or hear, but continuous work especially in the field of mathematics has helped us solve many previously though illogical concepts.
I think we should keep working towards better understanding of everything, and hope that one day we understand the holographic thing this life is.
Atheists say, “we see it then, we believe it”. But In religion there is a saying, “believe and then you shall see it”.
Well the “Logical Positivists” are true in every context but human beings are poor emotional creatures they make decision based on emotions and they want to believe in God. They want to think that someone is up above there who is watching them. And as you said you can be completely logical and believe in God. Thanks for the post
Some loaded questions for loaded comments:
“It assumes that everything we experience is purely the result of blind cause and effect.”
If one claims that a famous Van Gogh painting was the result of just taking some buckets of paint, splashing them against the canvas and voila! it came out a masterpiece, how quickly would that person be believed? Or even, just taking a paintbrush and mindlessly stroking lines on the canvas. The point I’m making is, some things need to be pre-meditated, just as some experiences we endure.
“It scoffs at the idea that there is any such thing as God or metaphysics.”
Prove that air exists and, if it does, how it allows us to live and our brains to function the way they do. Better yet, prove the mechanics of the brain, and even the eye.
I can go on and on.
“The universe is incomplete, therefore God exists” is an obvious non sequitur — even if your analogy between formal systems and the physical universe were valid. (For instance, the universe could be inconsistent. Or, something else other than God could complete it.)
With that said, Godel’s proof is about additional assumptions completing a set of axioms. Not a supernatural being completing a physical universe.
IS the universe a logical system? Your examples illustrated how you can make logical systems correspond to things and events in the universe, but not that the universe IS a logical system. So at most you can draw the conclusion any logical systems instantiated in the universe are incomplete (or inconsistent), and can be completed only by additional assumptions (not by a supernatural being).
In general this argument glosses over probably a dozen important distinctions, and makes another dozen leaps in logic.
Richard.
If you feel there are distinctions I have overlooked, you are invited to address them point by point.
I have already addressed a large number of objections identical to yours at http://www.perrymarshall.com/articles/religion/godels-incompleteness-theorem/ – read the comments.
Any set of axioms is itself a system and therefore contingent on some other axiom. Eventually you logically arrive at the necessity of a single axiomatic assumption which cannot be further subdivided. The logical conclusion is that the universe is contingent on something that is indivisible, immaterial and boundless. A metaphysical entity. We can quibble about the details but regardless, it sounds an awful lot like God.
Again this is completely based on logic. You will find that the reasoning remarkably resembles that of thinkers like Aquinas and Aristotle.
My logic does hinge on the assumption that the universe is logical. I cannot prove that the universe is logical. You are welcome to assume that it is not. But if you do, then from that point forward you are forbidden to engage with me (or anyone else for that matter) on the basis of science or mathematics or logic, because your assumptions invalidate all of those things. Believe in an illogical universe if you choose.
If the universe is logical, if mathematics apply to the universe, then the universe is incomplete and contingent on a metaphysical entity.
OK, after reading through much of the discussion on the other page, I see that reader Matt has very patiently tried to point out several places where you engage in hasty generalization, non-sequiturs, false dichotomies and such. I see no evidence that you’ve ever slowed down long enough to even consider what he is trying to say to you. You seem to follow up with the same rhetorical flourish each time, challenging him to either agree with you, or give up on science altogether.
Let’s just take one distinction you’re missing — probably the main one. In Matt’s words:
“you appear, once again, to be conflating the universe with our model of the universe.” — comment 22 (this is like the 4th time he’s tried to point this out to you)
It very much seems that your argument HINGES on this mistake.
And I don’t see you even acknowledging the distinction, let alone the fact that you are relying on it.
Richard
Universe:
2 rocks + 2 rocks = 4 rocks
Mathematical model of the universe:
2 + 2 = 4
Are both statements true, or not?
Does the latter correspond to the former?
Does mathematics, which is our model of the universe, tell us the truth about the universe, or not?
I am fully and acutely aware of the distinction. I am relying on it. I say it tells us the truth.
What say you?
Perry,
This was another point that bothered me about the proof.
You started by saying a complete mathematical representation of the universe (a theory of everything) cannot exist, because it will always rely on something outside itself.
But the universe isn’t a mathematical representation. It simply IS – whether we model it properly or not doesn’t affect the nature of its existence.
The blow to the materialist argument was that a complete model is impossible, and therefore God’s existence cannot be disproved. That is not the same as proving God’s existence.
Moreover, Goedel’s proof shows that, if the assumptions of the mathematical are unprovable – and if you’re claiming THOSE assumptions is where God exists – then you’re acknowledging proof of God is impossible.
Patrick
I think you need to be very careful in trying to say that the universe simply “is.” It came into existence 13.8 billion years ago, along with space and time. Before then there was no time. Something that was not, came to be. The mathematical / logical position is that since it is a computational system, then if it is consistent then it depends on something outside of itself to exist. You can’t have an infinite regression of axioms so at some point you arrive at an original axiom. An axiom which simply “is.”
The cause and effect point of view says that something had to cause its existence. You can’t have an infinite regression of cause and effect so at some point something has to be uncaused. The temporal nature of the universe says that the universe itself is not its own cause. Something outside of space and time has to be uncaused. God just “is.”
There is something in Christian theology which exactly corresponds to this, by the way. God appears to Moses. Moses says “who shall I say sent me” and God says “I AM” has sent you. Jesus, when challenged by the religious authorities, said, “Before Abraham was I AM” referring back to the Moses passage. The Alpha and the Omega, the First and the Last.
Gödel’s proof does show that you cannot prove God, yes, you are right. But it shows that you have to take God as axiomatic, otherwise you cannot form a coherent model of the universe. God is unprovable but a necessary assumption.
Perry,
Truth is always outside the individual seeking it; else opinion reigns. God reveals himself to those that hunger for truth. He doesn’t waste His time with the unbelievers. There is a much easier way to prove the existence of God and the resurrection of Jesus Christ than intellectual masturbation.
Wishing You Plenty To Live,
Tom Doiron
Atlanta
What some judge to be “masturbation” is active consideration and engagement for others. “God doesn’t waste his time with unbelievers” is a statement that would hardly stand up to a reasonably careful study of the Bible.
Perry,
God can recognize a goat faster than any human, because He has x-ray vision of the heart and perfectly knows the future.
He calls His lambs home, but leaves the goats outside the fold. Show me in God’s Word where the hardhearted are born again of God’s spirit. They make their choice, not Him, He just knows the outcome ahead of time.
Is 40 years worth a reasonably careful study of the Bible? Just that, the Bible, God’s Word; not everybody’s opinion of it.
Perry the mind of man at it’s best is dummer than God at His worst. Reason does not cut it.
Daniel 4:
34 At the end of that time, I, Nebuchadnezzar, raised my eyes toward heaven, and my sanity was restored. Then I praised the Most High; I honored and glorified him who lives forever.
His dominion is an eternal dominion;
his kingdom endures from generation to generation.
35 All the peoples of the earth
are regarded as nothing.
He does as he pleases
with the powers of heaven
and the peoples of the earth.
No one can hold back his hand
or say to him: “What have you done?”
36 At the same time that my sanity was restored, my honor and splendor were returned to me for the glory of my kingdom. My advisers and nobles sought me out, and I was restored to my throne and became even greater than before. 37 Now I, Nebuchadnezzar, praise and exalt and glorify the King of heaven, because everything he does is right and all his ways are just. And those who walk in pride he is able to humble.
John 7
15 And the Jews marvelled, saying, How knoweth this man letters, having never learned?
16 Jesus answered them, and said, My doctrine is not mine, but his that sent me.
17 If any man will do his will, he shall know of the doctrine, whether it be of God, or whether I speak of myself.
Matthew 7
17 Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.
18 A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit.
19 Every tree that bringeth not forth good fruit is hewn down, and cast into the fire.
20 Wherefore by their fruits ye shall know them.
21 ¶ Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.
22 Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works?
23 And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
24 ¶ Therefore whosoever heareth these sayings of mine, and doeth them, I will liken him unto a wise man, which built his house upon a rock:
James 2 –
12 So speak ye, and so do, as they that shall be judged by the law of liberty.
13 For he shall have judgment without mercy, that hath shewed no mercy; and mercy rejoiceth against judgment.
14 What doth it profit, my brethren, though a man say he hath faith, and have not works? can faith save him?
15 If a brother or sister be naked, and destitute of daily food,
16 And one of you say unto them, Depart in peace, be ye warmed and filled; notwithstanding ye give them not those things which are needful to the body; what doth it profit?
17 Even so faith, if it hath not works, is dead, being alone.
18 Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works.
19 Thou believest that there is one God; thou doest well: the devils also believe, and tremble.
20 But wilt thou know, O vain man, that faith without works is dead?
21 Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar?
22 Seest thou how faith wrought with his works, and by works was faith made perfect?
23 And the scripture was fulfilled which saith, Abraham believed God, and it was imputed unto him for righteousness: and he was called the Friend of God.
24 Ye see then how that by works a man is justified, and not by faith only.
To me, these verses make it clear that our status as a “believer” or an “unbeliever” is as fluid as our next choice to “do his will” or to choose otherwise. In this fluid structure, it’s hard for me to even define what God “wasting his time with unbelievers” would mean.
It certainly doesn’t mean he prevents his prophets from preaching to sinners and warning them against their doom.
There’s also no space in the bible for it to mean that a man, or even an entire city, who was an unbeliever can’t hear and react to the message and become clean.
And I’m certainly not comfortable with the idea of God refusing to send a “wake up call” my way now and then because he’s deemed that he’s wasting his time with me.
So, I’m left to think that Tom’s criticism is directed at the use of logic and reasoning as a way of reaching out to unbelievers.
In the opening of the post, Perry states “I’m every bit as interested in science, philosophy and engineering as I am in business.” This is his blog where generally like-minded folks come to engage in
“active consideration and engagement” and thus I have strong doubt that Perry’s intent in posting the article was to draw out and convert every atheist who reads his Marketing Blog.
But, in the spirit of “active consideration and engagement” I would ask Tom for some clarity on the difference between “intellectual masturbation” and Christ’s use of parables, or the language of Isaiah’s prophecies. Both used language that require active study and intellect to decipher. And neither were addressed to those who openly opposed the gospel. They were directed to Jesus’ followers to increase their understanding.
So, if someone reading this post on Perry’s blog is staunchly against Christianity and unwilling to open themselves to the logic presented… the post will land somewhere on the scale between meaningless and offensive. But, the vast majority of people are not in open opposition. The majority of American’s do believe in God, but haven’t put a tremendous amount of time and intellect in to deciding what that means for them.
It is true that conversion to Christ happens by the simplest of means – humility and faith leading to a choice to obey God’s commandments – followed by confirmation from the spirit and the blessings of heaven. But, once we’re on that path… are we done? Certainly not.
So, I for one appreciate a good dose of “active consideration and engagement” even if others deem it to be “intellectual masturbation.”
Your way of making the distinction seems wrong to me.
It’s more like:
Universe: simply contains 4 rocks that do what they do.
Model of the universe:”if you take two of those rocks and group them together with the other two rocks, you have 4 rocks in the group”
(Note: the term ‘model’ seems a little strong with this simple example, since there are no dynamics involved. I’d probably just use the term ‘description’ at this point.)
The Universe itself does not CONSIST OF a set of logical axioms. (or even Empirical generalizations)
It might be true that the Universe is more or less orderly, and follows our empirical generalizations fairly closely.
But this does not make it CONSIST OF a set of logical axioms.
It CONSISTS OF matter and energy that simply does what it does.
HOWEVER, . . .
There’s an even bigger problem with your argument.
Here is the rhetorical flourish you seem to keep coming back to people with:
“My logic does hinge on the assumption that the universe is logical. I cannot prove that the universe is logical. You are welcome to assume that it is not. But if you do, then from that point forward you are forbidden to engage with me (or anyone else for that matter) on the basis of science or mathematics or logic, because your assumptions invalidate all of those things. Believe in an illogical universe if you choose” [cited from this thread, but similar statements are all over your replies to others on the other page.]
People who “say the universe is not ‘logical’” are not claiming it is not orderly. They are simply claiming that the universe does not “CONSIST OF” a set of logical axioms. You have to keep that distinction straight.
Also, consider that arithmetic is either incomplete or inconsistent.
That doesn’t mean we have to throw it out. We can still do accounting. Why does a system of axioms that’s incomplete need to be completed at all?
I’ve never personally “completed” the axioms of arithmetic with an “outside” axiom, yet I am perfectly comfortable using arithmetic.
So if any axiomatic system instantiated in the universe (or read onto it), or whatever, never gets completed, so what?
As I read through the discourse on the other page, I spent time trying to figure out your MO, Perry.
You seem to start with a conclusion (God exists), find a neat mathematical result (Godel’s theorem, fractals, power laws), and then you do very quick free association strings of reasoning that conflate a lot of distinctions on your way to “deriving” your conclusion from the mathematical results.
Fair enough. We’ve all been caught up in the excitement of finding a compelling argument that quickly moves from high status intellectual premises to our favored conclusion, and *hoping* it holds water on closer scrutiny.
But when others come along and point out distinctions you’ve overlooked, you have to slow down and take a look. Especially when several smart people independently all seem to point out the same problems with your argument.
I don’t think you’ve shown a proper respect for your objectors. You brush past the meat of their criticisms, pick on some minor point, and then challenge them to agree with you or abandon logic (based on equivocal uses of terms like ‘logical’).
Here is an initial list of terms I think you equivocate on:
“logical” (orderly, vs operating according to a system of formal axioms)
“complete” (god “completes” the universe, vs. an assumption “completes” an axiomatic system)
“the universe” (the stuff that makes up the universe vs our models of the universe)
Your argument only seems to work because you are not seeing these different uses of terms as you move through your argument.
Are you familiar with the confirmation bias? Or motivated reasoning in general?
My hunch is that if you disagree with a conclusion, you are very good at making the needed distinctions to pick the argument apart.
When you agree with the conclusion (and have personally designed the argument), it seems you are very bad at seeing the distinctions that spell doom for an argument.
We are all susceptible to motivated reasoning. But good thinkers are aware of their susceptibility and try to take measures to compensate for it. They listen to others when they make the distinctions, and they try to keep the distinctions in mind in subsequent discussion.
Anyway. I’m sorry if this sounds harsh, but you strike me in other places as someone who prizes intellectual virtue, so I thought I’d suggest you take a closer look at how you’re conducting yourself in this debate.
Richard
I did not say that the universe consists of a set of axioms. I said that the universe, if it is consistent, depends on an axiom.
When I say the universe is logical, I mean that in the universe, 2+2=4 and 2+2 never equals 5.
If you wish to say that the universe is orderly but not logical then you need to define precisely what you mean by that.
Arithmetic is either incomplete or inconsistent. You may not care that it is incomplete but logicians and mathematicians do. Because they seek to trace everything down to its roots and they find they always end up with an unprovable axiom. So it’s impossible to prove everything. You always have to make an assumption and then prove it out logically.
Atheists (the Infidels website in particular) have made an assumption that there is nothing outside the universe.
I have made an assumption that there is something outside the universe.
Gödel’s theorem contradicts the atheists and it confirms my hypothesis.
I work in advertising. I of all people understand confirmation bias. Everybody has confirmation bias. Not everybody clearly explains their views on their blog, backs them up with mathematical statements and invites everyone in the world to challenge their logic.
I use the word “logical” in the same way that a logician would define it.
I use the word “complete” in the same way that Gödel used it.
I use the standard definition of “universe” – Wikipedia – The Universe is commonly defined as the totality of everything that exists,[1] including all physical matter and energy, the planets, stars, galaxies, and the contents of intergalactic space
If you disagree with any of these definitions then you’re welcome to define your terms and construct an argument.
Nick,Perry, & others,
God divides mankind into three groups: Jews, Gentiles(unbelievers), and Church of God. The rules have changed since the time of Daniel or even the Book of Matthew. God says He would have all men saved and come unto a knowledge of the truth. He also promised that any one that hungered for righteousness will be filled. Are all men saved, do all hunger for righteousness? Will some convert? Absolutely and God has called them by name. However there are others that will not accept the accomplished work of Jesus Christ. It is those I spoke of as the unbelievers God leaves to their own devices. Even Christ told his disciples as he sent them out two by two to shake the dust of their sandals and move on if a person was not hungry for truth.
Worshiping the human mind is no lesser a form of idolatry than worshipping money, sex, or drugs. The human mind is incapable of proving of disproving the existence of God because it can only record and process the information gather by one or more of the five senses. God is spirit which means He is extra-sensory or beyond the realm of the senses. God cannot be known through reason. It is believing that builds the bridge between the natural man’s mind and the heart of God. God’s Word states that the believing that builds the bridge comes from hearing God’s Word. It has stood the blows of all the critics throughout the ages and is still here to make know the heart of God for His people. Without it we would know little or nothing about God.
So spend time with your “active consideration and engagement” to delve into the literature of eternity and see what happens.
Wishing You Plenty To Live,
Tom Doiron
Atlanta
Tom,
Isaiah 1:18 “Come now, let us reason together,” says the LORD.
1 Peter 3:15 (New International Version)
15But in your hearts set apart Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect…
Romans 1:20
20For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that men are without excuse.
I am not worshipping the human mind. The human mind is capable of perceiving the existence of God through the senses. Every single revelation of God to a prophet came through peoples’ five senses.
1That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked at and our hands have touched—this we proclaim concerning the Word of life. 2The life appeared; we have seen it and testify to it, and we proclaim to you the eternal life, which was with the Father and has appeared to us. 3We proclaim to you what we have seen and heard, so that you also may have fellowship with us. And our fellowship is with the Father and with his Son, Jesus Christ.
It seems to me that you are deriding something which you resent or perhaps to not relate to. Nowhere in scripture do I see any place where we are encouraged to throw our brains away or believe God on blind faith. Consider how Jesus reasoned with the teachers in the Temple even when he was 12. It makes no sense to speak of hearing without also speaking of the mind and its understanding of what it hears. Note in the passage I quoted to you about Nebuchadnezzar, God restored his mind and he returned to God.
Perry,
I’ve heard this argument before, although you stated it with more thoroughness.
We can agree that a mathematical explanation relies on fundamental assumptions, and proving each of these requires more math, and another set of assumptions.
The flaw in this argument is that the assumptions get smaller with each iteration, not bigger. Eventually we need to stipulate basic things like “I am alive – I’m not just imagining it.” or “The things I perceive with my eyes are real.”
Eventually we get to an assumption which is sufficiently small that we can all nod and say “I can live with that. This concept has been proven to my satisfaction.”
If we want name that uncertainty we feel, God, then I can live with that too.
What I can’t live with is when we assign, to that uncertainty, all manner of unproven and assumed traits, like a benevolent, watchful, caring Father Figure in the Sky who has a purpose for our lives we are intended to divine.
What I can’t live with is when we get handed a book full of mis-translated, second hand accounts about a man who claimed to be God’s son personified – who was happy to prove himself then, but is not willing to provide proof of himself now – and then we’re guilt-tripped into shaping our lives around it.
You and I have debated on this before, and you pointed out to me that religion’s purpose is to teach a moral code (I’ve always appreciated that observation, by the way).
Don’t you suppose there is an easier, better way to spread morality – and to provide the fundamental assumptions required for the rest of the world to exist – without relying on those contrivances?
I wonder if religion would be met with so much opposition from those who aren’t looking for something to believe in (ie. the atheist, the agnostics, and the materialists) if it endeavored ONLY to teach morality and explain the world, without restricting and trying to redirect our lives.
– Patrick
Patrick,
The logic that I used will get you to deism.
If you want to go further than that then you’re in the realm of theology. I think you’re misrepresenting the New Testament with your description of “second hand accounts” etc. A good starting point for this would be Anne Rice’s essay at http://www.coffeehousetheology.com/anne-rice-atheist-christ/
Proof of Jesus now – see http://www.coffeehousetheology.com/miracles/ – a recount of my own personal experiences and scientifically documented miracles that I’ve accumulated over the last few years.
You cannot teach morality without attempting to restrict or redirect peoples’ behavior. It’s inherent to the very idea of morality. That human behavior has certain obligations and that other people have the right to enforce those obligations. All laws do that. Even atheists who don’t want religion taught in classrooms are doing that.
I understand that atheists, agnostics and materialists are frustrated by religion and i understand their many legitimate objections. But morality always has to have some source of authority. I think that if you look at the world through a wide lens you will see that the atheist version of morality has largely failed. Is it merely a coincidence that the three worst tyrants of the 20th century (Lenin, Stalin and Mao) were all rabid atheists? Is it merely a coincidence that atheist governments killed more people in the last 100 years than all religious wars in all centuries combined?
Years ago I had an atheist friend Mark Vuletic (you can Google him), he said to me that the most perplexing problem with atheism is it has no basis for asserting any kind of absolute morality. Most atheists generally assume that the operating principle of the world is Natural Selection. And that’s about as amoral of a system as one can conceive of.
It’s a common mistake to apply Godel’s theorem to natural sciences. The theorem states, that a theory cannot be proved without accepting an unprovable axiom. In natural sciences a theory is derived by analyzing previously acquired evidence and is only considered valid for as long as it can accurately describe and predict new knowledge.
For example, for thousands of years geocentric theory of astronomy was considered perfectly valid, because it allowed to accurately predict the movement of visible planets and stars. When better optical devices were made, the geocentric theory became invalid because of new evidence suggesting that the visible universe was actually heliocentric.
There is no place for logical “proof” in natural science, because natural science is based on knowledge that was previously proved by reproducible experiments or observations. Mathematical theorems used in natural sciences are only formal descriptions of previously gained scientific knowledge.
We could say that mathematics is a “language” of science, a way to describe and extrapolate knowledge.
In a few words: Godel’s theorem is not applicable in natural sciences, and using it to prove the existence of God is the same as saying that God exists because there is a word “God”.
Viktor,
Your statement is tantamount to saying “it is a common mistake to apply mathematics to natural sciences.” Is that a statement you’re willing to stand by?
The relationship between math and science runs both directions and both directions are valid. Mathematics makes true statements about science and vise-versa. You can derive an algebra or calculus equation for a falling object and in doing so you invoke both deductive and inductive reasoning, both mathematical proof and scientific inference.
Gödel’s theorem is a proof. My extension of it is not a proof, it is an inference based on the unprovable axiom that the universe is logical and mathematical. Mathematics is more than a descriptive language, it is a predictive model.
In a few words: Gödel’s theorem is just as applicable to natural science as any other mathematical proof ie those of Euclidean geometry. I have used it to infer the existence of God. If the universe is consistent it is incomplete, ie it is contingent on something outside of itself.
Perry,
As it happens quite commonly in religious debates, you have distorted what I’ve said. I’ll say this again in other words: mathematics doesn’t influence real world. It is only a way to describe knowledge. Mathematical model doesn’t affect the system it describes: consistency of a mathematical theory doesn’t make all the aspects of described system true. If some data in that theory is wrong, then the whole theory is useless.
Again, until there was a way to gather enough evidence to contradict geocentric universe theory, all the mathematical models describing it were correct. Atoms were considered indivisible, alchemy was considered scientifically possible – all these fallacies were supported by consistent logical theories.
I’ll say this again: I am not saying that it is a mistake to apply mathematics (or any other formal science) to natural sciences. I am just saying that you can’t PROVE reality of something by applying mathematical theories. Please note, that I am talking about natural sciences, where scientific method is used.
Anyway, I don’t think that this is a productive argument. I wrote my comment not to disprove the existence of God, as it is impossible to both prove or disprove His existence. I wholeheartedly believe that everyone is entitled to an opinion and mine is that Gödel’s theorem is not a valid proof of God’s existence. If you are willing to argue that it is, I always enjoy debating with a clever and educated opponent.
Viktor,
You are distorting what I am saying. I did not say that mathematical models influence reality. I said that they describe reality.
And I didn’t say that I proved God existed. I said that if we accept the proposition that the universe is logical then according to the incompleteness theorem, we also must accept that the universe is incomplete.
Perry,
That’s right, you didn’t say that you proved the existence of God. In your post you said that belief in God is necessary from scientific standpoint. You also said that you “have used [Gödel’s theorem] to infer the existence of God”. The whole point of my comments was to point out that mathematical models only describe reality. They may be incorrect, if initial assumptions are wrong. If you infer something from a mathematical model it does not mean that your inference is correct until it’s proved.
But I think we are arguing about different kinds of mathematics. If we lived in a world of pure mathematics, then Gödel’s theorem would certainly require the belief in God. In the real world it doesn’t. To quote Einstein: “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
I would like to know the precise context of Einstein’s quote. What I do know is that Einstein is famous precisely because he produced mathematical models that corresponded to reality better than the previous ones did. And the position I am taking is that the more advanced our math and science, the more exactly they will both correspond to reality.
HI Perry,
I love to let God’s Word speak for itself. In my previous comments I was lazy and paraphrased the scriptures. Here I will quote them
1 Corinthians 2:12 Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God.
1 Corinthians 2:13 Which things also we speak, not in the words which man’s wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
1 Corinthians 2:14 But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
Romans 10:17 So then faith cometh by hearing, and hearing by the word of God.
I never suggested we “throw our brains away and believe God on blind faith”. We need our brains to study His word because from the Word of God comes the believing that bridges the gap between the natural man and the believer.
2 Timothy 3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
2 Peter 1:21 For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost.
Luke 1:15 For he shall be great in the sight of the Lord, and shall drink neither wine nor strong drink; and he shall be filled with the Holy Ghost, even from his mother’s womb.
(speaking of John The Baptist and his mother, Elisabeth)
Luke 3:21 Now when all the people were baptized, it came to pass, that Jesus also being baptized, and praying, the heaven was opened,
Luke 3:22 And the Holy Ghost descended in a bodily shape like a dove upon him, and a voice came from heaven, which said, that ye heard the word of truth, the gospel of your Thou art my beloved Son; in thee I am well pleased.
Ephesians 1:13 In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise
Ephesians 3:16 That he would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man;
Colossians 1:27 To whom God would make known what is the riches of the glory of this mystery among the Gentiles; which is Christ in you, the hope of glory:
God’s Word has a number of different writers, but only one author. God can manifest Himself in the senses world as He sees fit. His Word is as much a part of Him as anything, but there are records of voices, visions, messenger angels, etc. Otherwise we must have His spirit for Him to communicate with us.
God can speak to His spirit which He put upon the Old Testament saints, even Jesus Christ. Since the day of Pentecost which was the birthday of The Church of God, His spirit is within the believers.
Perry, I am thankful you are bold enough to talk about God in your blog. The truth has never been popular and probably never will be. I mean to offer no derision or resentment. I do not defend the truth, but I am called to be an ambassador for Christ. It is the love of God that leads a man to repentance and I will concede that logic and reason at times can help. However, I do get bothered at times when people act like the Ford was smarter than Henry.
Wishing You Plenty To Live,
Tom Doiron
Atlanta
I think the existence of God can be verified by the fact that we live in an environment that recycles resources. That there is food for us to eat and air for us to breath.
There is an order and disorder to creation that is mathematically beyond our abilities to equate devised by a Being that surpasses our ability to comprehend.
Nice thinking. It’s always fun to watch good minds at work.
However, if you just add another axiom to the system, it’s still either incomplete or inconsistent. You just apply Goedel to the new system including god, and nothing really changes.
Yours is basically a variation of the uncaused-cause proof. So the question is simply, why not apply the same logic to god as to everything else – what caused god?
The point is, sooner or later you have to stop regressing and arrive at a first cause. The first cause by definition has to be uncaused.
Give a reason for having to stop the causation, please.
http://en.wikipedia.org/wiki/Infinite_regress
Perry & All,
Along this line, the first word in the bible is GOD. The ancient manuscript render Genesis 1:1 as “GOD created the heaven and the earth in the beginning.”
My pee brain deducts that if you are to explain something, then you must be bigger than it is in some way. I know of nothing bigger than GOD to explain what caused GOD.
Wishing You Plenty To Live,
Tom Doiron
Atlanta
I agree this proves a metaphysical entity. I also agree there must be a Creator or First Cause.
But I don’t think this proves that this entity is necessarily equal to the Christian God nor that the Bible is completely correct.
You are correct.