Perry, it still looks to me as though several assumptions are being made. For instance, this topic is called “Godel’s Incompleteness Theorem”.

It’s not Godel’s Incompleteness LAW. It’s a theorem. So, even though it describes what we might not know about something else….the fact that it’s a theorem says that we can’t 100% know for sure that Godel’s perspective is right.

Take the first line: “Draw a circle around anything and you must go outside that circle to explain it.” That is certainly true with bicycles and gravity…..but just as you mentioned that the sun might NOT come up tomorrow (and that is taken on faith), it’s equally possible that Godel’s theorem doesn’t apply to everything.

For instance, you stated that — if we draw a circle around the Universe (or all the possible Universes) — “there has to be something outside that circle. Something which we have to assume but cannot prove”

That’s not necessarily true. We might not even need to assume it. It’s quite possible that drawing a circle around everything all the known universes would include a perfect explanation and provide a Single Unifying Law.

“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”. — Again, this is assumptive. How do you know that it cannot explain itself? This would only be a true statement if we actually had all the knowledge about the Universe (which we don’t).

“Whatever is outside the biggest circle is boundless.” There is nothing outside the circle. By any standard definition of “universe” or “universes”, if it exists, you’ve drawn a circle around it. It’s bad math to say “Draw a circle around all the known universes” and then to refer to something outside the universe. If there were something outside the circle, you would have drawn the circle to include it!

We can go on and on…but (with respect) this doesn’t seem to be a logical argument. It seems to be an argument based on certain presuppositions. And I’m not saying that’s good, bad, right or wrong….just that this argument has too many assumptions to conclude that there’s no possibility of a Unifying Theory.

Perry, I’m not making this an issue of “right” or “wrong”. It’s simply a matter of workability.

Draw a circle around all matter, energy, space and time and label it “Universe” and you cannot definitively say that it is dependent on something else outside it. You can speculate that it might be….but there is where the line is drawn between theorem and law.

Simply put, we don’t have enough information to say emphatically that Godel’s theorem is true. That’s why it’s a theorem. We can point to multiple ways that it IS true. But, it still makes its own assumptions in matters that cannot be observably demonstrated.

Thanks for the dialogue!

Tony

I agree with your logic, Perry (and Godel’s), thanks for sharing.

Any assumptions that are made when discussing where the universe came from seem to me to be related to the law of causality…anything that begins to exist has a cause. I think that’s a safe assumption.

Philosopher William Lane Craig puts it like this:

Premise 1): Anything that begins to exist has a cause.
Premise 2): The universe began to exist.
Conclusion: The Universe had a cause.

1) The ability of things popping into existence from nothing without a cause is not worth arguing.

2) Both science and philosophy support the idea that the universe had a beginning.

Therefore…it must have had a cause.

It doesn’t specifically point to the Christian God that I believe in, I have other reasons for that belief.

However, based on Godel and a finite universe I don’t think one can argue that the idea of a god of some sort is illogical.

What caused God? It’s not a coherent question. By definition God is eternal…uncaused…was always there, unlike the finite universe.

So “What caused God?” becomes “What caused the un-caused being?” Doesn’t make sense.

Always interested in this kind of discussion, though don’t usually have so much to say…thanks for posting!

Rod MacKenzie

Very interesting stuff.

This is a bit off topic but I find myself saying, “Yep; something must have created the universe”, but then the next thing that pops into mind is “so what”? Why do people go to such extraordinary lengths to ‘prove’ it to others (like you do Perry ? Even going as far as killing people.

How does that faith help us or impact our lives? Obviously the answer to that depends on each person’s concept of what the creator is, but to me it doesn’t help and shouldn’t make a bit of difference to how we behave.

Perry says:
‘You are invited to demonstrate a flaw in Gödel’s logic if you can. And I will certainly be happy to post that argument here on my blog.’

Well, it’s not that hard to point out the flaw in Godel’s argument. It isn’t something that can be put into a few lines, but you can see it here:
http://jamesrmeyer.com/godel_flaw.html

and in simplified form, together with a simplified explanation of Godel’s proof here:
http://jamesrmeyer.com/ffgit/GodelSimplified0.html

I am a mathematician, and I can tell you for sure that you have a basic misunderstanding of what the theory of everything is; the theory of everything is a grand unifying field theory. It has nothing to do with having a system that is entirely self contained, but rather a system that can describe the fundamental forces simply. Your assumption that a conscious being must be the external observer seems kind of ridiculous to me, and is a giant jump. You might as well be Descartes with his cogito ergo sum, ergo deus. What a ridiculous notion.

Perry,
I thoroughly enjoyed your article, and the mental, logical, and theological exercise it plays in. There’s nothing like hangin’ out with smart people to make you smarter.
So frankly, with all the smart people you attract, I’m surprised no one’s mentioned this…
Just as “I am lying” is a paradox, so is Godel’s theorem. All we need to do is draw a circle around all the things that Godel’s theorem applies to. Outside of that circle must be all the things that the theorem doesn’t apply to. Therefore, Godel’s theorem does not apply to all the things that Godel’s theorem applies to.
Oh! (smoke coming from my ears) My head hurts!
Is there a flaw in this application of Godel’s theorem?
-Mark

p.s. All my best wishes for a healthy, happy, giving and prosperous new year, Perry.

I loved the article until it stop being descriptive and tried to argument for the existence of god. You made some really big jumps there, pal.

I liked your approach to explaining the existence of god, but you have to be honest with yourself.
At least you are not the kind of christian who believes Jesus used to ride a velociraptor.

cheers!

It seems that you have grossly misunderstood Godel. There are actually two theorems.

Number 1:
“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,[1] but not provable in the theory (Kleene 1967, p. 250).”

Number 2
“For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.”

(Pulled from Wikipedia.)

These do not apply to all systems. They only apply to those that express arithmetic.

Wow, thought provoking post. It’s not often that I see proofs of Gods existence of such high quality. That said, I’m curious to know how your take on two points that didn’t quite jive for me.

First, does Godel’s Theorem apply to itself? Can it truly ever be proven, if it’s making assumptions that it can’t prove? If it can, then the theorem is proven useless, and if it can’t, then how can anything in the universe ever be proven? (If nothing can be proven, what evidence for a god could we have?)

Secondly, using the circle analogy, if there is something outside of the largest circle that it is possible to draw, then that something must be infinite. If it is infinite, then it is everywhere. If it is everywhere, how has evaded detection of scientists for so very long? If a creator is boundless, then science must have found evidence of its existence, and if not, it could be encompassed by a circle. Paradoxical…

Again, thanks for a well thought-out post.

Dire misunderstanding of Godel’s theorem. It was all going so well until you took the metaphor you’d constructed around the maths and tried to apply it to the universe. As another commenter has said, the theorem applies only to mathematical systems. Specifically those systems that are complex enough to derive arithmetic from.

The real “incompleteness” is that when working with the axioms of those specific formal systems, you will find there are either things that are true that you cannot prove, or things that are paradoxical that you can prove – the system is either incomplete or inconsistent.

You insist on saying that the universe must be a formal system for it to be described by science, the truth is that science describes the world _using_ various formally phrased “laws”, but the universe itself is the “outside of the circle” (outside of our descriptive system) to point to in this case.

Our formal systems don’t define the universe; they’re a best approximation to what we observe, and the self-justifying element at the foundation of it all is the bald fact of the way things are. Reality doesn’t derive from axioms, it just is what it is, and because of that it doesn’t in any sense match up to what the Incompleteness Theorem was about.

“Gödel’s theorem applies to everything that reason and logic apply to.”

No, I believe you’ll find that it applies strictly to axiomatic mathematical systems; “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”

So if you start with a set of mathematical axioms, and those axioms are sufficient to express arithmetic, then it is also true that your system is either incomplete (there are truths that it can’t prove) or it’s inconsistent (you can prove things that are contradictory).

Now say it with me, the universe is not an axiomatic system of mathematics. There are no axioms of the universe, and hence no logical derivation of other propositions from the universe and no Incompleteness.

Empirical derivation of propositions, maybe (although that’ll run the risk of simple observational error), but I can’t repeat enough; the universe is not a system of formal logic. Further, it has no need to prove itself by formal logic – the universe just is. Its nature is a simple fact, that to some extent we observe.

I also take issue with your talk of “The origin of information”. The genetic ‘code’ is not symbolic and immaterial, it’s carbon-based chemistry. Not even very complicated chemistry to be honest. You claim that ‘information’ had to come from the ‘outside’, which seems to miss the fact that randomly combined nucleotides have just as much genetic information in them as the same length of useful DNA. The only difference is that genetic material that is conducive to its own replication will do just that, replicating more than other such material until it dominates.

“All codes we know the origin of are designed by conscious beings” is a barely concealed circular argument. It fails on the count that genes are not real codes (they are molecules – talk of information being coded into them is a convenient shorthand for talking about their chemical properties) and even if I let that pass, it fails on the second count that you use the assumption of all codes being consciously designed to argue that a specific code is consciously designed without any further evidence for your position.

“Naturalism is the hypothesis that the natural world is a closed system, which means that nothing that is not part of the natural world affects it. If you know Gödel’s theorem, you know that all systems must rely on something outside the system. [..] Because the universe is a system, it has an outside cause.”

Once again, the natural world is not an axiomatic system, and hence not something that Godel’s theorem is applicable to.

“Any system of logic (boolean algebra for example) is always definable in terms of axiomatic mathematical systems.” Agreed, but I don’t see the relevance.

“You are free to reject the idea that axiomatic mathematical systems accurately model the universe.” I didn’t, I rejected the idea that the universe itself is an axiomatic mathematical system.

To put it in your terms, the reason we can model the universe with logical systems is that we have an actual universe “outside of the circle” to “point to”. (Quotations used to express the fact that I dislike the terminology; it’s an oversimplification of the theorem and makes it too easy to misapply it)

The universe as we know it acts as the ultimate axiom – if the model contradicts the universe, we know the model is wrong. It may be that some physical ‘laws’ that we think are true turn out to be incomplete or inconsistent in their description of the universe, but that means we need an improved model, not that the universe needs some external factor to be explained.

As for genetic codes, it’s as I’ve said; even if I accept that it is a true code, you don’t have a valid argument. Saying that all known codes have a conscious origin, and that therefore a specific code has a conscious origin, is specious reasoning. To prove that all codes have conscious origin would require you to prove that genes have a conscious origin, which you have not done.

I can accept Yockey’s assertion that “the origin of life is the founding axiom of biology” — biology being the study of life it doesn’t make a great deal of sense to talk about pre-biotic biology.

Pre-biotic chemistry is another matter though; chemistry and physics do not depend in any sense on the existence or origins of life, and we can very usefully study the precursors of life in the form of non-living organic chemistry, and theorise on how such chemicals might become self-replicating and come to form something we recognise as living.

“The relevance of my first comment is that Gödel’s theorem applies to all things that are defined as systems.”

Mathematical systems and logical systems that are equivalent to mathematical systems, yes. I have never denied this. But the universe is neither; it’s a physical system. It doesn’t derive from axioms, it can’t be used to derive propositions, it doesn’t fit the bill.

The closest you can come to ‘deriving a proposition’ from the universe is to observe its behaviour and formulate a mathematical statement to describe that behaviour. Maybe the model is subject to Incompleteness but, as you’ve said, that just means it needs something outside of the model to serve as an unproven given. The thing outside the model is the universe’s actual observed behaviour. We can take that as an absolute axiom with respect to what our models should predict.

“But if math does accurately describe the universe, then the universe is just as axiomatic as the math that describes it.”

The model has, as far as we know, been accurate up until now. I don’t take that as absolute/unshakeable proof that the universe will always be consistent with our predictions. If the two things diverge we’ll need to come up with a new model because they remain two different things. Using an axiomatic model to describe a thing, however accurately, doesn’t make that thing, itself, axiomatic.

“The universe cannot be the ultimate axiom if you believe in cause and effect. The universe came into existence 13.7 billion years ago. Something had to cause it.”

I’ll take this seriously when you can convince me that a) your god doesn’t equally require a cause and that b) the universe (or some n-dimensional ‘higher’ universe) can’t be self originating in the same way as you propose that god is. If you’re going to restate the Cosmological argument, I feel quite happy using the age old objections to it. (If you manage the first one, you’ll still need to prove that your first cause has any attribute other than uncausedness. I know you think you’ve done that, you even put it bold, but that’s a whole other argument to have).

You don’t appear to have fully comprehended my point on the subject of “all known codes have conscious origin, therefore a specific code has conscious origin”. There’s no denying that the former implies the latter, but your argument is backwards – to boldly assert something about “all codes” you first need to prove that thing true of each specific code without reference to anything being true of “all codes”.

To put it shortly, “all known codes have conscious origin” is dependent on each specific code having conscious origin, so when you introduce “all known codes have conscious origin” to your argument about a specific code, you’re implicitly assuming that which you’re trying to prove. It’s not “straightforward inductive reasoning” at all, just partially obscured circular reasoning.

As a sidenote, I’m curious; why is a piece about Godel’s Incompleteness Theorem on a site that’s otherwise about Google-based marketing?

You don’t have to prove scientifically that god exists. You can just be faithful, its a more gracious way of being a believer than trying to push your opinions in a semi-literate way to everyone else…

I recommend Soren Kierkegaard.
Something out of context: ” Thus, faith is united with the truth by serving as the most extreme expression of subjectivity, and by representing the only manner in which the existing individual can accept paradox.”

http://www.schoolbytes.com/summary.php?disp=term&id=234
Check this site, i haven’t read it all, but it could be helpful to everyone like you. In some way, a more complex way you’re trying to do what every silly creationist tries to do in a more naive way, that is, trying to push a belief into science.

Sorry for the errors, english is not my first language.

I think you are putting god outside the circle boundary everything that is real;)

“My reasoning is not circular. It begins with an open question of not knowing where the genetic code came from and observing closely how all other codes came into being.”

Allow me to analogise for a moment. Imagine I were to examine all of the cats I could lay my hands on, I would find that to an animal they would all have tails. I might hence conclude that all known cats have tails, and thus that I believe all cats to have tails.

Then someone presents me with a Manx cat, to which my response is that we already know that all known cats have tails, so this cat must also have a tail. I think you are committing the same flaw of reasoning; hasty generalisation.

All human designed codes have conscious design. That much is tautologically obvious. The other class of ‘codes’ we have are those in the natural world. We know of no designer for these things, and it is faulty reasoning to conclude that because “all known codes” (excluding the natural ones under consideration) have conscious design, that the codes of the natural world must also have conscious design.

I submit, that the codes of the natural world, be they genetic, bee waggles, or any other, are the results of what I will term unconscious design. Brought into being by blind processes with no intent, no thought, no goal and no consciousness.

I’m talking about, of course, evolutionary processes. Amino acids form spontaneously under a variety of conditions, RNA strands have been found to assemble, using cyanide or the checker-board patterns of charge in ice as a template. RNA is also known to be potentially self-catalysing, and self-replicating. Once we have replication (and mutation via faults in replication), we have evolution. Some RNAs go on to produce proteins and DNA, which turn out to be advantageous because they can improve the process of replication and help the RNA that produces them to dominate the available resources.

That path may be hopelessly wrong; we may later find the evidence that shows it happened a different way, I entirely accept that possibility. But at the same time, having any plausible explanation that fits within the natural world without any awkward ‘nomological danglers’ hanging out is infinitely preferable to resorting to the supernatural as an ‘explanation’, because it does not really explain anything at all – no predictions to be made, no evidence to be found, no proof or disproof except the incredulous cries of “well how else could it happen”.

In your other article you dismiss out of hand the idea of naturally occurring codes, without any reasoning presented beyond … well, actually I don’t see any reasoning except stating your position again in slightly different ways; “Chaos can produce patterns, but it has never been shown to produce codes or symbols.” is another example of your circularity – assuming the general case as a way to prove the specific case, when the general case is dependent on the specific case. Maybe chaos has been shown to produce a code, in the instance of naturally occurring codes. Nothing you can say about “all codes” can rule that out.

[Sidenote: I would take exception to natural selection being characterised as chaotic; mutation is the only random step, everything beyond that is much more deterministic, except for true accidents of nature like the first carrier of a novel allele having the misfortune to be hit by a meteor or some such]

If you could prove to me, without any reference to “all other codes” or other generalisations that are dependent on the specific cases, that DNA as an information carrying molecule could not possibly arise by natural processes, then I would be most impressed. (Note also, that stating “Information itself is a separate entity on par with matter and energy” as a premise, without some very strong supporting evidence for that extraordinary claim, will not get you very far).

It’s late, I’m tired, but reply to this and the email notification will remind me to come back and say more about the universe as opposed to DNA.

Also, DNA is described as a code, but is certainly not DEFINED as a code. Similar to the way many people call every bit of music “songs.” It’s a convenient way to be understood, but it’s not the most accurate.

you are using a theorem within a system to explain something beyond the system. whut

using something we know to describe something which we cannot know is just faith. you jump from logic to faith when you use the incompleteness theorem to make a logical induction about something beyond “everything”. you “believe” that it applies to something beyond “everything”.

in other words: beyond the scope of the universe you cannot with certainty apply knowledge that is within the universe (otherwise it would be describable by the universe and therefore part of it)

what youre saying is that the same rules of logic that apply within the universe apply outside the universe. you cant say this with certainty. the applicability of the theorem ends with the “edge of the universe” because it is based on logic of the universe.

in short:The universe and not the universe are not the same. “Universal” logic cant apply to outside the universe by definition

Dear Perry,

Thank you for the interesting read on Goedel.
May I refer a small comment to your statement:

“In 1931 this young Austrian mathematician, Kurt Godel,
published a paper that once and for all PROVED that a single
Theory Of Everything is actually impossible.”

To my understanding Goedels incompleteness theorem can be
stated in simple english as:

A formal system of sufficient complexity is either
or .

I assume your above statement refers only to a contradiction-free systems,
which is indeed incomplete according to Goedel. Am I correct?

Well, my comment is the following:

If you consider for a moment a contradictive system with the potential of completeness,
would this not possibly allow the existence of a theory of everything? Of course
such a theory would then include contradicitve statements…

Here I do not want to think about such a contradictive system or discuss its
usefullness. But refering to your above statement I would like to mention,
that in my understanding of Goedel, there is the possibility of a single Theory Of Everything.
Even so it would (according to Goedel) necessarily include contradictive statements.

I might be missing a point
or miss-understanding Goedel, but at least I do see this possibility of a contradictive theory.
However I admit, that it might be never understandable by the human mind, because of its
contradictions. Would be nice, if you could let me know your opinion on this comment.

Thanks & Best regards,

Starbucks

So this is still sending me reminders… which is sort of useful; I’d forgotten about it. I wanted to jump back into the fray to say that you appear, once again, to be conflating the universe with our model of the universe.

Let’s say I accept your premises (you know I don’t, but for the sake of argument) then the conclusion is that if we came up with a Grand Unified Theory, that described all the behaviour of the universe (was complete), then it would also be possible to derive a contradiction from that model, i.e. model a situation where our one model can be used to predict two (or more) mutually exclusive events.

That is very much like self-referential statements like “This statement is false”, which tells you that the statement is both false and true at the same time depending on whether you take it at face value or think it through some more, and many other “paradoxes” where you look at it one way to get one result and then think through another line of logic to get a different, contradictory result.

The difference with a model of the universe is that we can go and determine by experiment which of the contradictory results is the right one. The model may have included a contradiction as an artifact of being made complete, but we still have an external reference to go to – empirical observation of what really happens.

I think I’m beginning to see that this is a little like the Cosmological Argument, dressed up for a new era in some slightly dodgy application of mathematics. If you’d allow me to paraphrase; “All systems must have something external to themselves, and an infinite regress of systems is impossible, therefore there must be a super-system with no external factors, and this all men call god”

It’s a nice variation on the old ‘first cause’ or ‘unmoved mover’ arguments, but with the one tiny flaw that the universe is not a system of logical propositions. Godel said nothing about physical systems, and there’s nothing to stop a physical system (such as a universe) being self contained.

Now I’ve been writing too long and made myself miss breakfast… must be off.

Your logic is very close to flawless. I very much liked this article, and honestly, impressed.

However, I do have an issue. I haven’t checked on the formal proof of the theorem yet, but I’ll take your word for it. You have an unwarranted assumption in your argument.

You assumed that whatever is outside the universe is boundless, and that is the assumption. If the universe is explained by something outside of itself, then that thing is also explained by something outside of itself, and this process would never stop, and we have an infinite amount of causes, and not one single cause. You have no clue or proof that suggests that we should assume whatever caused the universe cannot have a circle drawn around it. If the universe is any clue, circles will be drawn infinitely. Maybe the universe is part of a finite multi-verse that is part of a multi-multi-verse ad infinitum.

In summary: You proved that every ring of the chain needs a ring ahead of it, but then you assumed the chain we’re connected to is infinite, which is in no way a given. Looking at the ring we are, I say it is more likely that this chain is simply infinitely long, with finite rings.

Perry,

Having done a rather extensive amount of research on the subject and having discussed the matter both with mathematicians and philosophers, the concensus is that you’ve extrapolated to beyond what Godel was doing in the first place.

His First Incompleteness Theorem stated “Any adequate axiomatizable theory is incomplete. In particular, the sentence ‘This sentence is not provable.’ is true but not provable in the theory.

What he discovered and formalized was –

For any sentence s,
(1) is in PROVABLE iff s is provable.
Since the set of axioms is computably generable,
so is the set of proofs which use these axioms and
so is the set of provable theorems and hence
so is PROVABLE, the set of encodings of provable theorems.
Since computable implies definable in adequate theories, PROVABLE is definable.

Let s be the sentece “This sentence is unprovable”.
By Tarski (Undefinability of Truth Theroem), s exists since it is the solution of:

(2) s iff is not in PROVABLE
Thus
(3) s iff is not in PROVABLE iff s is not provable.

Now s is either true or false.
If s is false, then by (3), s is provable
This is impossible since provable sentences are true.
Thus s is true.
Thus by (3), s is not provable.
Hence s is true but unprovable.

Godel discovered that the sentence “This sentence is unprovable” was provably equivalent to the sentence:

CON: “There is no with both and in PROVABLE”.

CON is the formal statement that the system is consistent.
Since s was not provable, and since s and CON are equivalent, CON is not provable.

Thus –

Godel’s SECOND Incompleteness Theorem:

In any consistent axiomatizable theory (axiomatizable means the axioms can be computably generated) which can encode sequences of numbers (and thus the syntactic notions of “formula”, “sentence”, “proof”) the consistency of the system is not provable in the system.

The theories of real numbers, of complex numbers, and of Euclidean geometry do have complete axiomatizations. Hence THESE THEORIES HAVE NO TRUE BUT UNPROVABLE SENTENCES. The reason they escape the conclusion of the first incompleteness theorm is their inadequacy, they can’t encode and computably deal with finite sequences.

So… it’s a mischaracterisation AT BEST to try to use Godel’s theorem to extropolate the existence of god because, if math and science is correct, which we have every reason to believe, our universe HAS NO TRUE BUT UNPROVABLE FACTS. The notion of science is that at some point, everything is explicable.

And scene.

I think a significant problem with this discussion so far has been an ambiguity with the language used, which has meant a bit of back and forth with no real change in the arguments. There have also been some misunderstandings of Gödel’s theorem, which is understandable, as unless you have studied mathematics, analogies tend to obscure the strict meaning of it.
Firstly we can agree that a non self-referential statement is either exactly true, or not exactly true. Secondly Gödel’s theorem refers to a set of statements, split into two groups, those we label “axioms”, and statements derived from those. The theorem essentially states that if the “axioms”, which are the statements we assume to be true, are true, then there are also other true statements that cannot be derived from those axioms, and that those axioms cannot be proven to be true without the addition of a new axiom. The corollary is that if a proof of the truth of the axioms is derived from the axioms, then the axioms are not true (in their entirety). I’m going to use a bit of an analogy for this next part, if you can forgive me for that, as I personally find analogies highly dubious. In mathematics sequences of numbers can be of particular interest, and these can be generated through formulae, or can exist independent of any formulae. Now what is particularly interesting is that for any finite sequence there are an infinite number of different formulae that can generate the same sequence, so when attempting to find the formula for generating a sequence you may have found one that matches all available data, yet not be the correct one. I guess that wasn’t particularly an analogy so much as a cut-down version of universal laws, however that is not the point I am aiming to make. Within this analogy the universe is the sequence of numbers, the formulae which determines it’s behaviour are the laws of the universe, and our estimation of the formulae are our current laws of physics. Now the point that Matt was making, and perhaps you misunderstood, is that the sequence of numbers, and the formulae are different things, he was not arguing that Gödel’s theorem did not apply, merely reminding you that it only applies to sets of statements i.e. the formulae, not the sequence, the laws of the universe, not the universe itself. He is not arguing against logic, merely stating that you have applied it in the incorrect place. Now as it happens I am an atheist, I believe that there is no God, however I am not so presumptuous as to claim it as a certainty, indeed I do not believe it is possible to know whether or not there is a God. I am merely arguing that this particular path of logic is invalid.
With regards to causality, it can be broken down fairly simply, either everything requires a cause, in which case a being without cause does not exist by definition(granted this does not forbid a being with a cause which created the universe from existing), or not everything requires a cause, in which case the universe does not demand the existence of a God without cause(although one is possible). With regards as to codes, we really need to clarify what you exactly mean here in your argument, as if you define a code to be a message intended to send information, then all codes are the work of sentient minds merely by definition.

Sorry but ‘god’ must also have something ‘outside its circle’

Godel proved that you cannot have a god which explains himself.

Atheism also says that.

NOTHING can understand it all. God CANNOT exist.

Yea, so I have no problem with your logic in saying that “god” exists, but I do have a problem with the assumption that this god is the christian god. Every logical proof of “god” simply defines god as something undefinable. That does not, in any way, mean that the christian god is the god that created the universe. Religion is made up to answer unanswerable questions (or at least unanswerable at the time of its inception) and as a means of social control, and to give hope, and meaning and blah blah blah.

Also, almost every response you’ve made to people goes along the lines of, “If you think that, you obviously reject science and are an idiot.” Not very classy….

But, yeah, christians are illogical for saying the god of the bible is the god that started the universe. The only conclusion you can come to is that something must have started the universe, assuming Goedels theorem applies (which, as has been stated, really doesn’t apply to the universe, go ahead and tel me I’m an idiot for saying that, it’s fine).

Also, I would like to question, what is the significance of all of this? Does if affect anybody in anyway? I really don’t think it does. I’m just bored and want to get into this heated discussion, heh.

I’m sorry for my choppy/poorly thought out comment. ADD is not my friend this night.

Interesting article, but Matt did a very effective job of demonstrating that the universe is a physical, actual system, not reliant upon abstract axioms to prove its existence.

Sorry, but Matt is very clearly better informed on this issue. The language of the article oversimplifies the theorem so as to allow the author’s worldview to seem better justified. The comments made a nice read, though.

I haven’t read all the replies above so I am probably repeating some people but below are the flaws or premises that I disagree with in your argument.

1) You define God as what is outside the largest circle. As the number of circles is infinite it is meaningless to talk about the largest circle. Gödel’s theorem suggests that all things depend on something else, if a god exists and is subject to our laws of mathematics then it is no exception, therefore by use of modus tollens if a god is subject to our mathematics then it must be dependent on something else to exist.

The existence of a god is not necessary to explain how something can be true despite depending on an infinite chain of assumptions. It is clearly wrong to say that because each natural number requires you to assume that there exists a larger natural number that there must be a god that is larger than the largest natural number. The natural numbers and, if Gödel’s theorem is true, the ever increasing circles that depend upon things they do not contain are infinite

2) All codes must come from a conscious being. You are using a double meaning of the word code, its normal meaning is a message from one conscious being to another that has be altered to make it difficult for those who are not its intended reader to understand. DNA is referred to as a code because it contains information that is difficult to understand, the same could be said of many things that do not originate from a conscious being, pulsars (rotating neutron stars) are a simple example, we receive from them a brief burst of radiation which we can decode to gain information about the star.

3) A being can be conscious, boundless and without cause. To me conscious seems to cause problems when combined with the following properties; if something is conscious then it is aware of itself, if it is boundless then there is an infinite amount of itself that it has to be aware of, information from its farthest edges would have to travel with infinite speed to cover an infinite distance in finite time. If it is without cause then it must have existed forever, over an infinite quantity of time a conscious being would go through an infinite amount of thoughts and would end up unable to think anything new and robotically repeat through previous states, this is not a contradiction but is probably not how most would think of a god. The same problem occurs with an omniscient god as if truly omniscient it would know in advance what it was going to think and do and at the correct time would think and perform those actions like a robot.

4) In what little of the comments you mention the Holy Trinity so I shall assume you are referring to the Christian God. This is where your argument really falls to pieces, you go from trying to prove the existence of a potential creator to the existence of three very specific Gods. There is nothing in your debate on Gödel that applies to the Christian Gods and could not apply to Ra the ancient Egyptian Sun God or to the thousands of gods that humanity has worshiped throughout history, or to any of the millions that I could invent, name and create a back-story for right now. Assuming that all other points I have made are false and your argument is sound you have still proved nothing other than a vague conscious being outside our universe that somehow proves some things in our universe to be true.

Finally I would like to thank you for the excellent quality of the first part of you argument, it is one of the best explanations of Gödel’s theorem I have ever read, I apologize for the length of this piece but may add more if I think of anything else.

The “unknown” agent outside the circle always somehow seems to point to one’s favorite religion or metaphysics (the immaterial vs. material). The true incompleteness perhaps lies in the symbolic, linear conceptions human understanding is stuck with. This theorem FALSIFIES it does not give positive verification to speculations or personal convictions. It is much too easy and sloppy to interpret the limits of understanding as reflected by our greatest proofs as an excuse for thought termination and to fill in the cosmology of the unknown and unreachable with all too human answers.

As for “code” the human mind has a tendency to see patterns everywhere, even in vacuum energy. Using this as proof of supernatural intelligence (since these things are everywhere in the universe) violates the very theorem you are misusing (the circle would prove itself). Intelligence is itself recognized through quite finite and definable parameters that are always experienced well within the circle. If human intelligence and the tragic world of crude matter and its pointless replication and destruction are really some positive indication of what lies beyond, a perfect God would have to be exchanged for a perfect monster, which would have to “inductively determine” from the very cruelty of nature. A cruelty, by the way, which intelligence only seems to make MORE insanely devious, not less. God should do us a favor therefore, to remain an Impersonality.

Perry,
We think your main misinterpretation is that you believe Gödel’s theorem applies to the physical universe. You say, basically, that Godel’s theorem applies to science because science is made of logic. Therefore, science is either incomplete or inconsistent. We agree. But because humanity can change what it believes, science adapts to evidence to remain consistent. This leaves only the possibility that science is incomplete. We think you will agree with this.

But you then say that Godel’s theorem applies to the Universe and/or Multiverse, because it can be described by science. Wait, didn’t We just say that science is incomplete? That would mean that science does not fully describe the Universe/Multiverse, and therefore is in some way wrong. So Godel’s theorem cannot apply to the universe, because we do not actually know it is a system. Even if we did, we would not know it’s limits.

Additionally, Godel’s theory could be applied to itself if we use your ‘put something in a circle’ interpretation, which is wrong anyway. If we did this, it would prove itself wrong, meaning you entire argument is, in fact, invalid.

If you draw the biggest circle around everything, you’re not leaving anything outside, you have from the explainable to the unexplainable inside, it doesn’t matter if it can be explained or not, everything is inside thus there will be no need for outside reference.
What this theorem seems to do is first to expose some really good logic, it certainly is right in smaller scales and/or when using the adequate example (the bike for instance), once it has proved that this reasoning can work it proceeds to use the same statement with everything else, assuming that if it worked there it must always work.
I have to admit I was agreeing with it, but the part about inductive reasoning clearly reveals a flaw. While it is true that inductive reasoning can lead to mistakes, it isn’t the case every time, because you can prove things, even if you start looking at the facts from the inner circle. Gravity being of those provable ideas. You also have to keep in mind that some things, when explained or researched upon, give more questions than answers, and this is another issue used to support this Incompleteness theorem, but it’s just a part of the search for an answer, and raising questions helps to nothing but to better understand everything, the more questions the closer to the truth we get.
I believe this theorem can be both flawed and perfect depending on the circumstances. And that it suffers from the same misuse of general relativity Once I had a very fiery discussion with a friend who said that everything, from matter and energy to concepts are relative, to which I replied that concepts can be constant, as units like 1 meter, the concept of 1 meter can not be relative, maybe the tool used to measure differs, maybe it has shorter centimeters, but the concept will not change under any circumstances. Perhaps this is the case.
I want to finish saying that I don’t reject the idea, humankind will probably never discover the secrets of everything (I’d bet to 42 tho), but I had to speak up because I think that some of the logic in the article is somewhat off.

“* Whatever is outside the biggest circle is an uncaused cause, because you can always draw a circle around an effect.”

while this may be true, you can also always draw a circle around the CAUSE…therefore the cause cannot be outside the circle

“* All codes we know the origin of are designed by conscious beings.
* Therefore whatever is outside the largest circle is a conscious being.”

Oh, where to start? LOL
1) Information is a thing…maybe not in the physical sense, but it still exists, and is therefore IN the circle.
2)Just because all the codes THAT WE KNOW are the creations of conscious beings in no way shape or form implies that all codes must be such creation. It only suggests that there are codes that we are unfamiliar with.
3)once again, if someTHING exists outside of the circle to generate information, or anything else for that matter, logic would dictate that you could then draw a larger circle that would encompass that creator as well

If you want to make a logical argument, it usually helps to actually USE logic and not just tiptoe around it

1) All known plates are designed by conscious minds.
2) The earth has tectonic plates.
3) The earth was designed by a conscious mind.

This is what happens when you play fast and loose with semantics.Just because you’ve used the word “code” instead of plate people get all confused and mystified, but it amounts to the same thing.

Now let’s see what happens when you abuse metaphors:

1) All known sandwiches are created with the intention of being eaten.
2) The solar system is sandwiched between other galactic formations.
3) Therefore the solar system (and the starry loaves in which it is nestled) is going to be eaten.

Now let’s see what happens when you can’t tell the difference between a system (science, math, language, etc…) describing a thing and the thing itself (the universe).

1) “Apple” is a noun.
2) Nouns are found in the dictionary.
3) Next time you’re feeling hungry, open the dictionary up to Apple and chow down (with apologies to Gwyneth Paltrow).

Now after seeing Matt’s point-by-point rebuttals of your arguments and your refusal (or inability) to understand the strength of his objections, I can’t assume this will have any effect on you (why, for instance, you are troubled by infinite regress but not by the idea of an immaterial god who sits outside of existence but still affects it and – what luck! – requires no cause, is a mystery on par with that of the big bang itself) But hopefully this is a simple explanation of just a few of the flaws in your reasoning for people who read your article and aren’t wearing god-blinders.

It’s clear that it isn’t used the same way. The mere fact that human designed codes are self-evidently designed by humans and the genetic code isn’t is enough to show that. That there are resemblances does not make them the same. The fact that you are asserting that they are used in exactly the same way only serves to highlight your circular reasoning.

“I can take quotes out of context and misapply them too.” – Me in a different conversation that had nothing to do with this.

The fact that you would try to take Yockey and use his quotes to argue for intelligent design would be comical if it weren’t insulting. I won’t go into depth as to why it’s wrong here, because, thanks to the power and beauty of the internet, someone else has already done this for me. Here’s a teaser:

“I’m told creationists have started citing this new book of his in defense of their own argument that God must have started life on earth. I’ve not seen this abuse myself, but it wouldn’t surprise me, and at any rate, forewarned is forearmed. If that’s their plan, Yockey throws a bucket of cold water on it.” — To find out why you’ll just have to read the article. Here’s the link – http://richardcarrier.blogspot.com/2006/11/yockey-on-biogenesis.html

As for infinite regress and the uncaused cause, this is literally the kind of thing they do in intro to philosophy courses. I’m not going to reiterate the entire history of the cosmological argument and its objections, but you’re welcome to read a brief introduction to it at http://en.wikipedia.org/wiki/Cosmological_argument#Objections_and_counterarguments

I guess you think that by throwing Goedel in you can make an old dress new, but just like creationists attempt to rebrand themselves as “intelligent design,” it’s lipstick on a pig.

Cute bit at the end there. If you want to seriously insult my intelligence while seeming dignified you’ll have to apprise yourself of more intelligently designed slams.

Pretty sure I’ve already addressed your use of Yockey as a pro-creationist source. I also think I’ve made it clear that I’m not trying to convince you personally of anything. The posts above already refuted your argument days before I even read it, the fact that you don’t see that speaks volumes. You have been refuted and you don’t see it, so you’ll forgive me if I choose not to waste my time any more than I already have.

My commentary was hopefully just illustrative for anyone who didn’t see the plain flaws in logic. I don’t think I’ve said anything here or elsewhere to impugn you, as opposed to your arguments posted (and, as I said, refusal/inability to take any rebuttals seriously).. In terms of your arguments, arguments don’t deserve to be treated respectfully, they deserve to be attacked. Those that are strong enough will withstand the attack. Yours do not.

You will use 100% non-condescending ultimatums from now on or I won’t post anything else — I probably won’t anyway, I just wanted to let you know in my own special way that I found that to be gratingly paternalistic. Since this is only 93% respectful, you are welcome to delete it.

1. All types of rapid transit utilities (bikes, cars etc…) are designed by conscious minds and not naturally occurring.

2. Horses are a type of rapid transit utility.

3. Therefore, horses are designed by a conscious mind.

I will give 10 million rubles to the first person to show me a naturally occurring rapid transit utility — keeping in mind that horses don’t count, donkeys, ponies mules, bulls, buffalo neither (Half credit for a midget riding a lasso apso).

Seriously man, good luck with life and everything, but I am beyond done here.

Hy folks. Nice debate. Roy, you stated “What caused God? It’s not a coherent question. By definition God is eternal…uncaused.” Ok, but by who’s definition? What if the nether that harbors the multiverse is what is really eternal and infinite. What if it has always been. No one can prove otherwise and and the proverbial circle cannot be drawn around it. If this were the case then God simply fades into one possible explanation as opposed to “the” explanation. What of time? We experience time on a liner scale but that is a function of the brain (as opposed to Brane…couldnt help it), and no necessarily how time exist in its own dimension. Can you draw a circle around time? Can you prove you can? No, you cant. Time may well extend infinitely in all directions unaffected by gravity, energy, velocity, expansion, or the boundaries of the multiverse. Does this prove that all things are begotten from time?…maybe. Or is time the true God? Either that or time doesnt exist and is an illusion according to the reasoning of this article. Thats been proposed before but not readily accepted by science, much less proven. I think what we have here is a creationist trying to prove his view through a very guided discussion using a single mathematical concept; Gödel’s Incompleteness Theorem. To truely understand the implications of that theorem we would all need to be doctorate level mathematicians. A single simple tenet of this theorem was put in even simpler layman’s terms. Then that was used to try to argue a point as absolute. Gödel’s Incompleteness Theorem does not “prove” the existence of a god (much less a Christian, Buddist, Muslim, Jewish, Egyptian, Greek, African, or any other god invented by mankind). Yes! I whole heartily agree that the possibility of a cosmic conscience exists and that it might be Godly. I believe this because there is no way to completely disprove it either. If time is finite, which we cannot prove, then there is always another circle. Keep in mind. Time was just one of many examples. Replace time with an infinite multiverse, or nether that cant be circled or just consider that the larger circles are also infinite once you break past the multiverse. We have NO way of knowing and many of the variables to this conundrum and God is just one of many…it just happens to be the one you favor.
- Eric M.

“Pulsars are not digital commuication systems.”

Neither is DNA. You just proved to yourself that DNA is not a code by your definition…

Perry,

First please excuse any mistakes in grammer or spelling, English is not my first language, I accept Godels theory but only as a basic premise, it does seem to explain what “is” however as has been mentioned by you one needs to draw a circle around something to describe it and to refference something ouytside of that circle for a rational explaination of what it is. You use the word “God” to explain that which cannot be rationalised that which just is, but by doing so you necessarily draw a circle arround it. I think the answer which has been mentioned in some posts that perhaps the Universe itself is irrational. Take for example your circle (no matter the size or the object within), concentrate on the circle, the realationship of the circumfernce to the radius is (untill proven otherwise) incorporates an infinitly irational figure “Pi” in that it has no recursion. Although we have no problem seeing the circle as a whole? I think perhaps this is confusing to many but as we delve deeper into subatomic world we see more irrationality and duality. Is light a wave or a particle. It is as with the schrodinger’s cat thought experiment the act of measureing causes the breakdown in the paradox. So to return to your original premise that god must exist is your measurement and true for you untill further information is available to breakdown the paradox created by drawing the circle and breaking the Pi paradox that exists within that circle.

As a Buddhist I find this discussion very interesting. A concept called the Mystic Law refers to the unknown and inexplainable workings of the Universe, whether or not it is of a God or not, whether one believes this or not. I believe irregardless of an individuals beliefs, the workings of the universe are beyond our understanding; but this should not stop us from at least trying to explain us and our existence.

I’m not sure why nobody has said this so far. You’ve asked for a “naturally occurring code” multiple times. It seems to me that the answer is quite straightforward, especially as you’ve called it a code multiple times.

DNA

Is it not the product of natural processes? Why is it excluded from being considered a natural code? DNA is encoded and decoded every billions of times every day around the world as a consequence of the laws of physics which dictate the behavior of the molecules that make up DNA. Why is it not a suitable answer to your challenge?

This theorem says indirectly, that whatever we don’t know must be god’s work. But that’s how religion was born. There are certain things our brains cannot comprehend. One simple example: what is infinite?
Or, if somebody believes in the bible I would ask him/her: What happened before the first day was created. What was there than? What/who created god? If nobody/nothing, then what? These things are impossible to comprehend. Our brains are not capable to understand. I simply accept those things and don’t try to explain them with an entity named god. That’s why I don’t believe in the entity named god. And I am very content with that. The main difference between me and religious people is, that I don’t say that in what I believe is the right thing, and try to persuade others to think like me. Religious people believe, that their view is the right one and keep trying to persuade others to believe in what they do.

Time is real and I believe this can be proved through say the decay of carbon 14, or if I get out of a chair and walk across the room; and relative to my own consciousness, time exists.

Perry;
Thank you for this, I found it very engaging and enlightening. I do think, however, that you are making a logical maneuver that is not valid, yet I think there is an interesting dilemma posed… and perhaps a way out.

Godel’s arguement is essentially one of epistemology: how can we know. If I were to live in my house, and all the doors and windows were eternally blocked shut, I could know nothing of the outside world. Yet, to truly understand, objectively, my predicament would entail stepping outside my house and seeing it from the outside. Yet, this ‘need to know’ does not necessarily say anything objectively about what is outside my house, it only illustrates that fulfilling my need to know would entail stepping outside. In a sense we are like lab rats. Can the lab rat know anything about the observer? There is an epistemological directionality that must be observed – the need to know does not necessarily prove that that need can be fulfilled. While God perhaps can draw a circle around my house, does not mean I can draw a circle around Him. Or does it? Seemingly, something from outside the sphere would need to reach back.

Reading your article jogged my memory that Godel’s argument sounds suspiciously like something else much older. Many are familiar with Anselm’s Ontological Argument, and its over-simplification, but many are not aware that Anselm proceeded that argument in his writings with a clarification that runs something like this:

The comparative goodness of any two things cannot be determined solely by comparing them to each other, invariably a third ‘ideal’ is needed to set a standard of comparison. This not only holds true for any ‘goodness’, but also any goodness one can think of, such as ‘greatness’. This applies when comparing any two commodities one can conceive, regardless how great. Therefore, for thought to be possible, a supreme ‘Ideal’, or ‘Greatness’, higher than any conceivable ideal, must exist or any comparison or description would be stymied. It is this supreme Ideal Greatness we call ‘God’.

People have tried to criticize Anselm’s logic for centuries, yet it somehow bridges a gap that most don’t understand. His logic is often called Modal Logic. While this sounds very much like Godel’s argument, I think Anselm had provided something Godel hasn’t.

If I am still locked in my house, I may wonder what about all these things in my house that don’t have sufficient cause for existing within my house alone. There are no trees in my house, yet my furniture is all made of wood, etc. Something from the outside is indeed reaching back. For Anselm, this ‘thing’ that is reaching back, bridging the gap between my circle and God’s is rationality itself. To Anselm, rationality is not a sufficient cause in itself and provides perhaps a unique case of ‘reaching’ that doesn’t have the same limitations as other things might have.

While it appears that epistemology can only move one way, there does seem to be, according to Anselm, a certain capitulation in the act of knowing itself. Something ‘bounces back’ from the observed to the observer or the act of knowing would be stymied. While much of this might be an illusion or imagination (a movie about Avatars does not prove they actually exist), when applied to ‘knowing’ itself, it can’t be just an illusion or ALL knowing would just an illusion, a phantasm (certain ‘realities’ of the Avatars must exist such as existability or the movie would make no sense). Where Anselm succeeds and Godel fails is in the recognition of evidence needing to traverse the boundary in both directions. To Anselm, rationality itself is this ‘thing’. In Godel’s example, the question is not whether a circle can be drawn around us, it is can a circle be drawn around God.

“Well, our friend Dirac, too, has a religion, and its guiding principle is this: ‘There is no God and Dirac is his prophet.’” – Wolfgang Pauli, Nobel Prize winner in physics.

No. It will not. In my world god doesn’t exist.

Hey Perry,

I really admire you for taking the time to respond to every single comment posted here… It is for this reason that I now find myself writing a comment when initially I did not have the intention to do so.

I believe I have a slightly different take on the ‘DNA is designed’ argument from that of earlier commentators. Hopefully this new argument will interest you.

I take it you believe that since all observed codes that we know of (putting aside DNA) are designed by conscious beings, then DNA can be inductively assumed to also have been designed by a conscious being.

Now imagine, if you will (for just a few moments), that there was a world where it were possible that some codes occur without the input of a conscious being, and that they were around on that planet. And imagine, please, that in that world, we could thus divide all codes into two types: those created by conscious beings, and those not created by conscious beings.

Person A believes that there exist both types of codes. Person B believes that only consciously created codes exist.

How would person A, I asked myself, in that particular world, prove to person B that some codes exist without conscious creators? Perhaps he would take a code that has existed long before humankind, show it to person B and say, ‘Behold, this is a code not created by a conscious mind.’

But person B would merely say, ‘You have not proven that this is a code not created by a conscious mind – only that it is a code not created by humans. This only shows that a conscious creator of codes existed before humans, and that it was that creator who made this code. The same can be said of any code not created by humans.’

Of course, person B cannot be proven wrong, even in this world that we are imagining where some codes do exist without conscious creators. The simple fact is that no-one can prove that a certain code has no conscious creator, whether that is actually the case or not.

Hopefully you will realise by now that it is impossible to distinguish, using logic or other means, this imagined world from our own. It may be true that all codes in this world were created by conscious beings. But to say that it MUST be so because we cannot prove it false is a logical fallacy.

( From Wikipedia: The argument from ignorance, also known as argumentum ad ignorantiam (“appeal to ignorance”), or negative evidence, is a logical fallacy in which it is claimed that a premise is true only because it has not been proven false, or is false only because it has not been proven true. )

Once again, thank you for your patience and willingness to respond to the comments directed towards your article, and have a nice day.

Perry,

Thank you for your reply. While I’m glad to hear that you would be convinced by empirical evidence, I hope you do realise that an experiment to display the random event of code coming together ‘randomly’ would be impractical – I hear that even computer models would be inadequate to show such an event, though I myself am a little confused as to why.

Still, I suppose there’s not much room for manoeuvre on the ‘empirical proof’ side of the argument, so I will say that I am defeated, when it comes to that, and will merely hope that one day science will once again come to understand something that only religion is be able to explain for now.

I’ll go and read that Infidels thread you gave me the link to now, and perhaps I will return with more questions when I have finished. Thanks for your response!

Hey Perry,

I’m not a biologist, unfortunately, and even if I were, I wouldn’t necessarily know enough to understand the full workings behind this, but since I’d like to continue discussing this, I hope you’ll forgive me for my stabs in the dark and correct me where I contradict current evidence.

I have read through the Infidel’s riddle section of your website, and found it quite interesting. I guess I would have to say that I’m not entirely sure that I understand your argument as to why DNA can’t have ‘evolved’ (I know I can only use the word as an analogy at this stage) from earlier, simpler biological or chemical components… And why those components could not have arisen by chance from other chemicals. After all, I hear the earth had a few hundred million years before any real complex stuff arose.

If that sort of thing can happen, I don’t see how the whole ‘code/information’ bit is relevant. After all, that is only a consequence of what something like DNA consists of, surely?

Again, I hope you’ll forgive me for my tentative guesses – if I had more time, I would look into the subject properly and try to see if I could understand papers on the subject, but I am a student with not long before my exams, so now is perhaps not the best time for that.

(As for the ‘simplier biological/chemical components’ I mentioned, I believe the Iron-Sulphur world theory and the RNA world hypothesis are examples of this, though unconfirmed.)

The very basic fallacy and the wrong premise made in this argument is information’s being a product of a conscious entity. You cannot make this presupposition since information may also thought to be an emergent entity, rather than being a designed one. For more about this you can read Daniel Dennet’s Darwin’s Dangerous Idea:

http://www.scribd.com/doc/2573941/Daniel-C-Dennett-Darwin-s-Dangerous-Idea-Evolution-and-the-Meaning-of-Life

I’m no scientist, (wish I was because I’d be rolling in the dough!) but I’ve come to the conclusion that DNA is the “Language of the Creator”. Once we become fluent we will be able to talk to God. Or, I look at it this way. If DNA is a language, the the Human Genome or any other creature’s genome is a book.

To be correct, and fair, Darwin actually ‘lifted’ the Theory of Evolution in an act of out-and-out plagiarism, shifting it into the camp of Uniformitarianism. Darwin had no real observational evidence from which to derive the Theory, nor did the Theory appear in the first editions of Origin of the Species.

Darwin was Russel Wallace’s research contact person at home in England. Wallace was sending his overseas research to Darwin for safe keeping. Then Darwin saw Wallace’s Sarawak Law: “Every species has come into existence coincident both in space and time with a pre-existing closely allied species.”

Darwin rushed to take credit for the finding (Wallace was overseas and could do nothing about it) leaving out Wallace’s conclusion: “Because man’s physical structure has been developed from an animal form by natural selection, it does not necessarily follow that his mental nature, even though developed pari passu with it, has been developed by the same causes only.”

Then this statement from Wallace: “these speculations are widely held to be far beyond the bounds of science — a superior intelligence has guided the development of man… and for a special purpose, just as man guides the development of many animal and vegetable forms.”

See – ‘A Delicate Arrangement’, Arnold Brackman, (New York) Times Pub.

Hey Perry,

I have read your Infinite Chasm page and I understand where you’re coming from, mostly. I looked around for a while afterwards and came across this page with an article by Ian Musgrave (http://www.talkorigins.org/faqs/abioprob/abioprob.html). It’s not too long, and tries to justify all his statement with references to scientific papers.

Looking elsewhere, I found that the actual numbers used in that article were not accurate, since it was mostly to make a point, rather than to be 100% mathematically accurate. I found that the corrections for those numbers (http://www.infidels.org/library/modern/richard_carrier/addendaB.html#notemusgrave) did not apparently negatively affect his conclusions.

You have probably seen that article before, and since it seems to contradict your statements on your Infinite Chasm page, I was wondering if you’d be willing to explain what errors Musgrave has made (aside from the corrections found in the second link)?

Hey Perry,

It’s true that he never precisely mentions how those self-replicators get together from their individual parts. I guess the text reads in such a way to make the reader assume the ingredients can randomly stick together somehow, through chemical processes…

Well, I guess that’s the big question then, isn’t it? It’ll be interesting to see the progress that scientists make as they try to find the answer. It just goes to show how far we still have to go before we can fully understand life.

There is one last thing I’d like to ask you, now. In an earlier comment, you said “once we acknowledge the exacting design and purposeful nature of DNA all kinds of other doors will open for biological discovery. We need to acknowledge the facts we do have before we can discover new ones.”
This confuses me more than anything else, I must confess. Surely the only way to make progress is to keep probing, testing and doubting… What could be gained from accepting that DNA is designed?

If you could explain what you meant by that statement, I’d be very grateful.

I proved mathematically beyond any question that the logical system of simple addition is complete in and of itself.

“Every symbol you define in your system of simple addition has to be taken as axiomatic.”

No they don’t. Not even close. The symbols are arbitrary. They’re not bloody axiomatic, they’re just a convenient shorthand. Remember “computably generable?” A computer could prove addition with the FORM of my proof above. The symbols are irrelevant. You could use anything you wanted. The definitions are all INSIDE the system.

What’s more, Gödel’s Theorem is discussed at length by Torkel Franzen and specifically in his book “Gödel’s Theorem: An Incomplete Guide to its Use and Abuse” ISBN 1-56881-238-8

He spent a lot of his life specifically devoting his time to discussing this theorem and common misconceptions applied to it. You would benefit from reading his work.

While one could argue that there are several ‘things’ in the Universe, such as mathematics, that exist un-caused because they arise out of naturally occurring ratios etc., that in no way challenges the belief that those things whose existence is contingent, such as rationality and life, require a cause. Their existence is contingent on having been caused by something. As there is not sufficient reason within the bounds of the Universe for these ‘contingent things’ to explain their existence, it is very warranted to look beyond the bounds of the known Universe to explain their existence. While mathematics may have a certain ‘order of proportion and ratio’ within its own bounds, that order falls significantly short of explaining true order, the ability of an intelligence to recognize that order, and the ability to communicate the meaning of the order. While one rock plus one rock equals two rocks, what does either rock care about the other?

Further, the fact that someone might extrapolate an infinite regression of causes from a speculated ‘First Cause’ in no way undermines the need for that Cause. One could say I am caused by my mother, who, in turn, is caused by her mother, and on and on. Just because I can create a hypothetical infinite regression of ‘mothers’ does not undermine the fact I, indeed, had a mother. In fact, it is this very infinite regression that demands a ‘First Cause’ at some point.

“Each particular thought is valueless if it is the result of irrational causes. Obviously, then, the whole process of human thought, that we call Reason, is equally valueless if it is the result of irrational causes. Hence, every theory of the universe which makes the mind a result of irrational causes is inadmissible, for it would be a proof that there are no such proofs. Which is nonsense. But Naturalism, as commonly held, is precisely a theory of this sort.” – CS Lewis

Perry

I wish to add something which is off topic but of interest none the less. I have added comments before, and you have been kind enoughh to answer them. I have also stated hat English not being my first language may cause some confusion. I woud classify myself as an agnostic. Perhaps a cowards way out, however I have been invited to a bible study group consisting of people who in all but their unwavering belief in a christian god seem rational. I mainly take a back seat as I feel my scepticsm would be doing an injustice to their hospitality, however at a recent event (which they called the HOLLY SPIRIT night) I was privy to something that trully amazed me. I had heard that when invocing the Holy Spirit believers have been known to speak in tongues. At the particular event I attended one specific person seemed to go into a trance like state and started talking what seemed to me to be giberish (for reference the meeting was recorded!) after the meeting the person who had the experience was taken to one side and questioned by a mesianic jew who was also present it turns out she was talking in an ancient form of aramaic which he recognised part of. We are having the transcript of the meeting looked at by a scholar who hopes to be able to give a fuller explaination of exactly what she said, as she was as suprised as any of us. Had never learnt any arabic, latin or aramaic in her life… crazy no??!

“I’m glad you agree that the apples are being counted. I’m also sure we both agree that the computer is not conscious that it is counting apples.

Nonetheless it is counting.”

Agreed. But it never would have been counting without humans telling it to. So you really haven’t accomplished anything by pointing out what we already knew.

“I don’t want you to forget the larger point which is that computers, not just humans, can perform mathematical expression.”

In fact that’s the point of computers. A machine, designed by humans, to perform the operations we tell it to faster than we can perform them ourselves.

“Is that not the whole point of the Turing Machine, which was inspired by Gödel’s work in the first place? Turing proposed a mechanized way of doing computations and showed that even computers can produce undecidable propositions.”

Because branches of mathematics are incomplete systems and are by definition incomplete. Therefore, if you set a computer to computably generate the system, it will reach a paradoxical statement at some point. Again, this doesn’t do anything for your argument as the computers were created by and programmed by us.

“Everything mathematical that can be applied to a computer, also applies to the universe, because a computer is part of the universe.”

That’s a terrible leap in logic. I would almost call it obtuse. You might as well say, “Everything that applies to a banana applies to a supermarket because a banana is in a supermarket.” You’ll find that statement to be wildly inaccurate after a short while.

“A falling object that accelerates due to gravity is expressing mathematics: The velocity is the integral of the acceleration and the position is the integral of the velocity. That’s the concept behind an analog computer.”

A falling object is DESCRIBED BY US using our CREATED LANGUAGE of mathematics. Mathematics was created, derived from observation and thought, it was not created by the universe.

“All things that obey the laws of physics express arithmetic. To be more precise, they express the laws of physics and so far as is known to science, all such behaviors are mathematical.”

We, as humans, would argue that all things that obey the laws of physics can be expressed by arithmetic. But that’s not what we were talking about, even by leaps and bounds. We were talking about formal mathematical systems that can express elementary arithmetic. For example, Finite Mathematics. Finite math uses variables and symbols to express arithmetic functions within a closed system. Finite math depends on assumptions outside of it’s system to function. Hence finite math is incomplete. Although the fact that it is called finite should have been a clue.

But if you accept basic arithmetic as true (which we do), you can then use the basic arithemtic functions to attempt to describe things in the real world. To suggest that the universe itself somehow derived these higher functions of math, though, and is therefore incomplete is a huge leap in logic.

Hi, is an assumption that conciousness is quantifiable made? By assuming that conciousness exists then god can be proved (according to your reasoning), but what if it doesn’t? The human brain and what we assign as being concious is only a complicated series of chemical reactions, giving the illusion of conciousness which allows people can go about their daily business without going mad. In essense the human brain is no different from a computer with an added element of randomness generated by interaction with surroundings. Would be interested to see what you make of this.

You are assuming that the universe is the grandest scheme available and there is nothing beyond it capable of having a circle drawn around it. Basically you are assuming that the universe is finite, and while it is true that what we can currently perceive of the universe is finite that does not mean that there isn’t more to it.
If the universe were infinite Godel’s theorem would be true but there would be no necessity for some indivisible god. The process of drawing a circle is to limit the contents of the circle to a finite amount, no matter how large that amount is. But if the universe were infinite then by definition to take any finite amount of it would leave an infinite amount of something, however unimaginable, outside of amount defined by the circle. That would not mean that this infinity is indivisible, the opposite actually it is infinitely divisible, but no matter how you divide it there are still more larger “circles” that could be defined containing the previous circle.
Even if you could theoretically make a circle that can contain infinity, infinity contains infinite infinities. pardon my overuse of the word but i dont know any other way of putting it.

anyways those are just my thoughts after reading your article and some of the discussion. I hope the way i put it makes sense if not i could try rephrasing it.

I do not feel educated enough to make any real contribution to this arguement. Perry if you have effectively proved that God exists while reason and logic holds would publishing this finding in a scientific journal not be more worthwile than arguing with people on the internet? If you have already done this i apologise.

Hello Perry,

I don’t think it was Gödel’s intention that the undefined and unproveable rest outside the circle is called “god”. Most readers will associate many things (values, traditions,…) with this term and therefore it’s missplaced in this text.

Besides you described a theorem but it actually seems that you take it as a law (with religious intentions?). That made me distrustful.

Tim

I appreciate your valiant attempt to invoke Gödel’s Incompleteness Theorem (actually two theorems) as a proof of God’s existence. You state, “He [Gödel] proved that any statement requires an external observer.” I believe others may have already pointed this out, but simply put the proposition that you claim to be proving is, “God exists,” and therefore must be included in your formal system of axioms and rules which would allow you to make such a statement, and, in turn, should your system meet the necessary conditions of a “formal” system, would be subject to Gödel’s Incompleteness Theorem.

Gödel, as you aver, was a mathematical genius. He was also expressly interested in proving the existence of God. Don’t you think, if he could have figured out a way to use his Incompleteness Theorem to prove God’s existence, he would have done so? Instead, he pursued an ontological argument similar to that proposed by St. Anselm. Although it is rumored that he thought he was close to a proof, he apparently was never quite satisfied, and as a result we have no record of his efforts in this regard.

By the way, I want to thank you for recommending to your readers Rebecca Goldstein’s scholarly and entertaining book, “The Proof and Paradox of Kurt Gödel.” The irony of your recommendation cannot be missed as Ms. Goldstein is an atheist. For those interested, I would also recommend her recent novel, “36 Arguments for The Existence of God,” in which she satirically plumbs the contentious nature of faith and reason.

It’s 4010 and scientists have discovered and formalized all knowable laws of physics. Yet to your delight, you can still apply Gödel’s Incompleteness Theorem and exclaim, “athiests are irrational.” It’s a small consulation, but I’m not sure anyone will be listening. Good luck on fine tuning your theories.

What I was suggesting with the 4010 example is that even if science does create a formal system of all the “knowable” laws of physics, one can still appeal to Gödel’s Incompleteness Theorem and claim that we don’t know everything. For some this may be a problem, but for me it opens a world of possibilities of free inquiry and liberal discourse unfettered by the “airtight” dogmatism of any ilk; religious, political, or even scientific. What you have demonstrated is the beauty of mathematics not only concerning questions of the physical world but also of the metaphysical. As you state above, Gödel’s Incompleteness Theorem applies to the metaphysical statement “God exists” and by extension, I would add, “God is indivisible.” There is a delightful infinite regress in pursuing this course, which is something you feel is necessary to avoid although I think simply demonstrates the power and beauty of mathematics. Way back in the 6th century BC the Pythagoreans postulated that God is not a mathematician, mathematics is God. Your fascination with Gödel’s Incompleteness Theorem may lead you to the same conclusion. By the way, I would like to recommend to your readers Mario Levio’s book, “Is God a Mathematician?” It touches on many of the discussion points throughout this thread.

Perry

Can I ask is it the christian god you believe in? because I see some flaws with your argument (though I am not adverse to your basic premises) In believing in the Trinity you have drawn circles around three distinct identies and surely godels thoerum would then imply incompleteness..no?

I have heard the explaination that the trinity are distinct parts of the same entity and equal, but biblical texts would seem to contradict in many places some examples.
john 14:28 If you loved me, you would be glad that I’m going to the Father, because the Father is greater than I am.
mathew 24:36 “But of that day and hour no one knows, not even the angels of heaven, nor the Son, but the Father alone.

How do you metaphorically square this.

To all the people who say that this article is intended, or in some way attempts, to prove the existence of God: it does not. It simply says that by applying Godel’s theory, the people who believe in God have a logical reason for doing so. They have merely specified what they think is “outside the circle”. They may have taken this idea to certain extremes, but the basic tenet is logical. Any other belief that says the universe was caused by something outside the universe is equally logical. Not only that, but you cannot logically DISprove God, and while that doesn’t mean he exists, it means that you can’t say for sure that he doesn’t exist. Basically, people should believe what they need to believe to understand the universe and their own existence, as long as it is not harmful to other people, and belief in itself is not harmful. Taking that belief to extremes and inferring things from it like “anyone who doesn’t believe this should die” is simply human error. And I apologize for this not being organized, but I addressed the issues as I thought of them.

A professor of mine told us, “You throw enough s__ up and some of it is bound to stick.” You make an awful lot of assertions so I’m wondering if you could simply state for your readers the one “airtight” proposition that you claim follows from Gödel’s Incompleteness Theorem. If you’re interested in advancing your argument, I suggest this might be a way of staying on track.

Could you also provide the source for your initial quote, “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” and also, if you could, a citation for your statement that “He [Gödel] proved that any statement requires an external observer.” I find the “circle” and “external observer” analogies curiously provocative and would like to understand these quotes in their original context.

If you wish to be taken seriously, you shouldn’t ascribe to Gödel something he never said. It’s, of course, dishonest, quotation marks and all, and hardly a minor point. It’s the difference between what Gödel wrote and your interpretation of what he wrote. Others in this thread have strongly disagreed with your interpretation of Gödel’s Theorem, but your use of the “circle” and “external observer” metaphors, which, I believe, are in their very nature an expression of your belief, have rolled through the discussion thread. When you denude your argument of these images, you’re left with the reality of Gödel’s theorem and how do you get from it to your proposition: “if the universe is capable of computing arithmetic and if the universe is consistent (i.e. logical) then the universe is therefore incomplete.“ The connection is not at all clear as you have a herculean, if not impossible, task in defining your terms. For example, what do you mean by “universe? and what do you mean “capable of computing arithmetic?” Throughout history, these terms or concepts have confounded the most brilliant minds, which, in turn, have produced and continue to produce a diverse range of scholarly opinions, the depth and breadth of which takes my breath away. Even if you could climb this mountain, Gödel’s Proof would be there to tell you that you don’t know everything. Your use of “circles” and “external observers” are unacceptable shortcuts to the difficult task of climbing the mountain. You would do yourself and your readers a service by honestly stating your belief, which, in this regard, is simply that the universe is such that you can draw a circle around it and what’s outside the circle is God. You don’t need Gödel or the “authority” of science to make this statement. It’s your belief.

If you actually cared to consider what others and I have said, you would have to concede you have no argument. But astonishingly your argument is also based on a lie – not some incidental or vague lie but a deliberately calculated one in bold colored lettering with quotation marks around it. A lie that you repeatedly come back to in various guises in your article and throughout the thread – the word “circle” appears over 100 times. This lie has nothing to do with Gödel or scientific inquiry, but is the very foundation of your theological beliefs, which, at this point, I’m sorry to report, couldn’t stand up to a good wind.

Perry

Having taken much time and effort to read and watch all of your work and cross referenced them with my own experiences. I find myself at odds with certain assumptions and conclusions that you reach. I suspect that this may well be my last corespondence with you but (and this sums it up both metaphorically and literally) anything is posible.

As you try to reconcile logic and the acceptance of an uncaused eternal god I wish you good luck. I personally believe now that far from being irational atheists have a perfectly rational basis for their stance. Providing that the laws of physics at points in this universe can be “irational”

Main Entry: ir·ra·tio·nal
Pronunciation: ir-’ra-sh&-n&l
Function: adjective
: not rational: not governed by reason, mental clarity, or >>>understanding<<<

there will be at some scale or point where they will "appear" rational. We know so little about the universe from our tiny point of existence that even the circle you seek to draw around it is ireconcilable to its radius from here to the edge if it exists. without accepting irationality and taking an aproximation.

From any point on the circumference to a central point we cannot even reconcile the smallest circle (Pi x r^2) where pi is a non recursive number. To reach that central point exactly is imposible we would have to start drawing a line and at some point slow down and down untill the line to all intense and purposes had reached that centre. But magnify it; and we would see we have a little further to go (or we had gone too far!) at some point we would reach a quantum level at which point we see all sorts of "irational" behaviour. time itself starts to interact with matter and vice versa. We may start to see particles which are split and are able to convey information of change even though they have no longer any known physical relationship/connection to each other.

To state that DNA is too complex to have developed without a creator and even that this same creator must have created the universe we observe is an example of Dunning-Kruger effect. (which I fully accept I also am guilty of) We simply do not yet have enough information or the tools to be able to state catagoricaly that an omniscient, omnipotent being does or does not exist. I think that it is fair to infer it as part of our exploration into our own consciousness but to state it as fact, is like saying a+b=G it can have no proof untill all the atributes of a and b can catagorically be stated as complete.

Thank you for the time you have taken to answer my corespondences and good luck in your quest for the "unknowable"

Yours in Ignorance,
Hans

Your “circle” requires evidence or a proof. Then we can talk about the merits of your argument. Lying about what Gödel says and then jumping from his proof regarding formal systems to the universe, I’m sorry, doesn’t count. Maybe you could find some other scientist, of the caliber of Stephen Hawking, who has used the circle metaphor to describe the universe – I wouldn’t bet on it. The Wikipedia’s discussion on the universe, which most people would say is just the tip of the iceberg, is eighteen pages long, 8,500 words, 72 citations, and there’s NOT ONE single reference to an “encircled” universe. However, I bet there are some religious sources that use this analogy, but as I understand it that’s not how you want to develop your argument. By the way, on your insistence that the universe is capable of computing arithmetic, I’d like to refer you to Sir Michael Atiyah, one of the greatest mathematician of the 20th century, who argues that a concept as basic as that of natural numbers was created by man. I mention this only to assure you that this issue is far from settled as you would like people to believe.

Although I think your argument has been completely demolished, and ironically I think you should be happy for that, there’s just one last nail I’d like to hammer into its coffin. Let’s assume that somehow you can pull the proverbial rabbit out of the hat and prove that the universe is such that you can draw a circle around it, formalize all of its laws (past, present, and future), apply Gödel’s proof, find the universe consistent, but not complete, and conclude “there could be a God.” What I think you should find frightening about this scenario, is that in the process you would have created a completely formal, rational, mechanistic, universe – the very universe that you eschew – a universe in which miracles are no longer possible – Christ’s birth and resurrection explained away. You’re left with the possibility that there might be a God. You may want to be careful of what you wish for.