## Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century

In 1931, Kurt Gödel delivered a devastating blow to the mathematicians of his time

In 1931, the young mathematician Kurt Gödel made a landmark discovery, as powerful as anything Albert Einstein developed.

In one salvo, he completely demolished an entire class of scientific theories.

Gödel’s discovery not only applies to mathematics but literally all branches of science, logic and human knowledge. It has earth-shattering implications.

Oddly, few people know anything about it.

Allow me to tell you the story.

Mathematicians love proofs. They were hot and bothered for centuries, because they were unable to PROVE some of the things they knew were true.

So for example if you studied high school Geometry, you’ve done the exercises where you prove all kinds of things about triangles based on a set of theorems.

That high school geometry book is built on Euclid’s five postulates. Everyone knows the postulates are true, but in 2500 years nobody’s figured out a way to prove them.

Yes, it does seem perfectly “obvious” that a line can be extended infinitely in both directions, but no one has been able to PROVE that. We can only demonstrate that Euclid’s postulates are a reasonable, and in fact necessary, set of 5 assumptions.

Towering mathematical geniuses were frustrated for 2000+ years because they couldn’t prove all their theorems. There were so many things that were “obviously true,” but nobody could find a way to prove them.

In the early 1900’s, however, a tremendous wave of optimism swept through mathematical circles. The most brilliant mathematicians in the world (like Bertrand Russell, David Hilbert and Ludwig Wittgenstein) became convinced that they were rapidly closing in on a final synthesis.

A unifying “Theory of Everything” that would finally nail down all the loose ends. Mathematics would be complete, bulletproof, airtight, triumphant.

In 1931 this young Austrian mathematician, Kurt Gödel, published a paper that once and for all PROVED that a single Theory Of Everything is actually impossible. He proved they would never prove everything. (Yeah I know, it sounds a little odd, doesn’t it?)

Gödel’s discovery was called “The Incompleteness Theorem.”

If you’ll give me just a few minutes, I’ll explain what it says, how Gödel proved it, and what it means – in plain, simple English that anyone can understand.

Gödel’s Incompleteness Theorem says:

“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”

You can draw a circle around all of the concepts in your high school geometry book. But they’re all built on Euclid’s 5 postulates which we know are true but cannot be proven. Those 5 postulates are outside the book, outside the circle.

 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

You can draw a circle around a bicycle. But the existence of that bicycle relies on a factory that is outside that circle. The bicycle cannot explain itself.

You can draw the circle around a bicycle factory. But that factory likewise relies on other things outside the factory.

Gödel proved that there are ALWAYS more things that are true than you can prove. Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few unprovable assumptions.

Gödel’s Incompleteness Theorem applies not just to math, but to everything that is subject to the laws of logic. Everything that you can count or calculate. Incompleteness is true in math; it’s equally true in science or language and philosophy.

Gödel created his proof by starting with “The Liar’s Paradox” — which is the statement

“I am lying.”

“I am lying” is self-contradictory, since if it’s true, I’m not a liar, and it’s false; and if it’s false, I am a liar, so it’s true.

Gödel, in one of the most ingenious moves in the history of math, converted this Liar’s Paradox into a mathematical formula. He proved that no statement can prove its own truth.

You always need an outside reference point.

The Incompleteness Theorem was a devastating blow to the “positivists” of the time. They insisted that literally anything you could not measure or prove was nonsense. He showed that their positivism was nonsense.

Gödel proved his theorem in black and white and nobody could argue with his logic. Yet some of his fellow mathematicians went to their graves in denial, believing that somehow or another Gödel must surely be wrong.

He wasn’t wrong. It was really true. There are more things that are true than you can prove.

A “theory of everything” – whether in math, or physics, or philosophy – will never be found.  Because it is mathematically impossible.

OK, so what does this really mean? Why is this super-important, and not just an interesting geek factoid?

Here’s what it means:

• Faith and Reason are not enemies. In fact, the exact opposite is true! One is absolutely necessary for the other to exist. All reasoning ultimately traces back to faith in something that you cannot prove.
• All closed systems depend on something outside the system.
• You can always draw a bigger circle but there will still be something outside the circle.

Reasoning inward from a larger circle to a smaller circle (from “all things” to “some things”) is deductive reasoning.

Example of a deductive reasoning:

1.    All men are mortal
2.    Socrates is a man
3.    Therefore Socrates is mortal

Reasoning outward from a smaller circle to a larger circle (from “some things” to “all things”) is inductive reasoning.

Examples of inductive reasoning:

1. All the men I know are mortal
2. Therefore all men are mortal

1. When I let go of objects, they fall
2. Therefore there is a law of gravity that governs all falling objects

Notice than when you move from the smaller circle to the larger circle, you have to make assumptions that you cannot 100% prove.

For example you cannot PROVE gravity will always be consistent at all times. You can only observe that it’s consistently true every time.

Nearly all scientific laws are based on inductive reasoning. All of science rests on an assumption that the universe is orderly, logical and mathematical based on fixed discoverable laws.

You cannot PROVE this. (You can’t prove that the sun will come up tomorrow morning either.) You literally have to take it on faith. In fact most people don’t know that outside the science circle is a philosophy circle. Science is based on philosophical assumptions that you cannot scientifically prove. Actually, the scientific method cannot prove, it can only infer.

(Science originally came from the idea that God made an orderly universe which obeys fixed, discoverable laws – and because of those laws, He would not have to constantly tinker with it in order for it to operate.)

Now please consider what happens when we draw the biggest circle possibly can – around the whole universe.
(If there are multiple universes, we’re drawing a circle around all of them too):

• There has to be something outside that circle. Something which we have to assume but cannot prove
• The universe as we know it is finite – finite matter, finite energy, finite space and 13.8 billion years time
• The universe (all matter, energy, space and time) cannot explain itself
• Whatever is outside the biggest circle is boundless. So by definition it is not possible to draw a circle around it.
• If we draw a circle around all matter, energy, space and time and apply Gödel’s theorem, then we know what is outside that circle is not matter, is not energy, is not space and is not time. Because all the matter and energy are inside the circle. It’s immaterial.
• Whatever is outside the biggest circle is not a system – i.e. is not an assemblage of parts. Otherwise we could draw a circle around them. The thing outside the biggest circle is indivisible.
• Whatever is outside the biggest circle is an uncaused cause, because you can always draw a circle around an effect.

We can apply the same inductive reasoning to the origin of information:

• In the history of the universe we also see the introduction of information, some 3.8 billion years ago. It came in the form of the Genetic code, which is symbolic and immaterial.
• The information had to come from the outside, since information is not known to be an inherent property of matter, energy, space or time.
• All codes we know the origin of are designed by conscious beings.
• Therefore whatever is outside the largest circle is a conscious being.

When we add information to the equation, we conclude that not only is the thing outside the biggest circle infinite and immaterial, it is also self-aware.

Isn’t it interesting how all these conclusions sound suspiciously similar to how theologians have described God for thousands of years?

Maybe that’s why it’s hardly surprising that 80-90% of the people in the world believe in some concept of God. Yes, it’s intuitive to most folks. But Gödel’s theorem indicates it’s also supremely logical. In fact it’s the only position one can take and stay in the realm of reason and logic.

The person who proudly proclaims, “You’re a man of faith, but I’m a man of science” doesn’t understand the roots of science or the nature of knowledge!

Interesting aside…

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 all systems rely on something outside the system. So according to Gödel’s Incompleteness theorem, the folks at Infidels cannot be correct. Because the universe is a system, it has to have an outside cause.

Therefore Atheism violates the laws mathematics.

The Incompleteness of the universe isn’t proof that God exists. But… it IS proof that in order to construct a consistent model of the universe, belief in God is not just 100% logical… it’s necessary.

Euclid’s 5 postulates aren’t formally provable and God is not formally provable either. But… just as you cannot build a coherent system of geometry without Euclid’s 5 postulates, neither can you build a coherent description of the universe without a First Cause and a Source of order.

Thus faith and science are not enemies, but allies. They are two sides of the same coin. It had been true for hundreds of years, but in 1931 this skinny young Austrian mathematician named Kurt Gödel proved it.

No time in the history of mankind has faith in God been more reasonable, more logical, or more thoroughly supported by rational thought, science and mathematics.

Perry Marshall

“Math is the language God wrote the universe in.” –Galileo Galile, 1623

Incompleteness: The Proof and Paradox of Kurt Gödel” by Rebecca Goldstein – fantastic biography and a great read

A collection of quotes and notes about Gödel’s proof from Miskatonic University Press

Formal description of Gödel’s Incompleteness Theorem and links to his original papers on Wikipedia

Science vs. Faith on CoffeehouseTheology.com

### 223 Responses

1. Derek says:

1. Isn’t he using inductive reasoning to say that there are always more things true than can be proven true? He’s saying “In all cases I’ve seen, there are more things true than can be proven true”. This means that his theory may not in fact be true, and even if it was, it would have some kind of thing backing it up that would also be unprovable.

2. Wouldn’t this theory being true necessitate that there was something outside of the thing that is outside of the natural world, as well as something outside of that? You say that things outside the natural world would be immaterial, but if you assert that this theorem proves that there is something outside of the natural world, then there MUST be something outside the spiritual realm as well. That would prove that there must be something outside the spiritual realm, so there must be something outside of the something outside of the spiritual realm, and this would continue forever.

We would need to draw a line somewhere in order to stop this from creating an infinite amount of new things as the circle gets bigger and bigger. You say that we should draw the line at the spiritual realm outside of the natural one, but I don’t see any reason why we can’t draw the line at reality, the natural realm.

• Derek,

1) He’s not using inductive reasoning to say that there are more things that are true than can be proven true; he proved mathematically and logically that there is always at least one thing more that’s true than you can prove.

2) You can draw more and more circles on the outside, you can draw them anywhere you want, and you can do that ad infinitum. But every circle will still be finite. Gödel’s theorem shows us that there still has to be something outside the biggest circle you can draw, that is infinite.

• Derek says:

He has to be using inductive reasoning, because he is doing exactly what you defined that as, namely reasoning from a smaller circle outward. Even if he did prove it mathematically and logically, the circle that encompasses the natural world, as well as logical thinking and mathematics would be the only deductive reason that went on there. In fact, if you believe that mathematics and logic should apply to anything outside their circle, is that not also an incredibly unjustified form of inductive reasoning? So, all Gödel could have possibly done was prove that everything in the natural world depended on something else.

So the only way you could reasonably assume that there was something outside of the natural world would be to apply that mathematical theorem of incompleteness to it is if you also believed that the something outside was bound by the rules of logic and mathematics, something we would have no reason whatsoever to believe.

So, the result is a paradox, which is not incredibly unforseeable, since that is what Gödel started with by your own admission. You wind up with a truth being outside of all known truths in any natural system bound by mathematics and logic, but have no reason to believe that is the case outside of a natural system.

There very well may always be more truths than are provable in a system governed by logic and mathematics, however, to assume that a product of those very same logic and mathematics applies elsewhere is a MASSIVE leap of faith, and may very well not even be possible, since if math and logic applied to whatever was outside there circle, then whatever was outside their circle would actually be inside their circle, and therefore not outside of their circle. However, my conclusion is a process of logic, and therefore is not applicable. Do you see the impossible situation that is spawned when you try to apply a theorem that was spawned in controversy and is not even widely accepted and apply it as proof for a spiritual realm?

• Derek,

It’s almost maddening sometimes, isn’t it? But really it’s not so bad. I love what you have said here because it brings us to some new places. Let’s calmly consider:

If we put all the codified laws of reason and logic inside a circle, then they’re all contingent on something outside the circle that you have to assume but cannot prove.

The thing beyond the circle which you have to assume but cannot prove is real and it is in fact beyond the constraints of reason and logic.

log⋅ic
–noun
1. the science that investigates the principles governing correct or reliable inference.
2. a particular method of reasoning or argumentation: We were unable to follow his logic.
3. the system or principles of reasoning applicable to any branch of knowledge or study.
4. reason or sound judgment, as in utterances or actions: There wasn’t much logic in her move.

Reason and logic are themselves systems. They can bring us to the edge of the circle. As I said in the article, whatever is outside the biggest circle is boundless; infinite. It is not a system. Nor is it constrained by any system.

Since it is not a system, it is also indivisible. If something is indivisible then there can be no contradictions or disagreements. Therefore it cannot be IL-logical or IR-rational. It is simply above – superior to – reason and logic.

So far I have not made any leap of faith whatsoever. I have only used the rules of logic to deduce what the thing outside the circle is NOT.

One thing is certain: The thing outside the circle is there. It exists. It IS. It is by definition metaphysical. And we have arrived at all of these conclusions through a process of deduction.

Therefore we can conclude with certainty that metaphysics is real, and that the philosophy of materialism contradicts Gödel’s proof and is therefore illogical.

Now let us compare what we know so far to the Judeo-Christian concept of God and see if it matches:

-God is outside of space and time (that’s a match)
-God has no beginning (that’s a match)
-God is infinite (that’s a match)
-God is metaphysical not physical (that’s a match)
-God creates (that’s a match, since anything inside the circle is contingent on something else, thus the universe is by definition created)
-God is love (love is not a system, love is boundless, love is not a rule or law)
-God is conscious (as I said in the article consciousness is not a property of matter or energy, therefore consciousness comes from outside the universe)
-God does not lie, since there can be no divisions, contradictions or disagreements (that’s a match)
-God is beyond man’s reason and logic (that’s a match)

At this point I cannot deduce that the thing on the outside of the circle is God but I can infer that the thing outside the circle is God. This requires a step of faith, but it is a reasonable step of faith since inference is based on reason and logic.

Gödel’s theorem is quite helpful in this thinking process. Thanks for pushing the conversation forward.

Perry

• Derek says:

Assuming that you’re right, and there is something outside of our “circle”, then that whole list you of things you presented would be entirely correct. There may also be other things that you left out, such as nothing god could possibly do could be based on logic, and as such may not have a cause and/or an effect.

However, this is the issue I take with you argument

“At this point I cannot deduce that the thing on the outside of the circle is God but I can infer that the thing outside the circle is God. This requires a step of faith, but it is a reasonable step of faith since inference is based on reason and logic.”

Here is where your argument shoots itself in the head. You have made a simple mistake, one that anyone arguing from your position would have made. You have made an inference based on both REASON and LOGIC, when you know that that CANNOT apply to anything outside of the circle called reason and logic. The reason that you used to arrive at your conclusion might even work if god was inside the realm of reason, but if he exists, he is not inside the realm of logic and reason. This mistake was made because it is impossible for anyone to not think and act logically since we are in the logic circle. So, if the “god” you outlined does exist, then all the qualities would only apply if he was also inside the realm of logic and reason which he is not. In fact, to try and assign ANYTHING outside of the circle ANY traits at all is ridiculous.

There is no way we could deduce anything outside of the largest circle we know of, which we have defined as reason and logic.

• Derek,

There may be all kinds of thoughts that are possible when one stands outside the circle. But we can only speculate about that.

You’re forgetting that I reasoned from INSIDE the circle. I never left the circle to formulate my argument. Actually it’s impossible for me to leave the circle.

Therefore everything I reasoned about what is outside the circle is necessarily true.

If all the matter that exists is inside the circle, then we can absolutely know that what is outside the circle is not matter. And so it goes with every single point I have made.

If there were a contradiction in my argument, you could say that I shot myself in the head. Since I have made no contradictory statements, everything I have said is true.

will everybody outside the circle will also hold same opinion? or there will only “one” outside the circle.infact i only want to say that the concept of multiple circle ends as soon as “oneness” comes . that applies to our physical world also.no sooner we all are one the circle ends or u can say that all circles falls.
is it true or otherwiwse?

• Derek says:

You are trying to make logical statements about something that by its very definition cannot be logical. This means that nothing you reasoned could possibly be true. Or that it’s all true and not true, the area is outside of logic, it doesn’t make sense. All the more reason to believe it doesn’t exist.

I’ve got another question for you then, if there is always one more thing that cannot be proven true, and we’ve already got postulates and philosophy for things that cannot be proven true, why is a god necessary?

• Derek,

You’re making a blanket statement in mid-air. Please walk through my logic step by step and show where I have made an illogical proposition.

I’ve shown that according to Gödel’s theorem the universe has to be contingent on something you have to assume and cannot prove and I have shown what that thing is and is not. I have shown that some infinite metaphysical entity is necessary. If you can show a flaw in my logic then we will be able to reach a different conclusion.

• Derek says:

Perry, it doesn’t matter if you did or didn’t make an illogical proposition. In fact, logically, the only way if could possibly be right is if it WAS illogical, since the area we are talking about is outside of logic. I realize that I’m using logic to come to this conclusion, making it utterly worthless in this instance. We are both making the same mistake of trying to inductively reason about what’s outside the realm of logic.

You see, the reason I think that inductive reasoning can work is because we have what we know, what we don’t know, and logic, and we are able to make something of a sandwich with all these things, using what we know and logic to fill in the blank area in between of what we don’t know. This is fine with me, and I have no problem with this at all, although it does not always produce entirely accurate results based on what we know, it is sometimes the only way to do things.

What you are suggesting however, is that it is possible to take out the “what we don’t know” and place it outside of logic and still come to a reasonable conclusion based on what we know. I could not possibly disagree more, and if you think that you are right on this issue, or I am creating a strawman and that this belief is not necessary to uphold the rest of what you say, please explain to me why I’m wrong and you are right, or why I am arguing the wrong case.

It all comes down to whether you believe you can used logic on things outside of logic Perry. If we have the same answer to this question, then I would be happy to continue this discussion, but if you believe that it is possible to use reason to conclude things outside of reason, then I think we are just wasting each others time.

• Derek,

Logic is a system so it is inside the circle. Logic is CONTENGENT on the thing outside the circle that we are discussing. Therefore whatever is outside the circle is SUPERIOR to logic. It supercedes logic.

It is possible to use logic to make true statements about the thing that is outside the circle. Case in point: When we define the universe as all matter and energy and draw our circle around it, then by definition there is no matter or energy outside the circle. Derek do you agree with this statement???

Logic cannot tell me what “it” is but it can most certainly tell me what it is not. I’ve taken logic as far as it can be taken and I have not attempted to take it any further.

You either believe in reason and logic or you don’t. From what you’re saying you don’t (?!?)

• Derek says:

It is impossible to derive anything inductively without the use of logic.
The more I think about it, I’m trying to make logical conclusions about whatever might be outside logic, just the same as you are when I say that logically you cannot use logic where it does not apply. The only conclusion I can come to would use logic also, and that would be that you can assign absolutely nothing to whatever is outside the circle of logic. But since I came to that conclusion logically, it is entirely worthless in this discussion.

Go ahead and define the universe as all matter and energy. I will agree that in a system governed by logic, matter and energy cannot be where there is not matter and energy. Anyone would agree with that. However, we are not dealing with a system governed by logic in this scenario you’ve created, on the contrary we are dealing with an area that CANNOT logically be based on logic, but can apparently because it is outside of logic.

To answer your question, I do believe in reason and logic. I believe that looking for things that are outside of them is a futile search for the reasons that I’ve outlined above.

Think about this Perry, both of our arguments are products of logic. What we are talking about is outside of/ not dependant on/ SUPERIOR to logic. What is it that makes you think that either of our arguments could possibly be correct? I am genuinely interested to hear your explanation (which will also be a product of logic by the way) as to why logic can apply to anything outside of itself.

I would only accept your argument if you moved the circle of logic and reason to encompass whatever you wanted to talk about that was out of the natural realm. But what kind of God would be subject to any kind of laws?

I guess what I’m saying in a nutshell is this:
1. The use of inductive reasoning is necessary for concluding anything outside of your circle
2. Inductive reasoning can only function in a system governed by logic
3. The system outside the circle of logic is NOT governed by logic

Therefore, you cannot conclude anything outside the circle of logic.

I am entirely aware that I just concluded something outside the circle of logic with that, but that just means that a contradiction is created, and by quickly checking my premises I am fine with my ultimate conclusion that nothing outside the realm of logic exists at all.

• Derek,

Thank you for thinking much more carefully about ‘stuff’ than most people do. it’s refreshing when iron sharpens iron.

I’m following you just fine, and we get to this:

1. The use of inductive reasoning is necessary for concluding anything outside of your circle
2. Inductive reasoning can only function in a system governed by logic
3. The system outside the circle of logic is NOT governed by logic

Gödel’s theorem itself is deductive not inductive.

The inductive part of my application of it is my presumption that the universe is finite. We do not know that, we only infer that from scientific data. So yes this is an inductive argument.

I take exception with one word you used: The thing in question in #3 is not a system, because we cannot draw a circle around parts of it. I would call it an entity, not a system.

Your conclusion does have a contradiction. Since we are restricted to making logical statements, the only logical statement we can make is that the system inside the circle is contingent on something that is axiomatic. It’s not contingent on a non-axiom.

Your statement “Therefore, you cannot conclude anything outside the circle of logic” is a logical statement as you acknowledged. It is a statement claiming to know what is outside the circle and as such it is self-contradictory.

The only way to make that statement non-contradictory is to change it to say “You can conclude something outside the circle of logic.”

And the conclusion is: There is a something out there, not a nothing.

Thus the defining statement on the Infidels home page is a violation of the laws of logic.

• Derek says:

Sorry it’s been a while since I’ve replied, my email doesn’t always catch it when you reply and it’s kind of a pain to check manually, but I do it every once in a while nonetheless.

Taking exception to the word “system” in number three is perfectly understandable if you want to refer to god. However, every known entity is part of a system, so if we’re going to continue using logic where it doesn’t apply then when can inductively conclude that god is not the only thing outside the circle which reality is contingent upon. Whatever, that’s a minor side note and it doesn’t matter anyways because logic does not apply to that circle. The only statement I am comfortable with making about anything outside of logic is:

“I am unable to say anything about anything outside of the system of logic and reason”

This may be considered a weak and anticlimactic end to an argument that’s been going on for some time, but I think if you follow my logic you’ll be able to see how I came up with it.

The fact is, we are creatures of logic, living in a universe governed by laws that must be consistent for the universe to work. If we work our way to the very edge using logic, we can conclude that we can say nothing about anything outside of logic without leaving the circle of logic.

If you feel like you can say something about whatever is or is not out there, go ahead. I’m sure the “yes” men on your site will agree with you mindlessly and the “no” men on your site will just as passionately disagree with you for no clear reason.

The conclusion that you came up with is just as contradictory. While it may be impossible to say you can’t conclude anything outside the realm of logic using logic, it is just as unreasonable to say that you can conclude something outside of the circle of logic. It is not logically possible to use logic outside of logic, therefore it is still contradictory.

The real conclusion is: We cannot say anything about anything outside of the realm of logic.

I don’t know or care what the infidels home pages defining statement is by the way. I have never visited that site, and I never plan to. While I consider myself an atheist, I can’t say that I’d like to have most of the “internet atheists” these days representing me. I’m this way because I thought about it long and hard, not because I’m an angsty teen with a need to rebel against my parents.

• Derek,

The only sense in which reason and logic do not apply to God (or whatever name we give to the Thing that is outside the system) is that logic applies to relationships between component parts. Since the thing outside the circle is not divisible and not made up of component parts, logic cannot parse God.

You say: “I am unable to say anything about anything outside of the system of logic and reason.” However we can say one thing about it: We can recognize that even reason and logic have to have a source. They are contingent on some Thing. Some axiom.

There is nothing that I have said here that is contradictory. Quite the contrary – it is all perfectly consistent.

So long as you are willing to follow Gödel’s thought process and accept ONE axiom as unprovable but true, there are no contradictions.

• yanniru says:

Perry said: Since the thing outside the circle is not divisible and not made up of component parts, logic cannot parse God.

Richard replies: How do you know that? Isn’t that just an assumption or perhaps an axiom of your faith? Is that the ONE axiom you say is unprovable but true?

• yanniru says:

Perry, For your own good, your Godel argument is so riddled with errors from the beginning tio the end, that you should just abandon it completely else you will degrade the Argument for Intelligent Design. Richard

• You’re welcome to point them out.

• yanniru says:

Your first error is to claim that systems are incomplete because axioms are unprovable. That is not why they are incomplete. Godel proved that any consistent system based on unprovable axioms (as all axioms are) contain truths that are not derivable from the unprovable axioms of the system. However, an axiom can be shown to be true by introducing additional axioms and removing the original one.

Your second and more profound error is your assumption that god does not reside within the circle of logic. God exists every where and can have both rational and irrational components.

Along that line a third error is the claim that anything outside the circle of logic cannot have component parts. That is pure assumption on your part. The Trinity alone falsifies that assumption. Systems can exist without being logical. Likewise, God can be a complete system and still have component parts. Human logic applies to some aspects of God but not all of God.

Finally my original point in this discussion is that your statement: “Any system of logic or numbers that mathematicians ever come up with will always rest on at least a few unprovable assumptions.” indicates that you do not understand Godel. That is not what Godel proved. Your statement is a truism.

Best regards,
Richard

• yanniru:

Yes you can prove axioms by swapping out other axioms but all you do is move the unprovability around to somewhere else. You never get rid of the requirement of something that is unprovable.

Yes I agree God exists everywhere. However God is not provable or detectable inside the circle and God is the only thing outside the circle.

I believe the indivisibility of the trinity at the very least shows that God is not “effectively generated” ie “recursively enumerable.” God does not count Himself as separate parts. However I say this provisionally because I am still thinking about it. Initially it seems to me that “three in one” is how God is Gödel complete yet plural (and thus able to self-conceive) at the same time.

Gödel is saying that any CONSISTENT system of logic or numbers will always be incomplete, if it is effectively generated.

• yanniru says:

Perry says: Yes I agree God exists everywhere. However God is not provable or detectable inside the circle and God is the only thing outside the circle.

Richard replies: Perry. Are you sure you want to stick with this statement? It seems fraught with dangerous assumptions to me.

But instead of belaboring those assumptions, I prefer to relate your picture of reality to my Multiverse Cosmology. I would contend that your circle of logic represents the outer boundary of any universe in my cosmology.

Each universe within that boundary has properties that at least in part are derivable from the fundamental assumption of string theory that particles are extensive and have the property of supersymmetry. Even the number of dimensions can be derived from these assumptions. Dropping supersymmetry the number of dimensions has to be 26 and a theory of only force is obtained. Introducing supersymmetry allows matter to exist but the number of dimensions becomes fuzzy with viable theories in 9,10,10,10,11,11 and 12 dimensions- but they are all dual to each other, meaning they are likely to be the same overall theory in various approximations.

My fundamental conjecture is that the 26 dimensions are split between 12 dimensions for each universe embedded in 14 dimensions of an overall multiverse. A 14d theory does not exist yet. But I explain how it coild be derived from the 12d theory using Bar’s Two-Time physics.

So given this picture of reality, a multiverse with embedded universes, and the assumption that God is everywhere, it is reasonable to draw a circle of logic around each universe since each universe is governed by the gauge physics of matter interactions, whereas the multiverse is gravitational.

However, this yields a conundrum as there is a logic (eg., gravity) to the multiverse as well as a logic (ie., gauge physics) for each universe. The only resolution would be to draw the circle of logic around the entire multiverse. But I find this circle to be so far removed as to be uninteresting.

What is more interesting is Goedel’s claim that each universe and the multiverse contain truths that cannot be derived for the fundamental assumptions of string theory. For example, the 12d gauge theory does not contain gravity, yet we all know it exists in our universe. But if the assumption of the multiverse is introduced (my conjecture) then we find that gravity in the universe comes in via spacetime curvature in agreement with General Relativity.

But even more interesting is the Penrose claim that at least some of the underivable truths of the universe are responsible for consciousness. He and Hameroff derived a biological theory for human consciousness based on self-gravity. However, there is no reason why the same thinking could not derive a God or Cosmic Consciousness. In fact, in my Multiverse Cosmology I conjecture that the same self-gravity mechanism applies to the connection of the universe to the multiverse at each point of space and is the basis of a Cosmic Consciousness.

If true, then there is a Cosmic Consciousness within each universe but not outside, which is rather like your circle of logic. In short, what I am saying is that one needs logic plus incompleteness to obtain God Consciousness. None may exist outside the circle of logic of a universe. So God is a system, contrary to one of your assumptions about God.

Respectfully,

Richard

• Derek says:

I disagree, I wouldn’t say it’s riddled with errors, there’s only the one that I see, which is that it doesn’t apply where he’s trying to put it. Other than that, it’s just as good as the best arguments for a god I’ve seen to date. It’s lightyears ahead of saying “trees and sunrises are proof of god” which is what I usually get. I’d be interested to hear of any other errors you found. This was kind of a tough nut to crack for me. I guess it just goes to show that you should make sure you are both agreeing to the same premises before you get too deep into an argument. Perry believes that logic can apply outside of logic, and this is one of the primary foundations for this argument. I don’t believe that however, so we would never be able to come to a conclusion together.

• This conclusion is not from theology, it’s from logic. If the thing outside the circle WAS divisible and made up component parts, then it would be a system and we could draw a bigger circle and enclose parts of it.

• Derek says:

You are using logic to say there is something outside of logic again when you say that we can say something outside of logic. This is illogical because logic does not apply in the area outside of logic. You can’t say there is something out there, and you can’t say there isn’t. All you can say is what I’ve already said, which is you cannot say anything about anything outside of logic. That’s as far as you can get without creating a contradiction.

We can’t say anything about it, logic and reason would only need a source in a logical system. Whatever extra system there is outside of logic, logic does not apply and we can say nothing about it. It may or may not be contingent on something else, we don’t know, and at this point we can’t say.

Your conclusion of “You can conclude something outside the circle of logic.” is as contradictory as “We can’t conclude something outside the circle of logic” and they are both contradictory because logic does not apply outside the circle of logic.

This argument from Godel’s incompleteness has only done what the best theological arguments to date have done. It has made itself an irrefutable and unprovable “maybe” that might possibly convince an atheist who couldn’t see the contradictions to become a Deist. The only reason anyone would accept your final conclusion as truth being that they already believe something outside of the realm of logic. So congratulations Perry, you’ve gone as far as anyone else has, and most likely ever will.

• RDWallace says:

It appears that what is outside of the circle of logic is simply other than logic and unfathomable to us because it is be based on a different set of parameters other than reason and logic. However the inference that the inside of the circle owes its existence to the outside of the circle appears to explain the cause but is not the sum of the inside of the circle. For example, matter, space and time is said to have unfolded from the big bang. If we were to reverse this, it would appear as matter , space and time collapsing again into its primordial contituent. This constituent caused matter, space and time, however it is neither. What is in or on the other side of the singulaity caused us, but is not us. This defines a circle boundary of existence because normal physical laws as we understand break down–> just as logic and reason break down when we come to what is on the other side of it. If we draw a circle around the singularity where there are parameters and laws or lack of we can infer they caused it to exist and so forth until we reach the concept of God or infinity which mathematically is the sum of all possible sets of infinite sets–> which implies that all that can happen will happen and nothing is impossible, because all possibilities exist… infinitly.

• Derek says:

I read over this again a while later and saw something wrong with what I’d said. I really can’t say that there isn’t something outside of logic using logic, nor can I say that logic isn’t applicacable to whatever might be outside of logic. What I can say is that logic is only applicable to things that fall within the real of logic. These two statements may look almost identical, but in the first one I’m concluding something outside of logic, and in the second one, I’m merely using logic to conclude something about itself. I’m more comfortable with this conclusion

• Ralph says:

Perry, I want to thank you for the excellent article. It is intriguing how anyone could start with the liar’s paradox to end up with a universal truth that requires God, and even describes his nature. But because of some of the challenges made to your application of this, I think I will soon dig directly into Gödel’s Theorems of Incompleteness (and Completeness).

I read all of the replies. I would love to chime in on many things said by you and others. But I limit myself to the one that stood out to me the most. It was the longest running problem, and without resolution. If you agree that my solution correctly assesses the problem, perhaps you could notify Derek (though after 6 years, who knows if he’s even still reachable).

In the comments section, there was one mistake that you and Derek both kept making. He inductively reasoned that the only thing that could exist outside the “circle of logic” is illogic (whereas you deductively reasoned it could only be something superior to logic). Then upon that induction, he made several logical arguments that inevitably led to a false conclusion (as did you), all because he made a faulty assumption at the beginning (the same one you made). Before he made his inductive reasoning (and you your deductive reasoning), he first assumed that the “circle of logic” necessarily contained ALL logic (whereas you assumed it contained all “normal” logic, which was close, but still wrong). But the false assumption you both made regarding logic overlooks the fact that the only things contained within the biggest circle are the things which are part of the cosmos (by which term I mean to include all of creation, even all other possible universes, imaginary as they may be). That means that only the logic of the cosmological realm can be contained within the circle. And here, by “the cosmological realm”, I mean all dimensions, including the angels and where they live, and any other dimensions. All of creation, and all its logic, is contained inside the largest circle (which only has to be a circle large enough to contain the entire creation). So, the “circle of logic” cannot contain ALL logic, but only all logic that is accessible within the realm of creation. All OTHER logic (whether you call it supernatural logic, or super-cosmological logic, or whatever) is still logic, but is found only outside the “circle of logic” (the logic of the cosmos). All the logic which can be found or derived from everything knowable in the cosmos is still only a small subset of ALL logic. This is where Derek made his mistake, and you as well (which is why you never were able to address it properly). Arthur Moore came close. But he only nailed the other side of the equation. He failed to connect them together. And in your response to someone else, you almost stumbled upon it when you said something like ~“any system of logic which can be devised by Man”~. That identifies logic that can be derived within the universe, in distinction to logic that cannot. But you didn’t quite notice it.

I hope this insight is helpful. Thank you.

{{I wanted to attach this to the final response you made to Derek. And I wanted this reply to go to you rather than to Derek (no offense Derek). And of all the replies back and forth between the two of you, this one is the last one of yours showing a Reply button. And the next one is the last one of Derek’s showing a Reply button. If there is a reason for it being that way, then so be it. But I would not mind if you are able to attach my reply as a response to your final reply to Derek. In my opinion, that’s where it belongs. But you may disagree. Also, feel free to omit this final paragraph which I’ve enclosed in double brackets, if you wish, or not. I leave that to you.}}

• Thank you! – and sorry for my delay in posting your reply.

• Ralph says:

I’m reading the article again. And now I know why Derek took a wrong turn in his logic. It is because the article makes the same wrong turn, in a different place. It states, “Because all the matter and energy are inside the circle. It’s immaterial.”

True, sort of, but mistaken in its logic to get there. Every circle must be a subset of what is outside the circle. If you ever have a circle that is not a subset of what’s outside it, then you’ve made an error. Therefore, “material” cannot be a subset of “immaterial”, sort of.

The reality of “matter” is that it is energy that is inexplicably contained in bundles. What keeps those bundles together even though they should fly apart, nobody knows (but the Bible does). So, everything in the universe is energy, even matter.

That means that all matter and energy inside the largest circle is just energy. But that does NOT mean that ALL energy is inside the circle. In fact, since the energy inside the circle has to be a subset of what is outside the circle, and the energy inside the circle could not have bundled itself into packets of matter, we then know that what is outside the circle has FAR more energy than all the energy that is inside the circle.

• claudecs says:

Derek, all statements of truth are true/false/meaningless only from a given standpoint. Even though you cannot apply logic to things outside of logic if you are yourself situated outside of logic, it doesn’t follow that you can’t apply logic for things outside of logic if you are yourself within the realm of logic.
It’s all in the perspective. You work with the tools you have here and now to describe what is made known to you here and now. What the actual thing looks like from its own perspective is both irrelevant and forever outside the reach of your knowledge as you can never be that thing, you can only be Derek and not just any Derek but the Derek from here and now.

• Arthur Moore says:

An interesting article, but there are some things I don’t understand.

Why is not the solution to this problem that logic is an attribute of God, i.e., an immutable part of his nature? Who says logic is something one can draw a circle around? If it reflects God’s rational nature and the way God thinks, then it would at least be a larger circle than the material uni/multiverse. What if logic is not a system, but merely how God thinks?

How does one draw a circle around an immaterial abstract object such as the laws of logic? By definition immaterial the laws of logic cannot be limited to specific space-time coordinates, therefore space-time itself cannot be a boundary for it.

In that case, the unclosable circle of logic would be identical to the unclosable circle of God. Since there could be nothing outside the unclosable circle of the logical God, therefore God can fully explain/contain logic? Perhaps this also proves the Trinity by proving the Logos? I think you are making a mistake in thinking logic is something outside of God which he is subject to, rather than part of his nature. Think of the laws of logic as you think of the laws of morality, as expressions of God’s nature. God is rational as God is good.

Would not God himself be the theory of everything?

I’m sure I am misunderstanding how you are using “circles” and “systems,” and probably everything else about this argument. I don’t get it I guess. But I find it interesting b/c it sounds like certain presuppositional apologetic arguments.

• The laws of logic are indistinguishable from mathematics. And thus subject to Godel’s theorem. In order for something to qualify as an axiom on which all else can rest, it has to have different ontological properties from logic and mathematics.

Logic is not outside of God, God is not subject to logic. The reverse of both of those things is true.

• Billy clark says:

To me that is spiritual supersymmetry the same as 3+2 =5 or 2+3=5. My interest relates from an experience whether in my body or out, I do not know, but I was outside the circle and in the presence of the illogical, infinite, and Uncreated One. I know that physics has hit a wall with what they call the Big Bang, or the uncaused cause of our universe. Hammeroff and Penrose are close but they continue as most scientists with building their model on the crumbling foundation of the quickly dying illogical unscientific Theory of evolution. Hammeroff has altered the theory to include fun, sex, as the motivator for evolution rather than survival. The spiritual power from the Infinite, All, is found in the quantum field. It is our logical minds most powerful connection to the I Am. The microtubules inside neurons function on frequency, this frequency is transmitted and received both inside and outside the circle, both physical and metaphysical. The quantum field is the power of The Comforter, manifesting reality with each measurement (observation) of each conscious observer. Time is nonexistent in the QF we know this by entanglement, thus it is related to what could be called the Eternal or Infinite, or what I personally call My Father or Abba!

• Steve says:

Derek you’re trying to hard bruh. Let it go dude. You’re just drawing larger and larger circles and quite frankly just going around in circles.

• Bernie Pack says:

At about 12 years old, I layed on my back in a paddock (a field) and imagined myself flying up through the stars, and imagining what would be at the end. My small mind first imagined a wall. Probably indicating the extent of my life experience then, but then I imagined climbing over the wall, and it was at that point in time I realised there was lots of things outside my imagination reach (outside my circle if you like). Therefore I Hypothesised (if 12 year olds are allowed to hypothesise), that if I drew the longest possible straight line, it would eventually form a circle. Still, I was only 12 years old. At 72 years old, I relive this experience in my imagination regularly. The only logic I can resolve is my evolved belief or faith, that leads me to have my faith in God. QED. (At least for me).

• Andrei says:

I agree. Simply put, we cannot use reason and logic for anything outside of our “circle”, because if we do, then that thing would be INSIDE the “circle”.

Perhaps this means that something other than reason and logic supports reason and logic?

• John Storey says:

Hi Perry,

The world of science is directly the world of human perception ( except for data coming to us via instruments such as microscopes, telescopes, cameras, spectrometers etc etc).

Even this data from instruments becomes part of the world of human perception, but nonetheless where it corroborates our sense perceptions (for example, I take a photograph of the back yard and it looks much like how the back yard normally looks when I am simply looking at it) it lends some weight of plausibility to the idea that the world beyond my sensory experience, the world we infer (more accurately pre-analytically ASSUME) to be the CAUSE of my sensory experience, really is pretty much like how I see it.

Nonetheless that this is so remains an assumption, which we can never prove. As you probably know this idea was first systematically explicated by Kant. He refers to ‘thing-in-themselves’ as ‘noumena’ as distinct from ‘phenomena’ (the world of human experience). No one has successfully refuted this idea (as far as I know) which expresses the limitations of human knowledge (confining it to sense data, logical inference and deduction). We can’t even know for sure that the ‘real’ or ‘objective’ world does operate causally or exists in space and time (although it seems pretty obviously self-evident that it does and in fact we are incapable of really doubting that it does).

All of this preamble is leading to this: If the ‘noumenal’ world ‘in itself’ lies outside our experience we cannot really know what it is like, or even that it exists. All these terms ‘really like’ and ‘exist’ are terms derived from our world of experience, we don’t know whether they apply at all to whatever lies beyond it.
Kant used this unknowablilty to justify FAITH in God, the immortality of the soul, free will and ethics, but he was very clear that we can have no unequivocal RATIONAL knowledge of such matters and this was the basis of his refutation of all the traditional proofs of the existence of God, the ontological, cosmological and teleological proofs

.His conclusions, as far as I am aware, have never been successfully refuted and are consistent with Godel’s ideas. I think Godel himself was a believer based (at least in part) on his realisation of the need for intuition in mathematics (because of the unprovability of axioms and postulates), but I just remember reading this somewhere and could be wrong, so please correct me if I am.

All the best
John

• Caroline O says:

‘At this point I cannot deduce that the thing on the outside of the circle is God but I can infer that the thing outside the circle is God. This requires a step of faith,’ Is it necessary to ‘infer’ that this is God? Surely ‘God’ is just our name for the thing outside the circle, which exists, whatever we call it.

• rob says:

I see only one problem with this circle argument, and that’s the assumption that there is a circle. There is no circle everything is connected in one circle nothing outside for a very simple reason, everything is connected from the smallest atom to the largest black hole you can literally draw a line from one end to the other with no interruptions. Now let’s assume there was a circle even if there was a circle outside of everything how do we know that what ever created the universe was a god, why couldn’t this entity just be a scientist whose experiment went horribly wrong and explode or vise versa and went exactly right. By assuming there is a god you assume this entity ment to design everything everywhere and knows everything about everybody with every decision that every being in a universe 13.8 billion years old will make. By knowing every possibly there is no such thing as free will because there is no possibly of possibility no randomness and everything would boil down to one mathematical formula that would prove everything there by eliminating anything outside of the one circle

• Thomas says:

The truth is (try the same method) that there is no higher being.
The sun rising is no faith, it is an assumption that has reasoning.
To call the universal logic of planets acting as they did for millions of years is as clear as you waking up tomorrow as long as long as you don’t perish. Quite simple actually.

• fbone says:

This whole debate hurts my head & heart equally. I don’t mean to be rude or contrary honestly and the posters here are certainly “smarter” than myself but it seems to be this whole thing could be more aptly named “the theory of arrogance” ( ie the current HUMAN flaw ). The ultimate paradox, the entire theory rests on facts not in evidence, or simply facts based on CURRENT human knowledge in a specific TIME period. I freely admit I am a cynical person however there are smaller examples of human arrogance… “sceince” was sure the earth was flat, also their assumption that “advanced???” humans were approx 5,000 years old… hello this is Gobeklei Tepe calling. I guess my theory says we cannot PROVE anything as well simply in a different manner, who’s to say a couple hundred years on we won’t discover for certain teleportation is real in a far off place??? Just sayin??

• Cobalt says:

“there is always at least one thing more that’s true than you can prove.”

That’s known as progress as we discover ever newer things, but their origins can be traced back to what we knew before. With god, there are no real steps of progress which will lead to him.

• Hillary says:

Hi Perry! I really love your discussion with Derek and of course this article. Can you explain to me why logic is a system inside the circle but information is not?

• We don’t have any empirical evidence that you can get codes without intelligence being there FIRST. We don’t have any evidence that codes are an emergent property of physical laws. So the inference is that intelligence comes from outside the universe. Or maybe it’s intrinsic and we don’t know the connection yet. Thus the reason for the Evolution 2.0 prize, http://www.naturalcode.org.

• Timothy Barker says:

Perry, your article is excellent! Secular science and philosophy not only strive to place God inside their own circle of laws and theories but to eliminate Him entirely. For if he were subject to the laws of human reasoning and the wisdom of men, then he would no longer hold the supreme role of God, creator, ruler, and judge over all the universe to which to which men and their wisdom is held accountable. And you are right, we can always draw a bigger circle to encompass our brutal thoughts, hypotheses, postulates, theorems, and conclusions. As I once told a friend in a similar discussion, “We could discuss infinity to perfection, but then we’d nothing have to left to say about either nothing or infinity”. And as a Christian brother once answered an ensnaring detractor, “Yes, God could create a rock he could not lift but he wouldn’t”. As the heavens are higher than the earth, so are his ways above our ways and his thoughts our thoughts. I find it interesting that Gobel’s theory invokes the circle considering the circumference of our earth in miles at the equator, rounded off to the nearest thousand, (24,901.2)? 25,000, divided by pi is 7,957, the number of New Testament verses which were not numbered until 1551by Stephanus, 69 years before the English mile was established by Gunter. Likewise, the word “circle” is only used one time in the King James Bible, which is in Isaiah 40:22, the 788th verse of this first major prophet. As there are three major prophets, they have a total of 3,929 verses, rendering Isaiah 40:22 the 3,142nd (pi to the 4th place) verse from the end of Ezekiel. Nicely done Perry! God Bless, Tim https://l.facebook.com/l.php?u=https%3A%2F%2Fm.youtube.com%2Fwatch%3Fv%3DJpJlilEQ3Io&h=eAQGlik1C

• But Really, Godel’s Incompleteness Theorem and
One’s Interpretation Of Godel’s Incompleteness Theorem
is The Infinite Regress Of God Dominoes Problem in Disguise
Godel is Simply Echoing The Concerns Of Aristotle & Others.

A More Nuanced Formulation of This Intuition is The Statement:
‘There is No Asymmetry for Free’. That is, There is No
Asymmetrical Expression Of Possibilities Without
Asymmetrical Decidability Criteria. That is, There
is A Reason That Seeds Grow into Plants Here
Yet Not There. There is A Reason That This
Kind Of Organism Evolves Here & Not Elsewhere.

Asking Why Leads Us Back to The Question Why Itself
Why Does There Seem to Be No Asymmetry for Free?
Why Do I Ask For Reasons When My Expectations
are Broken? Why Now & Not Before?

Ultimately, The Question is The Answer to How
How Can We Evade The Infinite Regress
Of God Dominoes Problem

If Every Asymmetrical Event Of A God Domino Falling
Requires A Previous God Domino Falling?

More Accurately, How Do We
Evade Un-Decidability in The
Asymmetrical Expression Of
Possibilities(Pre-existentially
Disposed Priorities)?

The Resolution is To Decide Without Deciding Between
Pre-existentially Disposed Priorities. That is, A Snowflake
Occurs in These Conditions, But Conditions are Symmetrized
in Order to Enable The Decision to Express Other Variations OfSnowflakes, etc. Why The Evasion Of Un-Decidability One Might Ask. Un-Decidability is That Which One Cannot Mean, Literally Or Metaphorically. The Source is Empty. The World is Full
This is God Without God.

I Enjoy Your Work 🙂

• Ed Bodker says:

Perry and Deric, you are getting lost in the trees. There are logical facts and experiential facts. They are not the same but are none- the-less facts in both cases. A logical fact can be repeated and explained with the rational mind. Experiential facts are real to the person who experiences them, but they cannot be explained by the rational mind. Perry you seem to be arguing that testimony of a spiritual experience should be provable by logic rather than an act of faith. And Deric you seem to be argueing that logic can prove faith is not a fact. This kind of tail chasing serves no good cause.

• I’m not arguing that testimony of a spiritual experience should be provable by logic rather than an act of faith. I’m saying that all systems of logic invoke faith and that the theistic faith system is logical.

• pramodkaimal says:

It is mentioned:
[1] All codes we know the origin of are designed by conscious beings.
[2] Therefore whatever is outside the largest circle is a conscious being.

In both [1] and [2] statements ‘conscious being’ is distinctly mentioned. In [1] it is also clearly mentioned ‘we know’.
Knowing is an act of Consciousness. Without Consciousness Knowing cannot be. Consciousness is what IS (is capital) Knowing is INTELLIGENCE. Intelligence is in the objective realm of Known like two sides of a coin. Immeasurable ISness /Awareness Knowledge (Intelligence?) Bliss ALL Pervades take any CIRCLE without the requirement of any restricted Finite BEING. Manifestations are just Mental Images FIRE being both Light and HEAT (cold to Human sensation fire too exist). Truth is that which was, is and will be ad infinite.

• Nate says:

There has to be an “uncaused first cause”. Since we know the universe is not it be must look beyond, it’s that simple. Outside this realm we cannot know anymore than if I were to kidnap you and put you in a room,you would know there was something outside that room but you would have no idea what it is.

• James says:

you’ve made the point you’re criticizing! Eventually, you have to have something that cannot be proven!

• Alick Stewart says:

No – you can’t draw a circle around infinity – it stops with the Infinite God.

• Carlos Lampley says:

The answer is that there is no infinit regression which is a part of logic. One need only go back to the first mover once. This was pointed to in the above statements.

• Tom says:

That’s not scientific. Why would be put a line around nature when it’s obvious there’s something more than nature? For Derek.

2. wmorrison says:

Perry, isn’t Godel’s point that there are situations for which the truth value cannot be determined? That is, you simply cannot prove whether an assumption is true or false based on the system which uses it?

You might be asking too much if you are going to use this as a basis for a stance either pro or con, since the implication is that for statements of this type, no truth value can be determined. Something like, “Well, it’s obviously true.” Takes you outside the sort of thing Godel had in mind, since for example, it isn’t obviously true to everyone or you wouldn’t bring it up.

Bill

3. Cobalt says:

Shame on you, Mr Marshall. Having received your latest email I came to this site and found I was not automatically logged on as Jim Diamond. My password did not work either, so I used my email address in case I had remembered it wrong to recover my password and found that despite receiving your latest offering, my email account was not recognised, as in you must have removed it. Well, that’s one way of winning a debate, by being the only person in it.

Your argument here is that since we do not know everything, then god must have made the universe. It is the sort of logic I have come to expect from creationists. If you study any field of knowledge, you’ll find that everything known is built on what has gone before it, like the discovery of electricity eventually led to the TV. Faraday could never have imagined a plasma TV but after countless steps he (and many others) helped invent it.

Many religionists work in science but none have found any evidence in their field to back up their religious beliefs. A ll religions are without evidence, so there can be no trail from simple known processes which will somehow lead us to find god. The fact that we cannot presently explain how the universe came to be is not evidence that an impossible being who goes against every rule we know could exist and could have made it.

Since god obeys no rules we know of and since he has never provenly done anything, we have no reason to believe in him, other than a book that is wrong on so many levels that it should be ignored.

Maths is how you work out things. Randomness is how you build universes. You start with sufficient hydrogen and sufficient time and you get to where we are now. No god needed, which pushes the god of the gaps into ever smaller spaces till he fades away completely.

• Jim, we installed a registration system and started from scratch. It didn’t recognize you because your email wasn’t loaded in. Nothing personal.

Please provide proof for your statement “Randomness is how you build universes.” From what I understand the universe is governed by a precise set of laws, not randomness. Also according to Freeman and Dyson, the expansion of the big bang had to be fine tuned to 120 decimal places of precision in order for stars to form. That doesn’t sound very random to me.

Where do you get the hydrogen to start a universe? And why is it there in the first place?

Please provide a logical argument as to why you think my use of Gödel is wrong. Atheist bumper sticker slogans and accusations will not suffice in this forum.

4. MSABBAH says:

Thank you Perry, As always your articles come to be convincing to any human mind that seeks truth. My question to you: According to the “Incompleteness Theorem”, Jesus can not be God, since: 1- For the duration of his existence on Earth, he constituted a part of the closed system, and he needed external source for proving him (His mother on the next level circle, as well as God at the most out circle), 2- Jesus was a system composed of parts (he was not indivisible), 3- Jesus had a start time when he was born.
Also, I wanted to ask you: How did you infer that God is Love? The fact that love is not a system, and it is boundless, and it is not a rule nor law, does not give you the logic to conclude that God is Love. Why not Mercy? Why not wisdom?
Thank you!

• I hope I have answered this question in the other post below. Christian theologians have always considered the 100% divinity and 100% humanity of Christ to be a mystery. I don’t think there’s any way around that. However it makes sense to me as I shall explain:

Yes, Jesus as a human being was a system but Jesus’ spirit existed for all time as One. Jesus was not like all other prophets, because all of them had a beginning. But Jesus said to the pharisees, “Before Abraham was, I AM” – a reference to Exodus 3:

13Then Moses said to God, “Behold, I am going to the sons of Israel, and I will say to them, ‘The God of your fathers has sent me to you.’ Now they may say to me, ‘What is His name?’ What shall I say to them?”
14God said to Moses, “I AM WHO I AM”; and He said, “Thus you shall say to the sons of Israel, ‘I AM has sent me to you.'”

Now, as to the question of God being love – how is this different from mercy and wisdom?

The Bible says God HAS mercy and wisdom. But that God IS love. Let’s think about that for a minute.

In 1 Corinthians 13:8 Paul says:

8 Love never fails. But where there are prophecies, they will cease; where there are tongues, they will be stilled; where there is knowledge, it will pass away. 9For we know in part and we prophesy in part, 10but when perfection comes, the imperfect disappears.

He is saying that love will outlast all other things, even knowledge and wisdom. Knowledge and wisdom and mercy have boundaries; but God’s love knows NO bounds.

So I conclude that one of the attributes of “the thing outside the largest circle” is necessarily LOVE.

5. guitarmas5 says:

If you believe that Gödel is correct then you cannot believe in God, at least not in the traditional sense. According to his theorem, I can never fully comprehend my own brain because I’m using that brain to try to understand it. Therefore, God can never fully comprehend himself. And even if you were to define God as the cosmic glue, the be all and end all of systems, Gödel proves that there would always be something more, which means that either God cannot exist or, if he does, then he cannot be omniscient and omnipotent thus destroying the classical religious definition of deity.

• You are correct, you can never fully comprehend your own brain because you’re using that brain to try to understand it. Everyday experience confirms that – the mind is largely still a mystery.

Since God is one and indivisible, God is not complex thus God does not have this problem. God is not a system and is not made of divisible parts. See the conversation I had with Derek about the nature of what is outside the circle.

The conclusion I have made is a logical outworking of the premises and the steps of logic. If you disagree, then identify the specific mistake I have made in my logic.

• guitarmas5 says:

If God is one and indivisible then he cannot be a being, for all beings are systems by definition. By your logic, either god does not exist or he exists as something conceptually at odds with every notion theology has thus far devised. There may be some cosmic, metaphysical force responsible for “creation” but that force cannot be both conscious and free of systems. In effect, your arguing what scientists already believe, only calling it something different.

• You said: “all beings are systems by definition”

– Christian theology has always defined God as a being and has never defined God as a system. “God is one, without diversification within God’s self. The unity of God is such that God’s essence is the same as God’s existence. ” -St. Thomas Aquinas, ~1250AD

From the Aquinas entry on Wikipedia:

Concerning the nature of God, Aquinas felt the best approach, commonly called the via negativa, is to consider what God is not. This led him to propose five statements about the divine qualities:

1. God is simple, without composition of parts, such as body and soul, or matter and form.
2. God is perfect, lacking nothing. That is, God is distinguished from other beings on account of God’s complete actuality.
3. God is infinite. That is, God is not finite in the ways that created beings are physically, intellectually, and emotionally limited. This infinity is to be distinguished from infinity of size and infinity of number.
4. God is immutable, incapable of change on the levels of God’s essence and character.
5. God is one, without diversification within God’s self. The unity of God is such that God’s essence is the same as God’s existence.

Notice the similarities between Aquinas’ use of pure reason 800 years ago to argue what God is based on what He is not in the Summa Theologica; and my argument from Gödel’s theorem to make statements of what God is not.

• MSABBAH says:

Dear Perry,
I have two questions:
Q1: Was Jesus a system?
Q2: How can we use Godel’s Theorem to prove Jesus was not God, but rather just another Messenger of God sent to the Sons of Israel?

I really wish you give me detailed analysis of the applicability of Godel theorem to Jesus (Peace and Blessings Be Upon Him).
Thank you

• MSABBAH,

What a great question.

I am a Christian and as such I am going to start with Christian theology and then talk about what relation this has to Godel.

Jesus was fully God and fully man. He had a physical body like all human beings and was born of a woman, therefore physically he was a system. However his Father was God and he eternally existed from eternity past:

-Isaiah 9 says, “For unto us a child is born; unto us a son is given

-In John 8 he says “Before Abraham was, I AM”

-Hebrews 1 says the following:

1In the past God spoke to our forefathers through the prophets at many times and in various ways, 2but in these last days he has spoken to us by his Son, whom he appointed heir of all things, and through whom he made the universe. 3The Son is the radiance of God’s glory and the exact representation of his being, sustaining all things by his powerful word. After he had provided purification for sins, he sat down at the right hand of the Majesty in heaven. 4So he became as much superior to the angels as the name he has inherited is superior to theirs.

5For to which of the angels did God ever say,
“You are my Son;
today I have become your Father”? Or again,
“I will be his Father,
and he will be my Son”? 6And again, when God brings his firstborn into the world, he says,
“Let all God’s angels worship him.” 7In speaking of the angels he says,
“He makes his angels winds,
his servants flames of fire.” 8But about the Son he says,
“Your throne, O God, will last for ever and ever,
and righteousness will be the scepter of your kingdom.”

God in His non-human form is not a system, i.e. is not made of divisible component parts. So now we have the question of the Trinity and what is its relation to Gödel’s theorem?

First of all God is not divisible – which is to say Father, Son and Holy Spirit are never at odds, never in disagreement. Always in communion and always in harmony. So God is not a system.

The Bible says God has a lot of characteristics: Righteousness, truth, light, justice, mercy. These are all characteristics of Himself that are relative to that which He has created. But the Bible says that God IS love. Not “has love” but “IS love.”

How can God BE love? What is there to love if God is completely monolithic? What is there to love if God is one?

The Trinity is a community of being – one being, three manifestations in which love is the unity of the three manifestations. Love is the aspect which says the essence of God [Father], the expression of God [Son] and the understanding of God [Holy Spirit] are in complete oneness.

God the Father is hidden and unknowable apart from his revelation of Himself.

God the Son is the revelation, the expression of God and is the exact representation of His nature (Hebrews 1). The Son is the WORD (Greek word “Logos”) – John 1 “In the beginning was the Word and the Word was with God and the Word was God. He was in the beginning with God.”

In John 14 Jesus describes the Holy Spirit: 26But the Counselor, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you.

Mark 13:11 And when they arrest you and deliver you up, do not be anxious beforehand about what you are to say, but say whatever is given you in that hour; for it is not you who speak, but it is the Holy Spirit.

The Holy Spirit imparts understanding and wisdom of what has been revealed through the Word of God.

The Father, Son and Holy Spirit cannot be separated, thus they are not a system of component parts. Rather they are the attributes of the divine consciousness which is not divisible.

Now in this I also see a very interesting correspondence between the Trinity and information theory.

Information theory says that a communication system consists of three parts:

Encoder – code – decoder.

Communication cannot occur without all three elements. If you are the only person on earth with a cell phone, it is completely useless. If two people have cell phones and they use compatible signals, communication is possible.

The original message is encoded by the encoder.

The code represents that message symbolically.

The decoder makes the coded message understandable to the recipient.

In order for communication to take place, there must be simultaneous agreement in advance between all three elements. A breakdown in any of the three destroys communication. Communication always requires desire for understanding on the part of the person who designs the system. In a very real sense we can call this desire for agreement love. Love is the desire for unity.

I would propose to you, then, that every instance of successful communication is a human-made system that reflects the nature of the Trinity. The Trinity itself is not a system but it possesses attributes that must be present in all successful communication systems.

Evil is successful communication of that which is not true. Evil comes from hate, not love. It comes from pride which sets itself up as more important than all others. Thus evil is a parasite that requires successful communication but inverts its purpose from love to hate.

To summarize, then, God is a single indivisible being, desiring agreement and unity in conception, in expression, and in understanding. Conception, expression and understanding are three attributes of God as a conscious willful perfect being. Jesus is the expression of God in human form. And all successful communication systems are systems that possess these essential attributes of the Trinity.

Perry

• MSABBAH says:

Excuse me but I feel I am lost with what you have said:

Jesus was fully God and fully Human. Can this translate to the following equation:
Jesus= Fully God + Fully Human.
Also, if there is something called Fully God, then it should be logical to assume that there will also be something that is Partially God? or semi God? Can you give me examples of Partially/Semi God Beings?

God= Father+Son+Holy Spirit+love. Is this a correct formula concluded from what you have described? Please confirm
What about: God= Father= son= Holy Spirit=Love?
Or else, provide the correct formula, as it will make it more visual to me to understand the concept.

In our understanding of language, any Son can not exist before His Father, Right?
So the father has to be there before the son IS, Right? Both the Son and Father can not start being at the same instance of time. That makes the Son finite in start time, Right? And anything that is finite in start time presents a creature. So, if Jesus was the Son, then Jesus is finite in time, and he is actually a creature!

Also, Why did God spoke to our forefathers in the past through prophets, then all of a sudden decided to speak by his son? What suddenly or differently happened that necessitated this? What does Bible tell about that?
And then Jesus being partly a physical system like us, then he should eat and drink to maintain that system operational, but that makes him in need to go to the WC (Water Closet), which is not imagined a proper place for “the exact representation of his being”.
I have more questions, but I will stop here to have the answers for the above, before I proceed.

• MSABBAH,

Yes, Jesus = Fully God + Fully Human.

There is no such thing as something that is partially God. Totally impossible in Christian theology. Unthinkable, really.

I endorse the statement God= Father= son= Holy Spirit=Love. But I use that = sign with caution.

John 1:1 says: “In the beginning was the Word and the Word was with God and the Word was God.”

So I would ALSO say God= Father+Son+Holy Spirit+love. I would endorse both statements.

Jesus is a creature because He is a human. He is a son because he is born of a woman and He has a father. But his spirit is not finite. He Himself is outside of space and time and transcends all.

The Father is the essence, the Word is the expression and the Holy Spirit is understanding. So yes essence precedes expression but this is not in time. This is in revelation.

The coming of the Son was foretold by the prophets and the activity of the Son is present before Jesus’ birth. In Genesis 1 God says, “Let US make man in OUR image.”

When Shadrach, Meshach and Abednigo were thrown into the fire in Daniel 3:

19 Then Nebuchadnezzar was furious with Shadrach, Meshach and Abednego, and his attitude toward them changed. He ordered the furnace heated seven times hotter than usual 20 and commanded some of the strongest soldiers in his army to tie up Shadrach, Meshach and Abednego and throw them into the blazing furnace. 21 So these men, wearing their robes, trousers, turbans and other clothes, were bound and thrown into the blazing furnace. 22 The king’s command was so urgent and the furnace so hot that the flames of the fire killed the soldiers who took up Shadrach, Meshach and Abednego, 23 and these three men, firmly tied, fell into the blazing furnace.
24 Then King Nebuchadnezzar leaped to his feet in amazement and asked his advisers, “Weren’t there three men that we tied up and threw into the fire?”
They replied, “Certainly, O king.”
25 He said, “Look! I see four men walking around in the fire, unbound and unharmed, and the fourth looks like a son of the gods.”

The fourth man is generally understood to be Christ.

There are many prophesies about Christ in the OT: http://www.godonthe.net/evidence/messiah.htm

Jesus embraced ALL human frailties:

5Your attitude should be the same as that of Christ Jesus:
6Who, being in very nature[a] God,
did not consider equality with God something to be grasped,
7but made himself nothing,
taking the very nature[b] of a servant,
being made in human likeness.
8And being found in appearance as a man,
he humbled himself
and became obedient to death—
even death on a cross!
9Therefore God exalted him to the highest place
and gave him the name that is above every name,
10that at the name of Jesus every knee should bow,
in heaven and on earth and under the earth,
11and every tongue confess that Jesus Christ is Lord,
to the glory of God the Father.

Great questions. Thanks for your time.

Perry

• MSABBAH says:

Perry,
Do you really believe in this? Father=God=Son, so Father IS His Son??
To rational people this is called “Non-sense” or “Non-logic”, as it does not convey information but rather confusion. I thought that the mission of Prophets and Messengers and the message of all Holy Books, was to Guide the people and show them to some extent Who is their Lord, Who Is their God, and how He want people to worship Him. For this mission to be successful, the message should be very clear and easy to understand and free from any cause of confusion, provided that the humankind was already created with tendency to look for The Creator. The message comes to “guide” people not to confuse them. The Wisdom of God necessitates that: Any information that causes confusion or ambiguity concerning the original message should not be exposed to people because it will distract them from the original goal of the message which is: “Getting to know Their God, and knowing how He want them to worship Him”. Imagine when a father and his 3-years old daughter are watching TV, and she asks him this question: Papa, How did these people come inside our TV? Then he answers: See my daughter, actually these people are not real people, they are electromagnetic video signal transmitted on the UHF band, and our TV is actually nothing more than a UHF receiver to demodulate this signal, which was originally broadcasted … bla bla. and he goes on explaining the theory of Maxwell equations and Electromagnetic waves, just imagine this was the father’s answer. In the daughter’s brain, this answer will be decoded as “Bla bla bla”. Do you believe this is a wise father? Do you believe that was a good answer? Does that father expect his 3-years daughter to understand this level of information? and most importantly at the first place, Did the daughter need to know this information?!!
My understanding is that our One and Only God will guide us to know Him by sending Messengers, Prophets with Holy Books, and just like in the User Manual that comes with any appliance, the contained information and instructions should be clear and easy to understand for everybody and for any one without the need for mediators. Our relationship with our God should be direct without any priests or intelligent beings in the middle.
Perry, in your debates with the atheists you used scientific logic and reasoning approach, and I was expecting the same approach in proving that Jesus (PBUH) is the son of God and that the Trinity Doctrine divinely inspired, but instead you followed the approach of quoting from bible, as if all what is in bible is true and authentic to be sourced from God. I say not all in the bible is God’s, and hence we should not accept all what is in the bible for granted.
I say, that we should worship God as He sees appropriate. Our God is beyond our imagination. We should not refer to God as we refer to each other, and we should not expect God to be like us. We Muslims believe that Quran is the only authentic Word of Allah currently available, and I thought it might be interesting to you to learn what Allah says in Quran about Jesus (PBUH) and you People of book and Trinity Doctrine, so I hereby quote part of the English translation of Quran meaning from Surah.5 “The Table”:
15. O people of the Book! There hath come to you our Messenger, revealing to you much that ye used to hide in the Book, and passing over much (that is now unnecessary). There hath come to you from Allah a (new) light and a perspicuous Book.
17. In blasphemy indeed are those that say that Allah is Messiah the son of Mary. Say: “Who then hath the least power against Allah, if His will were to destroy Messiah the son of Mary, his mother, and all every – one that is on the earth? For to Allah belongeth the dominion of the heavens and the earth, and all that is between. He createth what He pleaseth. For Allah hath power over all things.”
18. (Both) the Jews and the Christians say: “We are sons of Allah, and his beloved.” Say: “Why then doth He punish you for your sins? Nay, ye are but men,- of the men he hath created: He forgiveth whom He pleaseth, and He punisheth whom He pleaseth: and to Allah belongeth the dominion of the heavens and the earth, and all that is between: and unto Him is the final goal (of all)”
65. If only the People of the Book had believed and been righteous, We should indeed have blotted out their iniquities and admitted them to gardens of bliss. 66. If only they had stood fast by the Law, the Gospel, and all the revelation that was sent to them from their Lord, they would have enjoyed happiness from every side. There is from among them a party on the right course: but many of them follow a course that is evil.
72. They do blaspheme who say: “(Allah) is Messiah the son of Mary.” But said Messiah: “O Children of Israel! worship Allah, my Lord and your Lord.” Whoever joins other gods with Allah,- Allah will forbid him the garden, and the Fire will be his abode. There will for the wrong-doers be no one to help.
73. They do blaspheme who say: Allah is one of three in a Trinity: for there is no god except One Allah. If they desist not from their word (of blasphemy), verily a grievous penalty will befall the blasphemers among them.
74. Why turn they not to Allah, and seek His forgiveness? For Allah is Oft- forgiving, Most Merciful.
75. Messiah the son of Mary was no more than an apostle; many were the apostles that passed away before him. His mother was a woman of truth. They had both to eat their (daily) food. See how Allah doth make His signs clear to them; yet see in what ways they are deluded away from the truth!
76. Say: “Will ye worship, besides Allah, something which hath no power either to harm or benefit you? But Allah,- He it is that heareth and knoweth all things.”
77. Say: “O people of the Book! exceed not in your religion the bounds (of what is proper), trespassing beyond the truth, nor follow the vain desires of people who went wrong in times gone by,- who misled many, and strayed (themselves) from the even way.

• MSABBAH,

You are asking me to explain Christian theology and then scolding me for quoting the books that these statements come from.

John 1 says:

In the beginning was the Word and the Word was WITH God and the Word WAS God. (Emphasis mine.)

Jesus is a distinct expression of God and Jesus is also in essence God.

Islam teaches that God is one. Note that Genesis 1 says, “Let US make man in OUR image.” God is PLURAL. This is necessary for God to be love, because love cannot exist without plurality. Ultimate love is the unity that comes from the completely harmony of the plurality of God.

We’re all familiar with sexual union, where husband and wife become one. What if the two TRULY became one in a way that is a million times more intimate than sex? If you can attempt to imagine that, you begin to grasp the nature of the Trinity. This is not non-logic. This is a phenomenon that is so superior to human experience, it’s what every human craves. UNITY with God just as Jesus is one with God.

Sir, I respect your Muslim faith and your commitment to it. I respect the fact that you believe that I am blaspheming by saying Jesus is God. I recognize the Islamic teachings about Christ. But what Islam says about Jesus is directly contradictory to what Matthew, Mark, Luke, John and the epistles all say about Jesus.

Ultimately you need to decide for yourself. I would encourage you to read the book of John and see what Jesus’ closest follower said about his experience of living with Jesus for three years.

Sincerely,

Perry

• RDWallace says:

Perry… You failed to include that since God encompasses and created everything then he is also evil, hate and all the negative things we try not to be. Whats more, if these things were not intended then that implies that a perfect God made a mistake. If man is fallen, then God has failed because we are one of many manifestations of his creation whch assumes that God created us with errors making God not perfect. This also creates the paradox of God knowing the outcome of all things which means that nothing we can do is wrong or God would have not intended for it to happen. However, conversely I believe the concept and definition of God is “without mistake” and therefore as Tao says, “All is as it should be.” What we precieve as evil is nothing more than the flip side of a coin. Hence, how can you know light if you never saw darkness, how can you know day if you never experienced night, how can you know good if you never experienced evil. This duality is simply for understanding the universe through comparison. As Godel shows, you cannot understand what something is until you understand what is not and have something to compare it to. The problem however is the means. Language is so flimsy in describing anything because we personify everything. We assign attributes that do no perfectly describe the unknown. For example, We call a UFO a “flying saucer” which is all we can compare it to. But it really is not that. Enter science which uses the perfect language of mathematics. 1+1=2 everywhere in the universe and can be understood by any advanced intelligence–> The universal language!

An Argument Against Jesus:

Mathematically, the observable universe is so immense that the probability of life existing elsewhere is highly possible. In fact if the universe is infinite, it is absolutely true because all possibilities exist in such a place. Suppose we discover intelligent life somewhere out there that is not human. Does Jesus represent them as a human or does he take on their likeness. Or is Jesus just for us humans? Jesus implies almost to a fault that in all the universe we appear as his favorite. How conceited of us. This line of thought would come to crashing halt if if ET ever arrived here. That event would rewrite our thinking about everything. Does ET get ressurected too. Frankly speaking, if I see any ressurected dead walking around on judgement day I’m getting my shotgun out and put them back where they belong–> With the dead.

• God sanctions evil:

6 One day the angels [a] came to present themselves before the LORD, and Satan [b] also came with them. 7 The LORD said to Satan, “Where have you come from?”
Satan answered the LORD, “From roaming through the earth and going back and forth in it.”

8 Then the LORD said to Satan, “Have you considered my servant Job? There is no one on earth like him; he is blameless and upright, a man who fears God and shuns evil.”

9 “Does Job fear God for nothing?” Satan replied. 10 “Have you not put a hedge around him and his household and everything he has? You have blessed the work of his hands, so that his flocks and herds are spread throughout the land. 11 But stretch out your hand and strike everything he has, and he will surely curse you to your face.”

12 The LORD said to Satan, “Very well, then, everything he has is in your hands, but on the man himself do not lay a finger.”
Then Satan went out from the presence of the LORD.

13 One day when Job’s sons and daughters were feasting and drinking wine at the oldest brother’s house, 14 a messenger came to Job and said, “The oxen were plowing and the donkeys were grazing nearby, 15 and the Sabeans attacked and carried them off. They put the servants to the sword, and I am the only one who has escaped to tell you!”

It is clear from the story that Job possessed free will to respond as he chose. The wager between God and Satan concerned what Job would do with his free will.

I somewhat doubt that you really feel that evil is just one side of a coin, when it happens to you.

The universe is not infinite. Finite space, finite time, finite matter and energy.

You’re asking questions about the theology of civilizations that you imagine might exist. Sounds entirely like speculation to me. If you’re going to indulge in that, then you should at least allow God, in his relationship to that civilization, to be at least as imaginative as you are.

• mostafa مصطفی says:

dear perry hello
i strongly advised to you to read deeply islam-shia imams lectures you can find great things that you have never heard before from anyone else

search and enter to those sites that their owners are Iranians

a little example

there are about 2000 signs of “The end time” i mean arriving of Jesus and twelve imam pbuth…

and now you can see about more that 1990 of them dramatically are already happened…

there are thousands of really wise lessons about anything and about god are there in theirs lectures

6. yanniru says:

Perry,

I believe that this following statement of yours is an incorrect characterization of Godel’s Incompleteness theorems:
” Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few unprovable assumptions.”

Assumptions or axioms are not meant to be provable. They are part, in fact the foundation, of any system of mathematics. I’ll quote from Wkik for what Godel did prove:
“any consistent computable formal theory which can prove some arithmetic truths cannot prove all arithmetic truths” of that theory. Therefore
“a complete and consistent set of axioms for all of mathematics is impossible”

• I am aware that axioms are not provable. The positivists thought they would be able to prove them, Gödel proved that some truths would never be provable.

This is fully equivalent to saying ”Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few unprovable assumptions.”

• yanniru says:

No that’s not equivalent. I am amused that you think so.
Every system rest on axioms.
That is not what Godel proved.
Richard

• yanniru says:

So this is how you Perry deal with comments that you are unable to respond to. You just refuse to moderate them.

• Comments that require thoughtful answers take longer. Will get to them.

7. yanniru says:

The essence of your Godel argument is not changed by my comment on the axioms of systems of mathematics. There still are mathematical truths in any system that cannot be deduced from its axioms. Penrose thinks that may be the basis of consciousness, for example. Is that what you mean by “a system” in reference to the Compact Manifold of string theory?

• I think Penrose could be right. It still appears to me though that a Compact Manifold consists of component parts and is therefore a system, therefore is incomplete.

• yanniru says:

Perry,

Does not that just say that the Compact Manifold could be conscious according to Penrose? Are you saying that God is complete and therefore not a system?

I hope you believe that God is conscious.

Anyway, that is beside my original point that you should edit your discussion of Godel’s Incompleteness Theorems and remove statement : ” Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few unprovable assumptions.” which has nothing to do with what Godel proved.
Richard

• Logically, The only thing something can be complete and consistent is to not be a system. God is complete, and therefore not a system.

Gödel proved that any system that is consistent is incomplete (therefore rests on an unprovable assumption) or else if it is complete it is inconsistent.

So if the universe is logical, God has to exist.

8. andrewnjeru says:

Here is my take on God and Trinity.

Its important to relaise that logi and dediction alone cannot lead us to the truth especially If we close our minds to the ‘black swans’ observed in history.

What of Trinity
A very provoking pencil-inscribed graffiti fades on the inside of a washroom door in a Christian Church somewhere a few meters from the city center; It goes, ’..Did God have to die? Was He enjoying us?…’ Wa He alittle insane?

I cannot help but speculate that this is a sincere mind of a hungry soul hungry for truth, unsatisfied with the answers he got ( I am almost certain that it’s a He for the inscription is in the gents washroom) This is a mind that reflects on this issue like a babe and is bold enough to get out of the closet and confront the issue.
I keep reminding myself of the need to focus on the Truth, This is the TRUTH; all else may change, The Heaven and Earth may pass away but His Word will by no means pass; We may sacrifice all our beliefs and doctrines but this one, the Word. It is and must be the rock upon which we return amid the turbulent waters. For it is the ultimate truth. Even the Einstein’s laws of relativity cannot stand it, for the word is light; Light is light, it is not darkness to one and light to another; LIGHT IS.
I find it fitting to remind myself of the immutable truths about the God; There is God the Father, the Holy spirit and God the Son.
Using my feeble mind I am not in a position to fully comprehend the nature of God, But I know this , that the almighty God is eternal ,immortal, infallible, omnipotent, not subject to anyone, or any force on this earth or anywhere in the universe, doesn’t need to please anyone;
Almighty God is the only one who is Good, Jesus acknowledged this when the rich young man called Jesus ‘good teacher’, and he corrected him on the spot. See mark 10:18

Trinity describes God and expounds on his nature: Is it common knowledge that the seven letter word ‘trinity’ is not in the Bible? Whether is common knowledge or not, it is the blunt truth. But then where did it come from?
Henry Chardwick in his book on the ‘History of the early church’ puts the early church into proper context. He gives the background of the time at which the issue of the trinity is supposedly to have been decided on, the council of Nicaea presided over by the pagan, Constantine the emperor of Roman empire;
The council of Nicaea was attended by 220 bishops almost all Greek only four came from the Latin west part apart from Hosious of Cordova, and two roman presbyters sent by Pope Silvester. The creed proposed for adoption had a concluding anathema that condemned the proposition that the son is metaphysically (spiritually) inferior to the Father. Henry observes although only two voted against the creed, that it was clear that the terms of the creed were not understood in a precisely identical sense by all the signatories. The creed declared that the Father and the Son are the ‘same’ But this was ambiguous; To some it meant a much broader , generic identity;

Whatever their conclusions would have been, should I just take their verdict as if it’s the TRUTH. These 220 bishops are simply defining Jesus; why don’t I just listen to Jesus’ own Word about himself? In fact the exact word the bishops used has been in controversy ever since, a controversy over a greek letter ‘iota’. We do have an english saying, to state how original some text is , its common for people to say that ‘I did not add or remove an iota’. For us to get the substance of the Son, we do not need to learn the greek language. Let’s look at the substance and the man Jesus in context.

I have quoted the verse where He stated that only God the father is good. Elsewhere, Matthew 24:36, Regarding that day of Jesus’s return to rescue his anointed ones, only the Father knows, even the son doesn’t know!

When asked whether he was the son of God by the Pharisees, remember that this was considered as blasphemous at John 10:34, in response, He quoted the book of psalms 82:6;’All of you are gods all of you are sons of the most high!’ Looking up at John 10:30, He says that I and Father are one, a verse popularly quoted in support of trinity. But another verse just down says something similar to this one is in John 17:21, If we are in union with Jesus, He will be in union with us just as he is in union with God; are we then part of ‘trinity’? if we are then, trinity is not the right word, Should it not be some other name representing a union of more than three?

But where did the term Trinity come from? Let’s put the spread of christianity over the Roman in context. The way the Christian faith spread in the Roman empire after the persecution ended seems to cause concern; It suddenly became fashionable to become a Christian after decades of persecution in the wake of the death of Jesus. Numerous customs seem to coincide with practices of Christianity like Easter celebrations, Mary and Jesus as mother of god and the image of madonna, change of prayer days to Sunday as if it’s a celebration of sun god. The pinnacle is the parallels in the three entities of Godship of Christianity and other pagan practices. The rest we can only speculate;
Should I have a problem with trinity as a doctrine as defined by the catholic encyclopedia? I absolutely have no semantic problem with the term trinity if it were to represent the unity of God; Probably not, but when I consider the implications of the catholic encyclopedia’s definition of the doctrine of trinity to the other Abrahamaic faiths like the Judaism, and the Islam and of course Christianity I have no option but to push myself harder to ponder over the question:
Before I go further do we have sufficient proof that Jesus was, lived, and died, rose and now lives; This is fundamental to Christian faith, the only foundation for truth in this world. I have a classic proof, one that I can recount over and over again with so much confidence that I keep forgetting that I have talked about it. That of regrouping of the disciples after his ascension.
I look at the definition of trinity as given by the Catholic encyclopedia: it quotes a third century theologian St Gregory a miracle worker: It says in part that ‘..Therefore that father has never existed without the son nor the son without the spirit ..,’

If this trinity is true, what happened at the cross? I need not be scared; with Jesus at the foundation of the faith my faith is intact. One author said that when he ask these kind of questions, He got the answer that Hell is reserved for those who ask these kind of questions; Yet I seem to have lived in a bigger hell for failing to ask the questions and fearing those who ask me the same question for they all see to be sent by the devil;

I can bet that the question can linger in my mind without a satisfying answer and if I don’t get one very soon, an atheist will come and convince me that God does not exist; This is what Nietzsche Freud. , the philosopher did. He basically used the bible to prove that God dies not exist or that, sadly I have to say it, He claimed that God is dead How sad that is that we as Christians kill our faith using our interpretations of the bible and we claim that the atheism is our enemy, I believe that we Christians are the worst enemies of Christ. In spite of Jesus giving the obvious statements that defines himself, we still box ourselves and refuse to accept God’s word; Does Christ need enemies with friends like these? Clearly Jesus who is God died, not the Almighty God.

Looking at the God from the Old Testament we cannot comprehend that God dying for his creation. Indeed at one point the nation of Israel enraged God so much that God would have destroyed the stiff necked nation of Israel and rebuilt from scratch with Moses as the father. How would I expect him to die for the sinful nation? He first of all is omnipotent and immortal.
If you fancied your toy that you made, and you have the resources, time, money, skills knowhow and eternity to build another one, would you die for it? I speak as a man but I know that I cannot speak as a god! If it confuses me then it’s not from God, 1 cor 14:33, God is nor the author of confusion.

I believe this is the burden we got for disobedience, that we have to decide ourselves and separate the truth from the lie; The fact that God had opted to guide us, meant that it is not easy to make proper judgments; gladly his Word is immortalized in the Bible; Its spirit lives on. He loved us so much that he sent his only begotten son; If the three are equal Why doesn’t the bible say that the father is begotten? Could God have come instead of the son? Why refer to Jesus as the son?
The reference to Jesus as the son shouldn’t taste immoral, There is a tendency for most of us, as mortal men to think of a son as resulting from a sexual filthy relationship with a woman, a sinful Mary; Indeed modern scientific discoveries have almost convinced us that it almost possible to get a baby without the help of a man, a sperm; Just what God is capable of? He created the immense incomprehensible universe, How much more power doses he wield to just do what we cannot imagine or ever hope to understand? A virgin birth sounds like childplay!

These reflections are so important at diffusing the seemingly dreadful but lame attacks especially by one pope of the atheists going by the name of Richard Dawkins; His attacks are more of attacks on the institution of the church and not the Christ; The rock of ages remain as lofty and untouchable as ever, Jesus’s teachings with an indelible mark of originality, command, authenticity and originality. We wouldn’t need to define God at all. We need not paint his images to understand him, for our images of him can be as many as and diverse as our infinite power of imagination can allow us; They only tend to confuse the very honest hearted ones, serving as a stumbling block to faith in Christ: Isn’t this why the scripture says that He is the stumbling block to the Jews and to the Greeks?

How I wish that just a tenth of Christians could heed to the sermon of the mount, love thine neighbor, love thine enemy, Instead of attempting to define the Godship. We need not We wouldn’t have needed the bloody crusades of the Middle Ages to win converts in response there would have not been jihads to retaliate; recall that the Roman Empire bent on its knees to embrace Christianity after killing its leader, and after persecuting the sect for hundreds of years, all without the Christians having to use the sword. I so wish that the Church adopted the ‘Didache’ the teachings of the early apostles; In fact the Didache clearly prophesied the rot in the Church;

It’s only when the church embraced politics that it sounded the death knell of its commitment to Christ; Jesus refused to be crowned King; His kingdom is not of this world neither are his disciples are part of this world; For how can one define the foreign policy of a worldly nation based on the sermon of the mount where you go an extra mile with your enemy, if they attack your capital city, you give them fighter jets to do it better next time?

We should not underestimate the power of the ‘love thy enemy’ law. The Roman empire bent on its knees to embrace Christianity after overseeing the murder of its Leader Jesus in just a two hundred years. The Romans could not even put up with the sight of the Christians worshiping. The early christians were hunted like world animals, they used to meet at night so as not to attract attention and persecution. They were reviled as nocturnal worshippers and cannibals. Cannibals because of the symbolism of the wine and bread as the body and blood of christ for redemption.

Clearly his final law and commandment of Love thy enemy is powerful. It was the magnificence and wonder of the ultimate law of the universe that sent the Roman Empire to humble itself before Christ who it oversaw being crucified. No other law is above this;

The law of Love, breaks down all barriers of hatred, strife, rivalry bigotry, tribalism, racism; The law of love needs no courts except the court of conscience and that is its problem in that it cannot be adopted as guide for a world so hell bent on greed and self interest; It cannot operate in a world driven by self interest as the motive to help others. To me self interest the force behind all men do for the their neighbours, as defined by the economists, is the spirit of the devil; It’s is diametrically opposed to the spirit of Love, a spirit so embodied by nature, the splendor of the seemingly infinite universe, working so harmoniously to just quench our longings for eternity; Supplying humanity with all its need in all times and seasons in this little oasis called earth in a seeming desert of lifelessness. The nature is just a series of miracles, miracles happening every millisecond that passes, not just at the birth of the universe or birth of the earth, or at the birth of life or at increasing complexity of life;

It’s too awesome to think about let alone to comprehend, with a series of unexplainable miracles, miracles that only the blind cannot feel;
The fact the we cannot understand why some things happen, like death and disease should inspire us to have faith and hope in the eternal goodness and Love, Almighty God. For in the end all shall cease; the prophesies , the signs, the speaking in tongues, but these shall remain, Hope faith and Love. For there is no option wherever I go, this is the only option, Faith and hope in the Lord our God; I need no other argument I need no other plea, it is enough that Jesus died and that He died for me!

The rest are unnecessary details obstructing the meek , lowly and the childlike ones on the path to life; the life that was so desperately lost when man chose freedom from God, the ability to choose for ourselves what is best for us yet we have always chosen destruction and death; It looks like we haven’t the lessons yet and we are still challenging God and His ultimate law of love; How much time to we need to try it ourselves to see if we can make it on our own? Hadn’t God offered his fast hand help to guide the nation of Israel yet they always slipped back to mediocrity? If you are doubting read the book of Judges:

The longer the time we ask to try it ourselves the more our generous God offers to simply satisfy our ego, and pride that we can do it alone without him; He has eternity; Mighty nations have been humbled by individuals with no fighter jets or nuclear arsenals; Yet these nations spend more to fuel hatred by building arms stocks instead of building trust and love and sharing generously with neighbors; The surest way to keep a burglar is to share the prosperity with him; Its often said, forgive your enemy, nothing annoys them as much;

The enemy gets confused when kindness is the payoff for an unkind act.
for those who still doubt the efficacy of love as a force, ask the Romans, They accepted Christianity after persecuting Christ! IT still puzzles me a lot that I cannot just imagine that it happened within about 200 years; How forgetful a lot we are as human beings; The terrorized Christians, who by the way used to worship at night in hiding in fear of persecution, did not have to use the sword;

Their joy and contentment, their admired spirit of charity among themselves
caring for the needy among them; This won converts for Christ across the empire; Unfortunately it marked a turning point in the Christian faith for most of the problems Christianity as a faith has today are as a result of the images of God, the interpretations of scripture that emerged from this time onwards.
It concerns me when the masses troop in one direction and do so very fast especially in peace time; for then the choices made in such times are almost always the most distant from the truth however convincing they may seem at the time. Its when the truth seems so distant that its just staring at us in the face; We just need to turn our eye glasses, or eye mirrors, upside down and there we are; As confident in our faith in Christ as ever! The truth knocks us so hard that like Saul on his way to Damascus, by the time we wake up we can hardly see anything; We start relearning all over again; Everything seems so alive and real, God becomes so real that the very innuendos of atheism are no longer threatening but laughable stupid absurd comedy at its climax so laughable that we cannot help but blush if off with such aura of confidence that we no longer fear to hold the meek ones, the babes who have their doubts and lift them by giving them the confidence that their ground is as firm as ever. As firm as the foundation of the earth and of the universe;
For the wise and the intellectual, God will deal with those ones, He shall prove their wisdom to be foolishness; Just look at the mystery of the education too much about the same thing; humanity still making the same blunders made ages ago?

Mystery is a word we attach to what we cannot understand, we still don’t understand ourselves, all literature about ourselves and the nature around us is simply a mystery; There as many intellectual opinions about the same phenomena as there are double the number of intellectuals, professionalls always give at least two opinions at any given time… Using the all too familiar line.. on one hand and the add on the other hand,… since they have two hands each. All these literature is too much and conflicting that it ends up as a mystery: With the field of mathematics, any intellectual can prove anything you just need to settle at a number, a probability of being right; Scientists are mathematically wrong about the existence of this universe, or the existence of life, or existence of the earth, or existence of the brain, the eye; How much more likely and it is real that they are wrong about our future; Even the pope of the atheist could not have the guts to have a subject in his book and call it ’Why God is absolutely certainly not there’ The power of reason could not permit the title to remain in the book and I am almost certain that it was in his manuscripts.

May we all have the humility to submit to the greater Benevolent force that explains all these unexplainable series of miracles including the most crucial one, that of the risen Christ; and the humility should drive us to hope in him and recognize that this life is not just it, We hope and look forward to the fulfillment of our Lords Prayer;

9. BlindSight says:

Hi there,

There’s a very simple solution to this problem. Let me first say that I’m most certainly Christian and believe God created the universe, still exists, and is still active. The problem here, though, is that this Incompleteness Theorem refers to the scope of human knowledge, not to creation itself. Creation does not have to prove itself, it simply is; therefore, the Incompleteness Theorem states that we simply cannot know everything without something outside telling us the secrets. In order to know everything, we would have to ask God.

I’ll be hopping around your site debunking a few of your posts =P I hope you don’t mind. I’m glad you’re here and doing this, because we need more Christian thinkers, but I’m also a strict advocate of solid reasoning.

Best regards,
BlindSight

10. Oldstyle says:

Our mind cannot comprehend infinity

This blog is a scientific discussion that often seems to be far less than scientific reasoning and Perry allows the comments to come in even as the logic is flawed, never mind their lack of science. So, maybe my unscientific, and perhaps illogical, perceptions will be allowed past the gatekeeper.

Logical analysis, scientific or otherwise, always embraces a duality or, if one prefers, a dichotomy. And therefore, the logical discussion of a supreme intelligence, or God, cannot have the depth of perception required to understand the subject in the first place because the mind cannot comprehend infinity. The mind may speculate about infinity but it cannot know infinity because it approaches the subject from its finite and dualistic limitations.

We can stand on either side of this mental construct (intelligence or accidental universe) and put forth our logical perceptions and never manage to step outside of this dichotomy invented by our logical mind. It can only be an exercise, or a game we play, to speculate and flex our mental comprehension, but we will never come to know infinity from this exercise. That doesn’t mean the discussion has no value, but we could be honest with ourselves about reaching anything like proof. There is never a proof to the existence of a supreme intelligence from our mind or the logic our mind embraces.

Perry explains this through Gödel’s incompleteness theory, that is, if the universe is logical. But what if the universe is not logical?

If we are going to intelligently grasp infinity then we need to come from a place that can comprehend infinity, but it will not be from a mental postulate. A wise man said that the mind is an excellent servant but a poor master.

Many people have, and do, grasp infinity because their perceptions and intelligence comes from the heart. And nowhere have I been told that the mind is our only source of intelligence. We know with certainty those things that come from the heart while our mind can only provide some measure of confidence.

Take the story of King Solomon when he was approached by two women both claiming to be the mother of a baby and they awaited his decision on the matter. He did not seek a logical analysis to find the true mother when he suggested that the baby be cut in half and thusly shared by both. This wisdom and intelligence came from the heart and because of that it solved more than one possibility.

The woman that agreed to have the baby cut in half may have been the “real” mother, but not the true mother. King Solomon knew with intelligent certainty that the true mother would be revealed by a heartfelt response to his suggestion.

When we believe in a God or a supreme being then we have certainty, not just confidence, because our belief comes from the heart not the mind. I am not referring to a half hearted belief or a speculation based on what someone else of authority has said is true.

Having certainty does not require proof; what our 5 physical senses tell us does not require proof; what our heart felt emotions tell us do not require proof; but our logic may never be certain and thus it requires proof.

I enjoy reading Perry’s articles as they are a real stimulation for the logical mind, and from this I take what I like and leave the rest. Actually, there’s not much I leave behind although I don’t take it all to heart. As with any intellectual speculation it is a more ephemeral substance than what I hold close to my heart. Day by day my grasp of infinity grows in the same vein as the expression that “love is eternal.” I am a mere toddler in kindergarten but my heart soars with innocent curiosity about life that is embraceable and embedded with wisdom and intelligence.

11. daksh says:

if christ was a desendant of god or a preacher of god then what r we…….i dont think there is a disimilarity between us and the god………..god is nothing but all the things constituting the whole of universe or say multiverse ……the situation here is like this that we are doubting ourself.we all make up to form the whole of body of god.yes god exists till we can .””we”” means not u or i not the earth but the whole of universe or multiverse as u say… its better to realise the reality which in truth is an iluusion. but reality is nothing its just an illusion. of past of present and t will be of future also.

thanks

12. qilin says:

The incompleteness theorem says nothing at all about circles, it reads in the original:

Jedes hinreichend mächtige formale System ist entweder widersprüchlich oder unvollständig –

Any sufficiently powerful formal system is either contradictory or incomplete.

Philosophers don’t agree about whether that applies to arithmetic systems only
or to other kinds of systems also. Following my late teacher in formal logic
I tend to the latter side – and observe that any religious belief is a system, too –
it’s either contradictory, or it doesn’t cover all. That’s my conclusion from Gödel.

13. dmthurman says:

I”m a Religous naturalist Perry. This topic of Godel’s incompleteness theorm is of deep interest to me. When we look at the raw organism “Brain” is a mirror of who we are. So how we see this raw organism in it’s biological nature is how we see the world around us. THe current way we see it, is the same as we saw it in the 1800’s but slightly more complex. All efforts to model this organism haved failed because alternative “Models” have attempted to model based on perceptions. Godel’s theorm needs to be written here how do we see this oganism, as it percieves into the world, what is it’s limitations what does it percieve. So As far as I can tell this has never been done where the biological is brought into and harmonized with iti’s perceptions. As long as Godel’s theorm is not applied we play “Whac a mole” on an infinite field of perceptions into who we are. Godel attempted to do what you say and it killed him, in his ontological proof of God. That is circular logic. He needed to take his theorm and apply it directy to the organism brain and then his ontological proof would have shown that abstract is real, as concrete, that God is a brain function of deep importance. He was attempting to define his feet and that was his greatest mistake. The question then arrises are we God and that is to not fully understand Plotinus all is one. The word God is the Depth of the brains capabilitiy as it looks into the world for understanding. We have an infinite depth to us naturally, but we are not that depth itself. It always trancends our biological limitations as it is also a part of our biological nature at the same time.

14. dmthurman says:

Perry,
I also have posted Application of Godel into the observable in regards to the brain on my blog site if you care to read. It’s a rough draft and it’s probably not brilliantly done. But at some point This will be applied as I have done so at the brain itself. It will break the body/mind dualists that most often times manifest up in Religion as reductive materialists (Literal resurrection) and reductive materialists (Atheists). They both suffer from a body/mind duality perception given to us by Evolution. This illusion is meant to be broken not embraced. No control runs that deep.
http://religiousnaturalist.blogspot.com/

15. vYzion says:

Some corrections.

First of all…Gödel’s Incompleteness Theorems (that’s right…there were two of them) ARE widely accepted. What’s not widely accepted is their implications. Most people actually have no idea, or a VERY confused one, about what the theorems actually say, and therefore they draw all sorts of “unacceptable” consequences from their misguided interpretations.

Which brings me to the second point. The description given on this page sounds like the 2nd theorem. Only the second theorem (nor the first) says nothing about drawing circles (I know is is meant as a heuristic device, but it’s a bad one and gives a false picture of what’s really going on.) What the 2nd theorem ACTUALLY says, is that no consistent set of axioms (of a certain complexity, which I will address shortly) can prove the the consistency of the system itself (hence, Euclid’s axioms cannot prove themselves consistent, and there are infinitely many geometries don’t use all the postulates. In fact, Einstein CHOSE a non-Euclidean geometry for Relativity…but more this shortly as well). It says nothing at all about “truth.” In fact, the theorems are “proof-theoretic,” not “model-theoretic” (if you don’t know the difference between the two, you really shouldn’t be discussing Godel’s Theorems). The reason the circles give a bad picture of what’s going on, is because the Theorem does not guarantee that a given system CAN be proven consistent. It just says that IF it is consistent, then that information is not encoded in the axioms themselves, unless the axioms are inconsistent. In order for your “circles” to be useful, there would need to be some way of guaranteeing that there is something “outside the circle”, i.e., that there IS, in fact, a consistency proof. Which more or less amounts to guaranteeing that the system is consistent, from within the system…which is exactly what cannot be done. I have a feeling that it is this talk of circles that led to the induction confusion, which is completely unrelated to anything the Theorem actually talks about. In any case…Nothing whatsoever is said about truth.

Third: The first incompleteness theorem does talk about truth, but in a roundabout way. What the First Theorem says is that a sufficiently complex, EFFECTIVELY GENERATED theory cannot be BOTH complete and consistent. (I’ll leave it to the readers to look up “effectively generated”). What this would mean for your “unbounded circle” (i.e. complete circle…since it includes everything) is that it is inconsistent, which makes it useless as far as proofs are concerned.

In logic, all truths are DEFINED. WE decide which statements we will make true. Granted, we may decide based upon empirical facts (The sentence “This post written in German” will be FALSE), but at the end of the day, WE decide. One thing that the 1st Theorem does is show that there are some sentences within a theory that WE would want to be true, or that WE find true in some obvious sense, that have no proof IN THAT THEORY (Euclid’s parallel axiom is the most often cited example). In fact, it shows that there are infinitely many such sentences. So, the theorem places a wedge between logical proof and “truth” in an everyday sense.

Fourth. The terms “proof,” “truth,” “theory,” “complete,” “consistent,” etc. are technical terms that don’t quite line up with common usage. Without explaining what these terms mean to logicians, your encouraging a VERY skewed picture of things. First, it should be noted that “proof” and “truth” occupy different disciplines in logic (proof-theory and model-theory). Now, it’s true that Godel’s COMPLETENESS theorem (no, I didn’t mis-type, he also had a Completeness theorem) link the two together, but it is a FAR FROM TRIVIAL proof. Proof theory deals exclusively with syntax. A “proof” in logic is a finite string of wff’s that proceed according to rules of inference that generates some other wff from a given set (called the axioms). It has nothing whatsoever to do with meaning or truth. It is purely syntactic and mechanical. Just like what your web-browser does. Model-theory is semantic in nature. It’s the one that deals with truth and what the truth of certain wff’s means for the truth of others. A “theory” is simply a set of wff’s…nothing more. Some of the wff’s are just assigned to be true (axioms) and some are implied by the axioms. But there is not interpretation (i.e. meaning) involved…just symbols on a page.

I keep speaking of ‘sufficently complex.’ This has to do with completeness and consistency and the constraints placed on the Incompleteness Theorems. In logic (since the Theorems are proof-theoretic, I’ll only talk about proof theory…the terms mean something slightly different in model theory), if a system is consistent, that means there it is not possible to prove (see def. above) BOTH a wff and it’s negation (i.e. there is no proof of ‘P & ~P’). When Godel talks about completeness (yes, there is another kind of completeness in logic) he means negation-completeness. If theory (see def. above) is negation complete, that means that for any wff, A, of the system, either A or ~A is a theorem of the system.

In order for Godel’s Incompleteness Theorem to apply, the system must be sufficiently complex.” In order to qualify, it must meet the following criteria:

1) They must be effectively generated (i.e. recursively enumerable).
2) The must be consistent (since inconsistent theories prove everything)
3) They must be negation-complete.

If the formal language in question does not satisfy all these criteria, then Godel’s Theorems do not apply to it.

With that being said:
“The Universe” is not a system to which Godel’s Theorem applies. And even if it were, you’d still have the burden of showing it’s e.g., consistent. And don’t forget, that according the 2nd proof, that can only be done from outside “The Universe.” So, the only way you can apply legitimately Godel’s Theorem is to step outside the Universe, prove the Universe is consistent, then step back inside the Universe to find the unprovable truths. And even if you did that, it wouldn’t get you anywhere. Godel’s Theorems only say that a sufficiently complex system contains wff’s (sentences WITHIN the system) that are not provable from within the system. Thus, the unprovable sentences are sentences OF the system, they don’t say anything about stuff outside the system. (in fact, they don’t say anything at all…WE decide what things they will apply to) So, YOU can say that they should be applied to a Supreme Intelligence if you want, bit there is nothing about the sentences themselves that say anything like that (Hume’s “Dialogues” makes a similar point). And others are equally at liberty to make the sentences apply to whatever THEY want. Godel’s Theorems simply don’t say anything about MEANING. They only talk about uninterpreted strings of symbols…nothing more than markings on a page.

Also, it is highly questionable that natural languages fit all three of these conditions. At the very least, a proof is required to show that they do. A proof that the subset of natural languages used for such discourse is consistent, negation complete and effectively generated will do, however. Unfortunately, the prospects of this are pretty dim. In order to apply Godel’s Theorems, you’d have to show that there is a rule to be followed that will, given enough time, be able to list ANY statement about religion. Then you would need to show that all those statements are consistent. Good Luck with that.

Once again, respect your inter-disciplinary approach, but this is why you really need to engage actual academics in the fields you invoke, not just concerned bystanders. If you had ran any of this by a logician (an honest to God working in the field publishing papers in peer-reviewed journals), they would have told everything I said here today.

In my opinion, it’s epistemically, and to some degree, morally, irresponsible for one to make use of topics of which they don’t have at least an elementary knowledge. A good portion of Philosophy Undergraduates could have pointed out the flawed nature of this presentation on Godel’s Theorems.

In short, I’m afraid Godel’s Theorem is not going to help you any. It quite simply has nothing to do with the issues you’re trying to address.

• VYzion:

“circle” is an explanatory device that makes Gödel accessible to regular people. It’s appropriate because Gödel speaks of “within the theory” and “outside the theory.”

I cannot prove the universe is consistent. I can only point out that science assumes that it’s consistent and philosophers assume that reason and logic do apply to the universe. Without that assumption, all human belief systems unravel.

Yes, I am stepping outside the universe (do we not implicitly do that when we say “big bang” or contemplate what else might exist outside the universe?) and then yes, stepping inside to find unprovable truths. All the laws of physics are unprovable truths.

And yes, Gödel implies that the universe makes statements that cannot prove themselves. Isn’t this rather obvious to the naked eye?

If strings of symbols have objective meaning, then Gödel infers not merely proof models but truths.

We can make statements about God with mathematical symbols, we don’t need to use natural languages. Gödel did this with his ontological proof.

Thus I don’t see that you have demonstrated that Gödel has nothing to do with the issues I’m trying to address. If the universe is as mathematical as physicists assume, then Gödel’s theorem makes a statement about the universe.

• I wrote a paper on Anselm’s Ontological Argument during graduate work. It was only slightly more exhausting than reading all the comments in this thread. I waited to comment until someone mention ontologies. It has been a fascinating “evolution” since Anselm. Plantinga’s restructuring has provided what even many atheists consider to be an incontrovertible explanation of ‘God, Freedom, and Evil.’ I just found your site within the last week. I will be sure to return. The intersection of Theology, Philosophy, Computer Science, and Information Theory is not heavily populated and I am glad to connect with others on a similar journey. Best regards to all.

16. phillipheath says:

The only circle here seem to be the circular reasoning. Faith by it’s nature should not need to be proved. We all believe. Either we believe there is a God or we believe there isn’t a God. The briliance of faith is that there are equal amounts of evidence to both prove and disprove the existence of God. If you believe in God you will find proof of His existence all around you. You will see the wonder of life and experience miracles. If you do not believe in God you will find evidence all around you that He does not exist. You will be able to explain everything away. Faith is a choice like the decision to wear a blue shirt or a white shirt. Neither is right, neither is wrong. You have to choose the side you are on and then you will find all the evidence to support you. Choose wisely.

17. jonno says:

Dear Perry . . . .
Thank you for your lucid explanation and open forum on the EVOLUTION OF HUMANITY. For a life-long and in-depth study of this topic read the works of Dr Rudolf Steiner whose books and lectures are available from the Anthroposophical Society Library in all cities around the world.
http://www.rsarchive.org
1. Theosophy, An introduction to the super-sensible knowledge of the world and the destination of Man.
2. An Outline of Occult Science

Jonno

18. Eric says:

Perry,

I want to start by saying that I do believe in a creator who exist outside of the reality that we know around us. I am impressed with your proof that God exist, and it might be the best attempt I’ve ever read, although, I don’t think its quite a slam dunk “case closed” kind of proof, because it still relies on certain assumptions. But I am afraid that this is unfortunately the way it is, and perhaps always will be. Regardless, I admire your application of the brilliance of Godel in your argument.

What I don’t understand, however, is how a man who is heavily rooted in logic and common sense, such as yourself, can apply such rigorous and methodical logic in certain arguments, and then turn around and throw logic out the window at other times. When you make your arguments concerning Godel, your logic and application is very sound, and obviously well thought out. But then, you turn around and start quoting scripture, and you throw it all away. I believe in God; better yet, I believe in a Creator. (I emphasize the difference becasue the word God means the personification, which I dont agree with, so I say Creator). I absolutley agree with your argument that Creator exist, but also for other reasons that you have not mentioned here. However, I absolutley despise the religions of the world, especially the Big 3: Christianity, Judaism, and Islam. I was very much a fan of yours until I saw you start mindlessly quoting scripture. How could you be so rigorous with your logic and thinking, and then be so sloppy to start quoting scripture? I am so dissapointed.

Don’t you understand that (the Big 3) religions of the world have hijacked God from the people and infused the very concept with ridiculous stories, ironies, and flat-out lies. A man of your intellect must be aware of the problems with scriptures when compared to the world of reason. The world will overcome this problem though, so long as we don’t destroy ourselves before we get there. But every generation becomes less religious than the previous one. On a long enough timeline religions will fall to reason; I just wish that I could be alive to see it happen.

It is time for a new philosophy to replace the dogma of the old world. A philosophy where the Creator belongs to the free individual to discover on their own terms, free from the garbage that has been shoved down our throat for millenia.

• Eric,

I would like to suggest that quoting scripture is not as illogical as it seems to you right now. That’s a pretty big rabbit hole, but if you’ll give me the benefit of the doubt for a moment, consider the following:

1) YES religion has been abused in every imaginable way. Doesn’t mean Jesus was a charlatan. I have an entire website http://www.coffeehousetheology.com which is oriented around the abuse of religion as it stands in contrast to what Jesus actually said. I would encourage you to subscribe to the emails, read the articles and carefully consider everything that is said there.

2) See http://www.cosmicfingerprints.com/blog/genesis1 and carefully examine the logic there. I think there are good reasons to believe that the Judeo-Christian prophets did get it right.

Finally I would like to suggest to you that Christian theology is precisely an enterprise of squaring scripture with reason and logic. And that Jesus did teach a philosophy where the Creator belongs to the free individual to discover on their own terms, free from the garbage that has been shoved down our throat for millennia.

• yanniru says:

Michael D. Wolok wrote an interesting Knol on Everett’s Many World
Interpretation of QM a couple of years ago.

It in essence says that if the world is rational then the Many World theory
follows. Briefly, the Many World thesis claims that rather than quantum wave
collapse to a single reality, every possible superposition of quantum theory is
obtained in reality. This theory resolves every paradox of quantum theory and
makes quantum theory rigorous and logical; otherwise reality is whimsical, if
not random, and that may require a cosmic consciousness.

I think it’s the best argument for a cosmic consciousness
that I have ever heard.

But that is a dilemma for most scientists who neither accept the idea of a
cosmic consciousness nor an infinite number of worlds in a finite volume. I for
one suspect that some sort of a cosmic consciousness is required based on the single photon double-slit experiment. When a single photon passes through a double slit the location of its impact on the detector screen seems totally random. But as additional photons impact the screen, the interference pattern fills in rather uniformly as if the process had a memory of prior photon
impacts.

Just to be clear on what the Many World thesis says, when that first photon
impacts the detector screen, that is just one of the many possible worlds. At
that first detection there are also countless other detections in other worlds
across the entire screen. And that happens with every quantum event leading to
the rather accurate approximation that there is an infinite number of realities
in a finite volume if the world is rational.

I prefer to believe in a single reality and admit that nature may be whimsical,
which implies a cosmic consciousness or at least a cosmic memory. That speaks to a more personal god than just a creator god.
Richard

19. ron taylor says:

The Liar’s Paradox – ” I am lying ” – is not strictly a paradox because the person ” I ” must be referring to an unkown statement and thus makes the truth value of it obviously undecideable but not paradoxical . It has been reformulated in many ways to more certainly illustrate a genuine paradox . For example : 1) The next statement is false . 2) The previous statement is true .