In 1931, Kurt Gödel delivered a devastating blow to the mathematicians of his time
In 1931, the young mathematician Kurt Gödel made a landmark discovery, as powerful as anything Albert Einstein developed.
In one salvo, he completely demolished an entire class of scientific theories.
Gödel’s discovery not only applies to mathematics but literally all branches of science, logic and human knowledge. It has earth-shattering implications.
Oddly, few people know anything about it.
Allow me to tell you the story.
Mathematicians love proofs. They were hot and bothered for centuries, because they were unable to PROVE some of the things they knew were true.
So for example if you studied high school Geometry, you’ve done the exercises where you prove all kinds of things about triangles based on a set of theorems.
That high school geometry book is built on Euclid’s five postulates. Everyone knows the postulates are true, but in 2500 years nobody’s figured out a way to prove them.
Yes, it does seem perfectly “obvious” that a line can be extended infinitely in both directions, but no one has been able to PROVE that. We can only demonstrate that Euclid’s postulates are a reasonable, and in fact necessary, set of 5 assumptions.
Towering mathematical geniuses were frustrated for 2000+ years because they couldn’t prove all their theorems. There were so many things that were “obviously true,” but nobody could find a way to prove them.
In the early 1900’s, however, a tremendous wave of optimism swept through mathematical circles. The most brilliant mathematicians in the world (like Bertrand Russell, David Hilbert and Ludwig Wittgenstein) became convinced that they were rapidly closing in on a final synthesis.
A unifying “Theory of Everything” that would finally nail down all the loose ends. Mathematics would be complete, bulletproof, airtight, triumphant.
In 1931 this young Austrian mathematician, Kurt Gödel, published a paper that once and for all PROVED that a single Theory Of Everything is actually impossible. He proved they would never prove everything. (Yeah I know, it sounds a little odd, doesn’t it?)
Gödel’s discovery was called “The Incompleteness Theorem.”
If you’ll give me just a few minutes, I’ll explain what it says, how Gödel proved it, and what it means – in plain, simple English that anyone can understand.
Gödel’s Incompleteness Theorem says:
“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”
You can draw a circle around all of the concepts in your high school geometry book. But they’re all built on Euclid’s 5 postulates which we know are true but cannot be proven. Those 5 postulates are outside the book, outside the circle.
| Stated in Formal Language: Gödel’s theorem says: “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.” The Church-Turing thesis says that a physical system can express elementary arithmetic just as a human can, and that the arithmetic of a Turing Machine (computer) is not provable within the system and is likewise subject to incompleteness. Any physical system subjected to measurement is capable of expressing elementary arithmetic. (In other words, children can do math by counting their fingers, water flowing into a bucket does integration, and physical systems always give the right answer.) Therefore the universe is capable of expressing elementary arithmetic and like both mathematics itself and a Turing machine, is incomplete. Syllogism: 1. All non-trivial computational systems are incomplete 2. The universe is a non-trivial computational system 3. Therefore the universe is incomplete |
You can draw a circle around a bicycle. But the existence of that bicycle relies on a factory that is outside that circle. The bicycle cannot explain itself.
You can draw the circle around a bicycle factory. But that factory likewise relies on other things outside the factory.
Gödel proved that there are ALWAYS more things that are true than you can prove. Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few unprovable assumptions.
Gödel’s Incompleteness Theorem applies not just to math, but to everything that is subject to the laws of logic. Everything that you can count or calculate. Incompleteness is true in math; it’s equally true in science or language and philosophy.
Gödel created his proof by starting with “The Liar’s Paradox” — which is the statement
“I am lying.”
“I am lying” is self-contradictory, since if it’s true, I’m not a liar, and it’s false; and if it’s false, I am a liar, so it’s true.
Gödel, in one of the most ingenious moves in the history of math, converted this Liar’s Paradox into a mathematical formula. He proved that no statement can prove its own truth.
You always need an outside reference point.
The Incompleteness Theorem was a devastating blow to the “positivists” of the time. They insisted that literally anything you could not measure or prove was nonsense. He showed that their positivism was nonsense.
Gödel proved his theorem in black and white and nobody could argue with his logic. Yet some of his fellow mathematicians went to their graves in denial, believing that somehow or another Gödel must surely be wrong.
He wasn’t wrong. It was really true. There are more things that are true than you can prove.
A “theory of everything” – whether in math, or physics, or philosophy – will never be found. Because it is mathematically impossible.
OK, so what does this really mean? Why is this super-important, and not just an interesting geek factoid?
Here’s what it means:
- Faith and Reason are not enemies. In fact, the exact opposite is true! One is absolutely necessary for the other to exist. All reasoning ultimately traces back to faith in something that you cannot prove.
- All closed systems depend on something outside the system.
- You can always draw a bigger circle but there will still be something outside the circle.
Reasoning inward from a larger circle to a smaller circle (from “all things” to “some things”) is deductive reasoning.
Example of a deductive reasoning:
1. All men are mortal
2. Socrates is a man
3. Therefore Socrates is mortal
Reasoning outward from a smaller circle to a larger circle (from “some things” to “all things”) is inductive reasoning.
Examples of inductive reasoning:
1. All the men I know are mortal
2. Therefore all men are mortal
1. When I let go of objects, they fall
2. Therefore there is a law of gravity that governs all falling objects
Notice than when you move from the smaller circle to the larger circle, you have to make assumptions that you cannot 100% prove.
For example you cannot PROVE gravity will always be consistent at all times. You can only observe that it’s consistently true every time.
All predictions about the future are inductive. Outside the circle. In Gödel’s language they are “undecidable propositions.” It’s probable you’ll still have your job next week… but maybe you don’t.
All scientific laws are based on inductive reasoning. All of science rests on an assumption that the universe is orderly, logical and mathematical based on fixed discoverable laws.
You cannot PROVE this. (You can’t prove that the sun will come up tomorrow morning either.) You literally have to take it on faith. In fact most people don’t know that outside the science circle is a philosophy circle. Science is based on philosophical assumptions that you cannot scientifically prove. Actually, the scientific method cannot prove, it can only infer.
(Science originally came from the idea that God made an orderly universe which obeys fixed, discoverable laws – and because of those laws, He would not have to constantly tinker with it in order for it to operate.)
Now please consider what happens when we draw the biggest circle possibly can – around the whole universe. (If there are multiple universes, we’re drawing a circle around all of them too):
- There has to be something outside that circle. Something which we have to assume but cannot prove
- The universe as we know it is finite – finite matter, finite energy, finite space and 13.8 billion years time
- The universe (all matter, energy, space and time) cannot explain itself
- Whatever is outside the biggest circle is boundless. So by definition it is not possible to draw a circle around it.
- If we draw a circle around all matter, energy, space and time and apply Gödel’s theorem, then we know what is outside that circle is not matter, is not energy, is not space and is not time. Because all the matter and energy are inside the circle. It’s immaterial.
- Whatever is outside the biggest circle is not a system – i.e. is not an assemblage of parts. Otherwise we could draw a circle around them. The thing outside the biggest circle is indivisible.
- Whatever is outside the biggest circle is an uncaused cause, because you can always draw a circle around an effect.
We can apply the same inductive reasoning to the origin of information:
- In the history of the universe we also see the introduction of information, some 3.8 billion years ago. It came in the form of the Genetic code, which is symbolic and immaterial.
- The information had to come from the outside, since information is not known to be an inherent property of matter, energy, space or time.
- All codes we know the origin of are designed by conscious beings.
- Therefore whatever is outside the largest circle is a conscious being.
When we add information to the equation, we conclude that not only is the thing outside the biggest circle infinite and immaterial, it is also self-aware.
Isn’t it interesting how all these conclusions sound suspiciously similar to how theologians have described God for thousands of years?
Maybe that’s why it’s hardly surprising that 80-90% of the people in the world believe in some concept of God. Yes, it’s intuitive to most folks. But Gödel’s theorem indicates it’s also supremely logical. In fact it’s the only position one can take and stay in the realm of reason and logic.
The person who proudly proclaims, “You’re a man of faith, but I’m a man of science” doesn’t understand the roots of science or the nature of knowledge!
Interesting aside…
If you visit the world’s largest atheist website, Infidels, on the home page you will find the following statement:
“Naturalism is the hypothesis that the natural world is a closed system, which means that nothing that is not part of the natural world affects it.”
If you know Gödel’s theorem, you know all systems rely on something outside the system. So according to Gödel’s Incompleteness theorem, the folks at Infidels cannot be correct. Because the universe is a system, it has to have an outside cause.
Therefore Atheism violates the laws mathematics.
The Incompleteness of the universe isn’t proof that God exists. But… it IS proof that in order to construct a consistent model of the universe, belief in God is not just 100% logical… it’s necessary.
Euclid’s 5 postulates aren’t formally provable and God is not formally provable either. But… just as you cannot build a coherent system of geometry without Euclid’s 5 postulates, neither can you build a coherent description of the universe without a First Cause and a Source of order.
Thus faith and science are not enemies, but allies. They are two sides of the same coin. It had been true for hundreds of years, but in 1931 this skinny young Austrian mathematician named Kurt Gödel proved it.
No time in the history of mankind has faith in God been more reasonable, more logical, or more thoroughly supported by rational thought, science and mathematics.
Perry Marshall
“Math is the language God wrote the universe in.” –Galileo Galile, 1623
Further reading:
“Incompleteness: The Proof and Paradox of Kurt Gödel” by Rebecca Goldstein – fantastic biography and a great read
A collection of quotes and notes about Gödel’s proof from Miskatonic University Press
Formal description of Gödel’s Incompleteness Theorem and links to his original papers on Wikipedia
Science vs. Faith on CoffeehouseTheology.com
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Gotta agree with the folk from scienceblog.com:
http://scienceblogs.com/goodmath/2010/05/the_danger_when_you_dont_know.php
You can’t just oversimplify a theory about formal mathematical systems, extrapolate this oversimplification to the entire universe and tell me that Godel said that’s cool.
The author seems unaware that so far as known to modern physics and astronomy, the universe is most definitely of finite size and space. It is not infinite.
I stand by my simplification of Gödel’s theorem as being essentially correct. He may be unaware though that I have expressed my thesis using Gödel’s formal statement as follows. The following is not simplified:
Godel’s theorem says:
“Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”
The Church-Turing thesis says that a physical system can express elementary arithmetic just as a human can, and that the arithmetic of a Turing Machine (computer) is not provable within the system and is likewise subject to incompleteness.
POSTULATE: Any physical system subjected to measurement is capable of expressing elementary arithmetic.
Therefore the universe is capable of expressing elementary arithmetic. Thus, like both mathematics itself and a Turing machine, the universe is also incomplete.
Mr. Chu-Carroll is welcome to come here and post if he wishes.
My Goodness.
This has to be the worst mangling of Godel’s theorem I have ever seen. The theorem does not say anything even close to what you are claiming here. You are starting from an oversimplified illustration of the theorem, and then you go from there to construct an entirely false argument.
(Not to mention some even more basic logic. In the mangling you chose to represent as Godel’s theorem, you claim that one can always draw a bigger circle. And the circle around the universe implies God outside the circle. So, I wonder what happens when you draw a bigger circle that encompasses universe AND God. What is outside of that, by necessity?)
It is very sad to notice the amount of effort expended on this site, when so many of the basic ideas it is built on are absolutely incorrect. I am a biologist (neurobiologist, to be precise), and you can imagine my surprise when I found the claim that we have never observed random mutation create information. Really? Nylonase is a classical example in the literature, but everyone who has worked in molecular biology has seen it many, many times with their own eyes.
It is mind-boggling that people would rather create such constructions and insist on such nonsense, rather then accept the limits of our knowledge. Science does not exclude the existence of God, but it does indicate that our ideas of him/her/it are woefully tiny. Instead of approaching the subject with awe and reverence it deserves, we get…this? In name of faith?
If you think I am saying that God is inside the circle then you did not even read my article.
As for random mutations creating new information – I absolutely stand by my statement. I am well aware of the Nylonase experiments. What evidence do you have that the DNA changes were random – and not a result of transpositions, horizontal gene transfer, genome doubling, or epigenetics?
Even some PhD biologists are unaware that none of these evolutionary changes are a result of random mutations. Randomness is always assumed, never proven. I dare you to show me one scientific paper that proves this assertion. In 5 years debating this topic no one has ever come forward with one.
One paper that argues forcefully against the randomness assumption is James A. Shapiro, “A 21st Century View of Evolution”: http://shapiro.bsd.uchicago.edu/Shapiro.2005.Gene.pdf
As for my Gödel argument, if you care to be more specific about what you think his theorem says, then come forward with your argument.
The link given in the further comment (to Mark Chu-Caroll’s analysis) explains why your interpretation of Godel’s theorem is incorrect. I really have little to add to that.
But since it is unlikely that you will ever click the link, I will explore one particular line of argument. While still not perfect, much more correct statement of Godel’s theorem is the one Mark mentions: In any valid, consistent, formal mathematical system that’s capable of expressing Peano arithmetic, there will be true statements that cannot be proved within the system.
You will notice that it says nothing about circles, “final circles”, or boundless things beyond final circles. In fact, it says that there can be no final circle.
You have done the following: you have taken a vastly simplified image of the incompleteness theorem, taken it literally, defined a thing that according to the theorem cannot exist (the circle that encompasses everything), then defined the area outside of it as unbound (with no reason or explanation, certainly nothing to do with the theorem), and then defined that area as God.
It is completely nonsensical and illogical argument. This isn’t about what I think Godel’s theorem says, it is about what it does say in very clear mathematics.
But it gets worse. Even if we fix the definition, we get an answer you won’t like at all.
You defined a “circle that includes the whole universe”. Ok, in terms of Godel’s theorem, we can imagine such a thing: it would be a system of laws and logic that describes everything that exists – all causes, all effects, all processess. If you had such a system, you could predict everything that will exist from what exists now.
What Godel’s theorem proves is that there are true statements that cannot be proven from within that system.
You define God as something that stands outside that circle. According to Godel’s theorem, you have just defined God as “a true statement that cannot be proven from within the universe”.
Joy. And before you jump on the words “true statement”, remember that this is a statement. Is God a statement?
It just doesn’t compute.
* * *
As for your randomness argument, it is similarly nonsensical. Nylonase is just one of several thousand documented instances where new genes arose in the lab (you *are* aware that it happened twice for nylonase – once in nature, and once independently in the lab, where the exact molecular event was followed?).
Nylonase arose (in both cases) through a random frameshift mutation, which RANDOMIZES the protein sequence from the point of the shift onwards. It is as random as random gets.
Perhaps you never spoke to people with good molecular biology background before, but claiming that nobody has shown randomness is so far away from truth it is mind-boggling.
Some reference to frameshifts in evolution:
Ohno S (April 1984). “Birth of a unique enzyme from an alternative reading frame of the preexisted, internally repetitious coding sequence”. Proc Natl Acad Sci USA. 81 (8): 2421–5.
Okamura K, Feuk L, Marquès-Bonet T, Navarro A, Scherer SW (December 2006). “Frequent appearance of novel protein-coding sequences by frameshift translation”. Genomics 88 (6): 690–7.
But, again, it gets worse.
One of the central cores of modern bioinformatics is the mutation probability modeling. We make matrices based on CHANCES that a certain amino-acid will RANDOMLY mutate into particular other amino acids.
These chances can be calculated to a certain extent (based on DNA codon usage), but they can also be measure directly.
These matrices are then used to calculate phylogenetic trees, and to analyze genomic information. And you know what? They work.
They work perfectly. If there was a non-random element to the mutations that produce variation, this would jump out of the statistics like a Mount Everest. But it doesn’t. It is all pure, unadulterated randomness. When you compare genomes, there are no statistically significant signs that anything beyond random mutation happened at any point.
Which isn’t surprising, given how essential randomness is to not only the working of subatomic systems, but even to the working of the cell. Without molecular randomness, there is no way for life to exist. But that is a separate story.
You have not provided any proof of your randomness assertion. You’ve just made a statement with no proof or supporting evidence and expected me to believe you.
Show me a peer reviewed biology paper that demonstrates (and doesn’t just merely assume) that the changes that drive evolution are random.
You also clearly did not read the paper I referenced: “A 21st Century View of Evolution”: http://shapiro.bsd.uchicago.edu/Shapiro.2005.Gene.pdf
Do not reply until you have read this paper and are willing to present the evidence that I have requested.
Dear Perry,
I will note that you have completely skipped over the explanation why your use of Godel’s theorem is completely bogus.
Then I will note that I have provided you with two references (one of which contains numerous other references), and yet you still claimed that I have provided no proof. I have mentioned one basic fact of bioinformatics (matrices based on chances of random amino acid changes), but you simply ignored that as well.
I am familiar with the Shapiro article. It is a very weak paper, and much like the Godel’s theorem, does not mean what you think it means.
But that is irrelevant, isn’t it? You don’t even see arguments that do not fit your worldview. Further discussion is pointless.
“If there was a non-random element to the mutations that produce variation, this would jump out of the statistics like a Mount Everest. But it doesn’t. It is all pure, unadulterated randomness.”
You sound as though you’ve never even heard of:
Transposition
Epigenetics
Ohno’s 2R hypothesis
Horizontal Gene Transfer
Symbiogenesis
Surely you’re not serious?
Are you aware that when DNA is assaulted with radiation it uses transposition and repair mechanisms to correct the damage, sometimes copying other parts of chromosomes to the damaged area? Barbara McClintock won the Nobel prize for this discovery in 1983.
“Many ways to induce mutations are known but none lead to new organisms. Mutation accumulation does not lead to new species or even to new organs or new tissues… Even professional evolutionary biologists are hard put to find mutations, experimentally induced or spontaneous, that lead in a positive way to evolutionary change.”
-Lynn Margulis, “Acquiring Genomes”
Because of this even a random mutation can result in a different feature than the parent, because of the error correction mechanism. It’s not the random copying error that gets credit for this, it’s the genome repair activity.
You insult Shapiro without even comprehending his work. This is a wholesale avoidance of legitimate scientific knowledge. Your position is anti-scientific because it’s an avoidance of a systematic model in favor of a stochastic model.
Below Godel’s picture I deal with Godel’s formal statement and why the church-turing thesis implies the universe is incomplete.
It is impossible to draw a circle around something that is infinite.
Please provide proof that the mutations that created Nylonase were random.
At the very end of your article: Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century, there reads the statement: “Math is the language God wrote the universe in.”
Since your name is close the famous statement, someone could construe that the statement is of your authorship.
This statement should be rightfully attributed to Galileo Galilei who wrote and published it in his book: Il Saggiatore (1623), which he dedicated to the then recently appointed Pope Urban VIII.
Most respectfully;
A. Quinones
Teacher of Mathematics
Thank you very much, I did not know that was from Gaileo. Page updated accordingly.
I wouldn’t waste my time if I were you M. I actually submitted a corrected version of Perry’s mangling of Godel’s Theorems about a month or so ago, and he never posted it. In fact, I submitted multiple problems on quite a few of Perry’s mis-interpretations of various issues he uses to “support” his argument, and none of them were ever posted.
I think it’s clear (by looking over the types of responses that are posted) that Perry is not really all that interested in debating the issue with qualified individuals like ourselves. He’s more concerned with providing solace to his own once faltering belief (yes Perry, I’m talking about the conversation you and your brother had…I have actually scrutinized your entire website) and the others like him. He offers that solace by repackaging the same old rhetoric with a pretty new bow. Apparently he and others are under the delusion that a minuscule amount of techno-speak with the phrase “Therefore God exists” at the end is all that is required to make a successful argument.
If it makes you feel better to think that you’ve updated the jargon and made talk about God “science-y”, fine…feel better. But don’t fool yourself, you’ve contributed nothing past the watchmaker argument of yore (i.e., you haven’t updated the arguement, which I’ve already told you once before but you didn’t post it). David Hume’s critiques (among others) are just as applicable to your arguments now, in 2010, as they were to the arguments offered before the 1700’s.
Not to mention, your response to M shows that you didn’t even read what he wrote. He didn’t accuse you of drawing a circle around God, he asked you why, in principle, you cannot. Godel never said anything about physical systems in his proof, yet you choose to apply it to physical systems, but not to the system of God + Universe (mixed physical/supernatural system). It seems, Perry, you’ve just arbitrarily chosen to stop drawing circles when you get to God.
M’s point is this: If M were to grant your application of Godel’s theorem beyond formal systems, then, without argument, there no reason to stop drawing circles when you get to the one around the universe, WHY CAN’T YOU DRAW ONE MORE CIRCLE!? One that includes God + the universe.
I’ll take M one step farther: If we did that, it certainly seems as if the Universe + God SYSTEM can express basic arithmetical truths…so that system is either incomplete or inconsistent. If it’s incomplete, then we need something outside of God+Universe to prove God+universe. If it’s inconsistent, then there is something that is both true and false in the system (of course, given that we’re talking about entities, and not statements, it’s not clear to me how exactly true and false apply…”The table is false.” is meaningless). In other words, M is claiming that you have just pushed the problem back one step…and he’s right. Sure, we need God to get the universe, but we need something else to get God.
Perry…you haven’t done anything except change the word “watch” to “code” and the “gear” to “DNA”.
I most certainly did post your comments, and I responded to each one of them.
http://www.google.com/search?num=100&hl=en&safe=off&client=firefox-a&rls=org.mozilla%3Aen-US%3Aofficial&q=vyzion+comment+site%3Aevo2.org&aq=f&aqi=&aql=&oq=&gs_rfai=
http://www.google.com/search?q=vyzion+site:evo2.org&num=100&hl=en&safe=off&client=firefox-a&hs=PLK&rls=org.mozilla:en-US:official&filter=0
Or just search the site for “vyzion”
The time I have to respond to questions on this site is *extremely* limited right now and I will get to your incompleteness post when I can.
Yes, as you say, I have replaced “watch” with “code.” The crux of Hume’s argument was that the analogy between a watch and a living thing was poor. Replacing watch with digital code re-affirms Paley and definitively overturns Hume’s argument with a rigorous, black and white definition of code from Information theory. This is all that is necessary. Codes in DNA are isomorphic with computer codes. When we speak of codes in living things we are not speaking in analogies.
Codes are found nowhere else outside of living things and human designs. So we have an unambiguous chasm between living things and non living things, placing the former firmly in the category of design inference.
Thus Hume’s argument has been refuted.
I have defined this explicitly at http://www.evo2.org/solve and if you can use the criteria I outline there to demonstrate a naturally occurring code I’ll write you a check for $10,000.00.
And finally, you can’t draw a circle around something that is infinite.
I can! An example of a naturally occurring code is RNA/DNA. Your argument contains a composition fallacy and thus risks being unsound. You are taking a biased sample from the codes we know of; you are only considering human-made codes, and you from there assume that all codes must be made from a mind. Logically speaking, “you can’t get there from here.” I would go so far as to say you’re taking a sample from a population (human-made codes) and applying your findings to a totally different population (non-human-made codes). If you were to apply that methodology in my stats class, it would earn you a fail. Notice that you’re asking for an example of a non-mind-made code, when you may have already found one, the very one you’re making an example out of. So $10k? It would really help with my grad expenses. If from this you’re deducing my religious affiliation, you might be surprised to find I have dedicated my life to Jesus Christ. I seek to honor him with all my work. That’s why I urge you to review your logic and your understanding of biology. I also recommend “The Language of God” by Francis S Collins, as your claims on this site represent a “God in the gaps” hypothesis, which he defines in this book. You run the serious risk of leading people to put their hope in this “fact” that DNA was by nature created by a mind, when years down the road (maybe not even..pick up a recent version of the journal Science if you can and check out the self-replicating RNA discovery) a quite plausible explanation for the spontaneous generation of this molecule may be available. Does this mean God doesn’t exist? No! He never posited that he had to have created DNA in order to maintain his existence. But you and those following you might find that a crushing blow to one of the pillars you are leaning on to “prove” his existence. Don’t rest your belief in God on science, because science is (and this is very important) *incapable of posing the question as to whether or not God exists.* Do not be fooled, science can only ask *how,* not *why.* So please, review, read up, and think it through, and I warn you, it may lead to a recant of what you have published and spoke about. But true humility allows us to learn as we go and sometimes eat our words.
I fully understand the risks of my “god of the gaps” argument.
But I also fully understand the nature of information and codes. And I’m going to point to this gap until someone either bridges it, or people acknowledge that the only thing that bridges it is a prior Intelligence.
Please understand, if someone discovers a naturally occurring code, it will be the biggest discovery since Einstein. I’m not kidding. It would fundamentally alter our understanding of the universe and it would almost certainly involve new undiscovered laws of physics. The universe turns out to be even more marvelous than we previously thought. That doesn’t eliminate God, it only makes the original creation event even more impressive.
I’m fine if that happens. But for now I am arguing for the most parsimonious explanation.
If you study the atheist arguments against me, you’ll see the thick wall of anger and denial that prevents them from even acknowledging the gap that is there. Which is sad.
I respect your view but I’m following the evidence wherever it leads.
vYzion, there are many flaws in your logic. But I wish to address only one of them. You speak of “the universe” as if it is not the “space-time continuum”. But that’s precisely what it is. Being that it is a space-time continuum, time is an integral part of it. In fact, time cannot exist outside of it. So, for God to exist outside the space-time continuum, it is the very definition of timeless. Therefore, time cannot be applied to God. Therefore, there is no such thing as “before God”. The mystery to me is how God, in timelessness, was able to make any decision, let alone the decision to create. More than that, the Bible says that he created by speaking. How can speech even work when time does not exist? How can speech work when air does not exist? Those things blow my mind. But for you to insist that something had to precede God requires an assumption that God be subject to time. And since he created the space-time continuum, you have made a false assumption. Therefore, all conclusions drawn from this false assumption are, by necessity, also false.
vYsion, if you wish to reply please use your full first and last name.
Apologies. I never received the email that said you commented on my posts. Sorry about that…don’t know what the issue was.
That being said…on to the interesting stuff.
“circle” is an explanatory device that makes Gödel accessible to regular people. It’s appropriate because Gödel speaks of “within the theory” and “outside the theory.”
Like I said…it’s a really bad picture. It gives the impression that the
theories are just sitting there, in some spooky ontological space, waiting
to be circumscribed, and that’s not the case. Not to mention, that there is
often intersections of theories. A single wff may very we be a member of
two distinct theories (i.e. a songle circle can’t be drawn around them).
Even worse, however, Godel’s theorems imply that you CAN’T draw a
circle around the theories. One of the post-Godel consequences is that
it’s impossible to list all the wff’s of quite a large set of theorems. If we
can’t list all the wff’s, then there’s no way a circle can be drawn. Your
circle basically “sets aside” a set of wff’s and says here is one theory.
But this simply can’t be done. In fact, it can’t even be done for
mathematics. Furthermore, you circles give the impression that a theory can prove that it has consistent subsets…but this is forbidden by Godel. E.g., if B is the circle around A, then A is a subset of B. Thus, B cannot prove the consistency of A. If anything, A and B would have to be disjoint. The circles just really aren’t all that in tune with what Godel is saying.
I cannot prove the universe is consistent. I can only point out that science assumes that it’s consistent and philosophers assume that reason and logic do apply to the universe. Without that assumption, all human belief systems unravel.
No…science doesn’t assume the universe is consistent…science
assumes that events in the universe are regular. Science assumes that the future will resemble the past in relevant ways (i.e. gravity will always operate in the same fashion). Science then assigns linguistic expressions to those regularities. Consistency and regularity are not the same thing. Furthermore, as stated above, consistency, in a logician’s sense, merely means that a formal system cannot prove both a statement and it’s negation (i.e. P & ~P). In other words, consistency is a property of sets of statements, not sets of empirical objects. e.g., A table, the thing you eat dinner off of, cannot be true or false. The things we SAY about the table can be, but not the table itself. And your stereotype about philosophers assuming that logic and reason apply to the natural world is wrong. There have been, and still are, very many opponents of logic. In fact, nearly every continental philosopher denies logic the place that it is given by the analytic tradition (Culturally, this is the tradition you, and most nearly every American, has been immersed in…it’s the tradition that shapes our school systems etc.) People like Heidegger, and even the later Wittgenstein, vehemently opposed the what they viewed as a morbid fascination with Frege/Russell’s logic. And no, it is false that all belief systems unravel without these analytic assumptions. Most Asian philosophies deny these assumptions (e.g., Bhuddism). Hegelian philosophers (and to some extent Medieval logicians) actually embrace contradictions, which are abhorred in the analytic tradition. And not even all analytic philosophers share the same assumptions. I myself deny the law of excluded middle (as do many other philosophers who do work in Quantum Mechanics) and there is work being done in three-valued logic systems. Even more fundamentally, your own position doesn’t allow you to say such things as “all human belief will unravel.” I assume what you mean is that all human belief will become inconsistent (the other choice would be that humans would fail to believe anything). However, this is not a claim you would be allowed to make…unless you have some unique vantage point outside
of your “universe” circle (or do you think that human systems of belief are outside of the universe circle?)
Yes, I am stepping outside the universe (do we not implicitly do that when we say “big bang” or contemplate what else might exist outside the universe?) and then yes, stepping inside to find unprovable truths. All the laws of physics are unprovable truths.
No…we do not step outside the universe when talking about the Big Bang. That’s like saying I step outside my body when I talk about my birth. And I can contemplate unicorns day and night…doesn’t mean there are any unicorns prancing around. So why does contemplating “what’s outside the universe” involve stepping out of it? No matter how hard I contemplate, I’m not going to see a unicorn, and you’re not going to step outside the universe. You obviously haven’t read Kant. And the laws of physics aren’t unprovable truths. They are certainly unprovable, but I’m not sure in what sense they are true. Because we say so? But even aside from the semantic difficulties of such a claim, you still have to contend with the “pessimistic induction.” I’ve seen nothing on your site that leads me to believe you even know what it is.
And yes, Gödel implies that the universe makes statements that cannot prove themselves. Isn’t this rather obvious to the naked eye?
No, it’s not obvious to the naked eye. Perhaps you could give me an example of a statement made by the universe? But it seems, that your saying this destroys your ENTIRE ARGUMENT. A statement would definitely be a code. All codes from conscious beings (I won’t even delve into the difficulties associated with the concept on consciousness…but it’s suspect at best). Therefore, the universe cannot make statements (since it is not conscious…and if it were, then it could make DNA all by itself, no God required). Maybe God can make statements…and maybe the universes is one of those statements. But statements can’t make statements…can they?
If strings of symbols have objective meaning, then Gödel infers not merely proof models but truths.
Not sure what you mean by Godel infers (I think you mean implies)…but in either case, you’re wrong. Godel’s theorems are proof theoretic. That is uncontested fact. In fact, that’s why he was able accomplish the “arithmetization.” And why should I assume that a string of symbols, ANY STRING WHATSOEVER, has objective meaning. This is blatantly false. strings of symbols don’t have objective meaning. Meaning is given by a community. The reason my sentences in this post have meaning is because the community of English speakers have ascribed meaning to the words I used. In fact, a “symbol” is an object that stands for another object. For your argument to work, a conscious mind must ASSIGN meaning to symbols. But whenever meaning is assigned, it’s clearly not objective. Seriously, how can a thing stand for another thing, intrinsically? You should read Hilary Putnam. (Something similar to this is the problem with you “Random Mutation Generator” which sadly, I can’t find a spot on your site dedicated to comments about it. However, it doesn’t do what you think it does.) Seriously Perry, if strings of symbols (codes) had objective meaning, then that means that DNA can stand for a human all by itself…no God required.
We can make statements about God with mathematical symbols, we don’t need to use natural languages. Gödel did this with his ontological proof.
Actually, we can make mathematical statements, and then claim they are about God, just like we can say F=ma and claim it’s about the world. But this is not the same thing as saying that such statements intrinsically reference God or the world. Like I said in my first post…there are merely interpretations. The symbols themselves are meaningless. And Godel’s Ontological Proof uses modal logic. Mathematics is not modal. The truths of math are necessary, therefore Godel’s ontological was not mathematical. I hope you aware that math and logic are not identical. The logicist project failed. Granted, there is significant overlap, but math is not reducible to logic.
Thus I don’t see that you have demonstrated that Gödel has nothing to do with the issues I’m trying to address. If the universe is as mathematical as physicists assume, then Gödel’s theorem makes a statement about the universe.
I don’t know what you mean by saying that the Universe is mathematical. As it happens, physicist have chosen mathematics to express regularities they happen to stumble upon, but this is an accident. They could have chosen a qualitative language to talk about such regularities (like Aristotle did). Also, the math used by physicist has changed quite a bit over the years. Prior to Newton they used algebra (and there science before algebra as well). Then Newton and Leibniz invent Calculus. Relativity and QM use Differential Equations. So, it’s not even true that all physicist would mean the same thing if they said (and I know none that do) that the universe is mathematical. Being mathematical, and being expressible with mathematics, is not the same thing. I describe a certain sensation as being “cold.” But that doesn’t mean that the sensation is ‘c-o-l-d’ like. The word “cold” and the sensation of cold have nothing in common. You seem to think that the meanings of words (and math expressions) somehow magically live inside the expressions themselves. Kind of like how Voodoo practitioners think that knowing someone “true name” gives you power over them. As if the word and the thing the word refers to are magically connected. They aren’t.
I’m sorry Perry, but you are simply not well versed enough to utilize the stuff you’re trying to. There is massive amounts of literature on meaning, logicism, semantics, language, referring, ontological status of mathematics, metaphysical status of scientific theories, epistemological implications of Godel, the concept of “truth” (I don’t even know what you mean by “truth,” are you a pragmatist, a foundationalist, a coherentist, an internalist and externalist??) and a host of other things, and you don’t appear to have read any of it.
The problem with an interdisciplinary approach, is that you actually have to be competent in numerous disciplines. I’m sure you understand computers well enough, unfortunately, your seriously lacking in these other areas I’ve pointed out.
If there is an “inside” and an “outside” then there is a boundary. You can call that boundary a circle, a sphere, a box, a region or a distinction. But now matter how you describe it there is still an inside and an outside.
Returning to Godel’s original statement:
Gödel’s theorem says: “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”
The Church-Turing thesis says that a physical system can express elementary arithmetic just as a human can, and that the arithmetic of a Turing Machine (computer) is not provable within the system and is likewise subject to incompleteness.
Any physical system subjected to measurement is capable of expressing elementary arithmetic.
Therefore the universe is capable of expressing elementary arithmetic and like both mathematics itself and a Turing machine, is incomplete.
I am probably incorrect in saying that “without assuming reason and logic apply to the universe, all belief systems unravel.” You are certainly correct in saying there are belief systems that deny various aspects of reason and logic.
Rather I should say that without the assumption of a logical universe, the western scientific belief system unravels.
When you talk about your birth you refer to that which is outside of your body. And when you talk about the origin of the universe, then if you believe in cause and effect, you refer to that which is outside of the universe.
Does the universe make statements? You caught me on that one. One point for you. No, strictly speaking, the universe does not make statements. Conscious beings do. And yes, there is an infinite chasm between consciousness and non-consciousness.
The universe does do computation, however. Children can do math by counting their fingers, water flowing into a bucket does integration, and physical systems always give the right answer. The computations it makes have to be taken as axiomatic. Isn’t that what is implied when you ask what it means for the laws of physics to be true?
If you reject scientific realism that is your decision. Most of my intended audience embraces scientific realism as do I – at least cautiously. I do understand the difference between your position and mine.
If meaning can only be assigned by a community then is there any objective way to determine if a community exists? Or do you have to take the community as axiomatic?
Does meaning exist or not?
In my definition, Meaning objectively exists when there is agreement between an encoder and a decoder.
Your choice of the word “cold” is a poor one because it’s not a mathematical term. -170 degrees C is a mathematical term and it has very precise objective meaning. And it doesn’t matter exactly what kind of mathematical system a physicist chooses to use to describe the universe, or if he uses Kelvins or Fahrenheit, mathematical systems of symbols do match the behavior of the universe.
I suggest that you try walking into a room of engineers or physicists or chemists and tell them that they really don’t know what they mean when they say that they use math to describe their work. I think they all know exactly what they mean. They all weigh things, count things and measure things, and it’s all exactly mathematical. You’re being flippant about this and I’m not sure why. If you think you can do science without math, then shoot us a video and post a link.
I’m sorry if this sounds judgmental but it sounds like the abstract philospher-speak of someone who’s never worked in a lab.
Hi
nice job. I have no question to ask. I’m a christian orthodox.
First of all I think no one can prove (scientifically) the existence of God. Faith does not need science to prove it. You can prove that the atheistic theories are false (because they really insult intelligence) but nothing more. Atheists will come with other theories more sophisticated.
Do you know what is the etymology for “theory” ? ( Theo – God – ria – sight , view) Sight of God – so to be correct there can be only one. We can make no theory, just thesis.
I’m an engineer too (aircraft designing) and the most beautiful (mystical) description of the Genesis I found reading the work of Dyonisos of Areopag (lived around 400 AD).
Gabi
Because of the existence of working consistent non-euclidian geometries, this part of the text is completely false and invalidates the conclusion of the author:
“The Incompleteness of the universe isn’t proof that God exists. But… it IS proof that in order to construct a consistent model of the universe, belief in God is not just 100% logical… it’s necessary.
Euclid’s 5 postulates aren’t formally provable and God is not formally provable either. But… just as you cannot build a coherent system of geometry without Euclid’s 5 postulates, neither can you build a coherent description of the universe without a First Cause and a Source of order.”
non-euclidian geometries are just as incomplete as euclidean geometries.
That is an irrelevent comment that does not refute my point. You say that we cannot build a coherent system without believing the 5 euclidian postulates which is blatlantly false! We can build many coherent incomplete systems geometry as we can build many coherent incomplete systems explaining the universe.
Finally, you base your spectacular conclusion that we cannot do cosmology without postulating a first cause and a source of order on that falsehood.
Any 7 years old with minimal logic can debunk you! what a shame.
Actually, Freddy, you can build an infinite number of coherent (by which I assume you mean internally consistent) geometries with only some, or even none, of Euclid’s postulates. In fact, Einstein chose a non-Euclidean geometry for his General Theory of Relativity.
And Perry, not all geometries are incomplete, and many don’t meet the criteria to fall under the scope of Godel’s Theorems. (David Hilbert was the first to prove the completeness and consistency of Euclidean Geometry in his landmark book “Foundations of Geometry.” Later, Tarski and his students proved that Euclidean Geometry can be expressed as a first-order theory that is both consistent and complete. The reason this isn’t a violation of Godel is because the FOT does not describe a sufficient amount arithmetic (see my earlier post on what constitutes a sufficient amount).
That being said, there is a sense in which Absolute geometry is “incomplete” (you can can add axioms ad infinitum…i.e., there is no finite set of wffs), but this is not the same type of incompleteness the Godel is talking about. Godel is talking about NEGATION COMPLETENESS which means that for any wff A, either A or ~A is provable in the system (I’ve actually explained this in a previous post). When Godel says, ala the Incompleteness Theorems, that a system in incomplete, he means there is some wff A such neither A nor ~A is provable in that system.
I would recommend that you do some historical research on the foundations of mathematics, mathematical logic, logicism, axiomatization of geometry and math and a whole lot more. All this stuff is inextricably intertwined with the rise of analytic philosophy, and each other, and those names you dropped in your article (and I now convicned that name dropping is all it was) were the developers of this stuff. They spent their entire careers formulating all this and you act as if you have condensed everything, accurately, in a mere 3 paragraphs. It’s painfully obvious to anyone that actually works in this field that you have never once read any of their original works.
Alberto Coffa’s “The Semantic Tradition from Kant to Carnap” offers one of the most lucid, not to mention entertaining, expositions to all this stuff. He masterfully ties together the work of the people you mention in your article (and others that you don’t e.g., Tarski)and explains the implications and correlations their projects have for each other.
Also, read a logic textbook (wikipedia just doesn’t cut it…”Language, Logic and Proof” by Jon Barwise and John Etchmendy is the industry standard.) When your familiar with that material, then you need to read a book on meta-logic (Godel’s theorem is a meta-logical one). Geoffery Hunter’s “MetaLogic” is the standard text. It comes complete with the Godel’s actual proofs, and the requisite proofs leading up to them. You should also take a look at “Godel’s Theorem: An Incomplete Guide to Its Use and Abuse” by Torkel Franzen (it’s written for the layperson with basically zero specialist knowledge in logic…but it will be more rich if you actually do have elementary knowledge).
It would be obvious to you if someone wrote a networking book with no networking knowledge other than the name Cisco Systems. It’s obvious to logicians and and mathematicians that you have no knowledge of these matters or the people that formulated them.
Please, learn the knowledge that you are trying to use from the creators of that knowledge and qualified commentators of that knowledge.
P.S. Here is a link to a pdf copy of the Language, Proof and Logic textbook.
http://ssdi.di.fct.unl.pt/~pb/cadeiras/lc/0102/lpl%20textbook.pdf
I am in agreement with vYzion. Perry should discard his arguments for the existence of God based on Godel’s Incompleteness because his arguments do Intelligent Design an injustice just because his agruments are so naive.
“The information had to come from the outside, since information is not known to be an inherent property of matter, energy, space or time.” But, let’s say that information is an inherent property of matter, energy, space, or time. Why should it not be? “We don’t really understand the origin or perhaps even the true nature of information” does not actually connect logically to “It had to come from the outside”.
“The codes that we make come from us, so anything that makes codes has to be like us” as proof of a self-aware First Cause is specious. It relies on some unexamined assumptions about what awareness is and is just shaky, overall. “Every code maker we know has fingers, so, all codes must be made by something with fingers” is equivalent.
The imaginary exercise of putting circles around things and declaring rules about how that process works is a bit bizarre. “You can put a circle around an effect”. Hm. You can put a circle around “an uncaused cause” , “a self-conscious code-maker” , “an indivisible unbounded outside-of-circley-thing”. You can put circles around infinity, and circles around things-that-can’t-be-put-in-circles. This is just verbal three card monte.
Hi Perry (Mr Marshall)
After reading the article, it confirms something that I have believed basically my entire life. Except for 1 thing, I do not think that God = Father + Holy Spirit + Son + Love, I would rather say that God = Father + Holy Spirit + Son = Love. After all – isn’t God = Love? You actually say the same thing in one of your answers.
This is my first post to one of your articles. And by the way – thank you for putting words to something I have believed – regarding all your articles – but could not express properly as I said before – basically all my life.
All my best,
Warwick
Good thoughts!
Dear Perry,
Please see this knol.
http://knol.google.com/k/dmr-sekhar/the-primacy-of-dna-as-a-unit-of-life/3ecxygf1lxcn2/32?hd=ns#
If you say,” I am existing”. Should one ask you for a mathematical proof for what you said?
Thanks,
Sekhar
@ Perry you still got Galileo’s last name wrong which helps little with the credibility of your attempts which at most was laudable.
@vYzion You seem to have given Perry a filibuster with all the lists of books he should read but frankly one doesn’t need to read entire Library of Congress to understand Perry’s motives. He used a friggin watered down analogy for God’s sakes. Jesus! And regarding LOGIC – to which you seem to be great awe- that was Perry’s point exactly. LOGIC is based on BELIEF. LOGIC is a closed system and unless you step outside of that system, there will be certain things which will remain unprovable. That was Perry’s point if I am not mistaken. You, on the other hand, gave an aura that LOGIC is the be-all-end-all of all universe yet the fact remains LOGIC is vulnerable to many attacks that many religious systems are. Yes, Godel’s Incompleteness Theorems don’t prove the existence of God but it does show that one has to transcend the system at some point because of it’s inconsistencies.
And speaking of Godel and God, are you aware of the fact that Godel himself proved the existence of God using modal logic? And I read Franzen’s book on use and abuse of the theorem but the author seemed to be more worried on trying to lay down his personal agendas. For those who wants to read the other side of the coin, give Penrose a go.
Perry, I understand your logic, but you skipped a step. Godel’s theorems didn’t apply to knowledge or logic in general, they specifically applied to natural numbers. I think it’s valid to extend the principles of his theorems to other systems of thought/logic than mathematics, but that would require considering the differences between math and other systems of thought, something that you don’t seem to have covered. Apart from being clear about the similarities and differences between math and for example logic or theology, we don’t know whether extending aspects of Godel’s theorems is appropriate, not appropriate, or how much of either.
Godel’s theorems apply to everything that logic applies to, because his original liar’s paradox is a logical statement. He coded it as a natural numbers problem but it applies to all logic.
[…] Gödel’s Incompleteness Theorem applies not just to math, but to everything that is subject to the laws of logic. Everything that you can count or calculate. Incompleteness is true in math; it’s equally true in science or language and philosophy. via evo2.org […]
Hi Perry, let me say first that I enjoy your writing and think your arguments are generally sound. (Here it comes!) But, in your Godel post you say: “Faith and Reason are not enemies. In fact, the exact opposite is true! One is absolutely necessary for the other to exist. All reasoning ultimately traces back to faith in something that you cannot prove.”
I have several quibbles. First is the equivocal use of the word “faith.” Faith in the 21st century generally means to have a firmly held belief for which there is no evidence. (http://www.merriam-webster.com/dictionary/faith) This is not what the Greek word used by the writers of the New Testament meant when they used the word. Faith in the NT almost always means one of two things. Either an act of the will, that is, to make a choice, or, a body of doctrine that is believed – based upon reason and evidence. Saying “faith” today is like announcing you are a moron. What person in his right mind would hold a firm belief in anything without any evidence at all?
The second is more serious. To say that reason ultimately traces back to “faith” is simply wrong. Perhaps a discussion of first principles will help. When I say that reason is the sovereign of truth, that statement is undeniable. Why? Because to deny it creates an internal contradiction. To argue that reason isn’t the authority in truth claims is to reason against the effectiveness of reason.
Reason is based on axioms, or first principles, this is true. But these principles do not rely on “faith.” They are self-evident. They do not admit of proof. They require no proof. To deny them creates contradictory statements. We directly experience them with our minds. The first principles of reason are being and identity. That something exists is the most fundamental thing that can be said of anything and existence cannot be denied. I cannot deny my existence without demonstrating that I do exist. No further proof of my existence is required. Anything that exists also has identity. It is what it is. Nothing can have identity without existence and nothing can exist without identity. The law of non-contradiction follows from this. If something is what it is, then it’s not also something else. It can’t be. It’s impossible. God can’t be God and not God, for example.
It really bothers me that more Christians don’t understand this. The idea that 21st century “faith” is Biblical in any way shape or form is nonsense. The entire book of John is written around 8 miracles of Jesus that PROVE He was who He claimed to be. We are never told to believe without evidence. Never.
In fact, God revealed Himself as the Personification of Reason in Exodus 3:14. He said “I AM WHO I AM.” In John 8:58 Jesus said “before Abraham was, I am.” God is the ultimate Being and Identity. He is the ground of human reason and that’s the reason that reason leads us to truth.
Therefore, I claim that all reasoning ultimately traces back to things that CANNOT BE DENIED, that is, First Principles, and ultimately, God.
The word faith doesn’t mean “moron” to everyone, not even the dictionary. I use it in the sense that the New Testament uses it. And I fight for a public understanding being exactly that.
What I am really saying is that faith and reason are intertwined. You CANNOT separate one from the other. I think we are actually very much in agreement and I’m using Godel to show that the biblical idea of faith is necessary to practice both science and mathematics.
“All reasoning ultimately traces back to faith in something that you cannot prove.”
therefore:
“…faith and reason are intertwined.”
this is just semantics, drawing on the idea that one can never actually PROVE anything, because there will always be a previous question (we can answer “how” but never answer “why”)… yes of course science emerged directly from religion (which can never be proven), but you can’t seriously be saying that having “faith” that the sun will rise in the east tomorrow is the same thing as having “faith” in an all-knowing and all-loving creator, right? I think maybe we need some new nomenclature…
also, probably worth discussing, is the difference between faith in modern times compared to faith in prehistoric or even prescientific times… before there were explanations for what thunder and lightning actually was, there was, in all likelihood, a simple a pervasive belief (or faith) that there was a supernatural hand at work in nature… who knows, maybe that idea was somehow reinforced in our genes so that to this day we instinctively appeal to some higher power when confronted with the unknown
you’ve argued before that in the absence of being able to fully prove something, making inferences is a reasonable alternative, so… we live on a planet, and there are other planets… our planet orbits a star, and there are other stars… our star orbits the center of our galaxy, and there are other galaxies…. our galaxy is part of the Local Group, and there are other galactic clusters…. our galactic cluster is moving through the expanding space of our universe, and there are other universes…..? how many possible circles can one draw?
if a being/spirit/god can be infinite, then why not the universe? I’d like to know what your views on the anthropic principle are, because if there were a huge or infinite number of universes, our orderly and life-friendly universe would be almost inevitable
the other statement that disturbed me was this:
“The information [genetic code] had to come from the outside, since information is not known to be an inherent property of matter, energy, space or time.”
every photon (wavelength/frequency) and quark (mass/charge/spin) inherently contains information, not to mention its vector and velocity, I’ve seen you state before that information is as fundamental an aspect of our universe as are matter and energy, and I agree… asking where the information came from is the same question as asking where the matter and energy came from, which is a fun thing to think about, but is 100% unexplainable, there can ALWAYS be a prior question, there can ALWAYS be a universe outside of our “circle” that doesn’t obey the same laws as ours
“faith” in axioms and “faith” in religion is NOT the same thing
The intertwined nature of reason and faith is clearly evident in the process of starting with intuitions and trying to prove things in mathematics. Scientific hypothesis is no different.
I want to be very clear in saying that Christian faith is much more similar to mathematical axioms than different. In fact it’s only different in the sense that belief that your mother really loves you and she’s not just fattening you up to eat you is also a kind of faith. I sincerely believe that you have a straw man conception of what faith actually is. Faith is not blind belief in something that can never be verified. Faith is a journey of hypothesis and discovery, knowing that there will always be some things out of your reach yet you can continually grow in understanding.
Why can’t the universe be finite? In theory perhaps it can. But we have no empirical evidence whatsoever of an infinite universe. We have evidence of a very finite universe of definite age, mass and size.
Photons, sunlight, etc do not communicate without the presence of a conscious observer. Take this list of things you mentioned and plug them into the model at http://www.naturalcode.org and see if you can demonstrate communication without that observer.
Perry, I am on your side but you need to understand that faith and reason are not “intertwined” except in so far that acts of the intellect (reasoning) precede acts of the will (faith). They are two different things. Reason is foundational to all truth seeking. It NEVER comes down to “faith.” Reason is based on first principles which do not need proof – they are self-evident, nor can they be proved, because they are FIRST. Love your blog. Keep up the great work. Thanks.
Tom
First things first:
I actually have a degree in Physics…just so you know. And, for the record, I should have made my assumptions transparent.
Yes, Perry, I am an anti-realist. That is, I don’t think there are such things as protons and electrons etc. These things are linguistic constructions that are defined completely and totally by mathematical symbolism. However, this view does not entail that I don’t believe physicists etc. don’t know what they are talking about. In fact, it’s the opposite…they know EXACTLY what they are talking about because THEY (or rather the community both past and present) have DEFINED them. There is nothing over and above an “electron” than the symbols that scientist use when talking about them.
And for the record, I’m not the only physicist that has held this view. Duhem was even less friendly toward Realism than I am. Ernst Mach (as in Mach 1 the speed of sound Mach) also held a view that denied the “reality” of protons etc. (He was actually a positivist whereas I’m much closer to a constructivist).
@Zeeshan…I actually don’t hold logic in awe at all. Logic has absolutely nothing to do with the way the world works. That is, the world does not follow “logical laws.” Logical laws do nothing other than govern symbol manipulation. And different logics manipulate symbols differently. It is impossible to empirically ground Deduction, that is, WHY should we believe Modus Ponens to be a valid form of inference (I refer you all to the wonderful, and short, Lewis Carroll essay “What the Tortise Said to Achilles”)? Which, yes, is Perry’s point. That at some point we “hit bedrock.” We must just SAY “we can go no further,” Knowledge is based on a decision, and here is where we decide to stake the foundation of our beliefs. (Actually, it was Wittgenstein, not Perry, that first expounded this view: Read “On Certainty” Carnap had a similar view that stemmed from his Principle of Tolerance.)
Now, for my responses:
1) You are really confused about what the Church-Turing Thesis actually does. The thesis says nothing at all about physical systems expressing mathematics. What the thesis does is provide a rigorous definition of an “effective,” or “mechanical” method. What the thesis states is that a Turing machine “can do anything that could be described as “rule of thumb” or “purely mechanical”.” Granted, the Turing machine is a physical system, but it’s not expressing anything. Imagine the Price is Right game “Plinko” where you drop the chip at the top and it tumbles over various pegs and reaches the bottom. What the Turing Thesis says is that those pegs can be placed in such a way that we can make the plinko chip fall onto any spot at the bottom we want. What exactly is the Plinko board expressing? You have basically read the thesis backwards…It doesn’t say that physical systems CAN express mathematics…it says that mathematics CAN BE expressed in physical systems. In other words, we can arrange the Plinko pegs (physical system) in such a way to express “5 feet from either edge of the plinko board.”(measurement). But the Plinko board isn’t doing any expressing in the sense of telling a child that 2+2=4. A sadness can be expressed in a painting, but the painting itself isn’t actually sad. The painting is merely a medium for the painter to express his sadness. (http://plato.stanford.edu/entries/church-turing/) If the physical system actually did the expressing by itself, that would more or less make it a codemaker in which case the physical system of DNA could very well “express itself.” P.S. What exactly is an “incomplete” Turing machine? An incomplete language is one where there is some statement such that neither A or ~A are provable. How does this carry over to an actual physical system? Is it one where they forgot to build the “on” switch?
2) No, belief in cause and effect does not place me outside the Universe. Cause and effect are spatially and temporally bound (at least in classical physics, QM may have a different story to tell). Cause and effect are aspects OF the Universe. IN our Universe every effect has a cause. This says nothing about outside our Universe. Why should we assume that cause and effect holds outside space and time? I grant that causes are outside their effects, but how does that in anyway point to an a-temporal/a-spatial being? Why assume the Universe (as a whole) is an effect? Further, why assume it is the effect of a single cause as opposed a bunch of them? If God is to be an un-caused cause…why is He a better candidate that the Universe? That is, if you grant that some causes do not themselves the effect of any other cause, then now you need to tell us why the Universe cannot fulfill that requirement.
3) And the Universe does not do computation. This is the same old confusion you had before with both the Turing Thesis and the claim that the Universe makes statements (which you have subsequently rescinded). When water flows into a bucket, there is no computation being DONE. Now, humans can come observe this process and DESCRIBE it with integration, but that’s not the same a saying that the Universe is integrating. The best you can get is that the Universe is describable by integration. If the Universe were actually DOING the integration, that would, it seems, amount to quite a complex statement by the Universe, which you have recently conceded is not possible.
4) About linguistic communities. Well, the development of language is still being studied, but it’s hardly controversial that language is a community endeavor. (See Wittgenstein of Private Language). So do I take the community as a given (axiomatic as you put it)…Depends on what you mean by “axiomatic”. I certainly maintain that community is a necessary component of a language. That is, no community, no language. But, I don’t see any reason to think that there need actually be any communities (that is, I can construct worlds without them)…there just wouldn’t be language if there weren’t. As for objectively determining the existence of communities, of course there is. Go out and talk to people. If you can match certain behaviors to certain utterances that are widespread amongst a group of people, then you have a community.
I’m really unclear on what you mean by “agreement” between decoder and encoder. First, the encoder spits out 1’a and 0’s while the decoder spits out sentences about foxes or whatever. So, clearly they won’t have a 1 to 1 match on symbolism (so that can’t be what you mean by agreement). Certainly you don’t mean that they come together, discuss the issues, come to decisions and then go back to the business of sending and receiving messages in accordance with what they decided. So, you must mean something like “If the encoder correctly reproduces the phrase inputted in the encoder.” But, in that case you have introduced a third party…someone, or something, must judge whether or not the phrases are, in fact, in agreement. This would seem to make it no longer objective. I’d be interested in hearing more about this objective”arbiter” of meaning.
5) And the word “cold” was just fine for my point (which you apparently missed). I agree 100% that -170 degrees Celsius (and all other technical terms of science) have exact meaning. I further agree that scientists by and large know what those meanings are. But that’s not my point. My point was that the symbols “-170 degrees Celsius” do not INTRINSICALLY mean anything. If I were to look at the ground one day and find that an ant had made the markings “-170 degrees Celsius” on the ground, would the marking mean anything? It seems not. The reasons scientist know so well the meanings of the terms they use is because they themselves (and their forerunners) IMBUED them with meaning. It’s not as if the work of a scientist to discover what “electron” actually means. The work of science is to DEFINE what it means. They go to the lab, record various things, and then label it electron. They don’t put the symbols “electron” through a barrage of tests in order to find it’s ‘objective’ meaning. The perform a barrage of tests and name their results “electron.”
6) And just because science CAN be done without math, doesn’t mean it should be done. I agree that the TOOL of mathematics is very useful. But it is just a tool, same as microscopes and centrifuges. Math is not some omniscient eye that allows us to peer into the fabric of reality. Math was created the same way as microscopes and telescopes. Started of simple as a way to fulfill a certain need (keeping track of livestock?) and evolved and developed as more needs came along. Math allows us to do many wondrous things and I seriously doubt science would have progressed so far so quickly without it…but it’s still possible to do science without Math. In fact, we did it as kids all the time. I’ll leave it to the reader to find his own examples, but they are plentiful.
Thanks for clarifying your philosophical position. If I think of a way in which it prevents us from understanding each other I’ll say so but for now I don’t think it does.
Yes, mathematics can be expressed by physical systems, but physical systems are not speaking or producing symbols.
What I say in my article is:
“Any physical system subjected to measurement is capable of expressing elementary arithmetic.”
Yes, this does require a conscious person. They may have to show up with a yardstick or a weigh scale. But the physical system does the computation and gives them the result. All they have to do is make a measurement.
You said:
“P.S. What exactly is an “incomplete” Turing machine? An incomplete language is one where there is some statement such that neither A or ~A are provable. How does this carry over to an actual physical system? Is it one where they forgot to build the “on” switch?”
From http://en.wikipedia.org/wiki/Undecidable_problem:
“In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes-or-no answer.”
The Turing halting problem is a good example.
A physical system cannot prove the consistency of physical laws that govern its own behavior. It cannot prove that if unmodified, it will still do the exact same thing tomorrow under identical conditions.
You asked:
“Why should we assume that cause and effect hold outside of space and time?”
We can only infer this based on what we do have experience with. One can only take the logical behavior of the universe as axiomatic.
As I’ve said, you can reject the notion that the origin of the universe is subject to cause and effect and rational laws. If you wish to reject rationality, that is your decision. You can choose to believe that a universe can pop into existence for no reason at all without any prior cause.
I say that is irrational. I choose to embrace rationality and because of that I assume that the universe has a cause.
Why isn’t the universe itself an uncaused cause? Because its age is finite. We know this because of entropy. If you walk into a room and see a candle burning, you know the candle has not been burning for an infinite amount of time.
Agreement between encoder and decoder: It can only be judged by an outside observer who is capable of inductive and deductive reasoning. However since human beings exist then observations about this are available to us. In living things we can infer and deduce the operation of the genetic code and we can observe cell replication errors and DNA copying errors and objectively classify them. In computers we can press the letter A on the keyboard and see an image of a letter A on a screen.
Encoders and decoders, symbols and 1:1 correspondence between certain inputs and certain outputs is confined to the realm of living things and human designed mechanisms. They are not known to exist outside of that world.
Sorry…one more thing (I thought this was on another thread):
No, Perry, Hume’s point was not that a watch/living thing analogy was poor. The watchmaker analogy was first published by William Paley in 1802. Hume’s Dialogues were published in posthumously 1779. So, unless Hume could see into the future, then it seems rather unlikely he was responding to an argument that had yet to be given. In fact, there is no mention of watches or machines at all in the Hume Dialogues.
Hume’s point is that you can’t infer a supernatural cause from natural effects. His point was that when you look around, all you see are finite things. Everything is temporally and spatially bound. Thus, your inference to an unbounded infinite being is not warranted. He then goes on to give some pretty entertaining alternatives to the Omnipotent God inference. So, even if I grant you that DNA is a code, AND I grant you that codes can only come from sentient beings (things with minds), then it still doesn’t get you what you want. It very well could be that Earth is an Alien petri dish.
(And before you cry “foul” for pushing the problem back a step, notice that I have not done that. I’ve only pushed it back a step if we assume that the Aliens have DNA. You have given no reason to make this assumption. You need an argument if you wish to say that ALL living things have DNA. Granted, on Earth this is true, but why should it be true in general? Why must our Alien designers be DNA-based? Why must they have developed from a “code” of sorts. Once again, even if I grant you that life on Earth is “coded,” it doesn’t follow that the this is true of life generally. Perhaps DNA is their experiment in order to better control the evolution and design of “life.”)
So, even if I grant you everything you need, you still don’t get anywhere close to where you want to be. You’re just as far away from God now as you were when you started. At best, you may be able to show that there is A designer…but you cannot say anything further than that designer has an intelligence (maybe more, maybe less, than our own (e.g., he may have discovered DNA by accident…sorta like bubble gum was)).
You have not refuted Hume. You don’t even know what he said!
Sorry, Perry, but this is really disappointing. Either you didn’t actually read the Hume (in which case it seems as if you are not really interested learning the issues well enough to have a quality debate) or you didn’t understand it (in which case it seems you are not really qualified to be debating since this is standard material in this area).
And don’t worry about sounding judgmental. I take no offense 🙂
You are correct, Paley lived after Hume. So yes I’m sure I sound stupid referring to Hume as though he came later.
Nevertheless, in all kinds of websites and discussions of this, including Wikipedia, Hume’s arguments are used against Paley’s. In the context of modern discussion, which argument came first doesn’t matter much because each is pitted against the other. The two arguments are mutually compatible.
So let’s look at my syllogism:
1. The pattern in DNA is a code.
2. All codes we know the origin of are designed.
3. Therefore we have 100% inference that DNA is designed and 0% inference that it is not.
Where in any of Hume’s writings does he ever get around this?
You yourself, in taking the alien route, have confirmed my own logic on this. You are perfectly free to take that route. You can choose to assume that the information in DNA came from an alien.
I have not necessarily assumed that the alien has DNA. However you certainly do seem to be assuming that the alien is a conscious being. Is it not true that all codes we know the origin of are designed by sentient conscious beings who speak language and are capable of making the symbolic choices necessary? Isn’t that why “alien” is a fairly obvious choice? The task of designing DNA would ostensibly have to be accomplished by the likes of some creature such as we see in movies.
If you can demonstrate the existence of aliens, you’re certainly one step closer to solving the problem. Can you?
If you can demonstrate a physical process not involving designers or DNA that produces conscious beings, you’re off the hook. Can you?
Show me a code that’s not designed. All you need is one.
Hey,
I thought you might like to know about my mathematical work connecting geometry and algebra to the modal logic of Gödel’s Incompleteness theorems. His theorem states that within a logical, rigorous system, there is a statement that is true, but cannot be proven within this system. This is true for algebraicization of Euclidean geometry. Please see:
http://www.scribd.com/mathangle for more information on this.
You can solve for the innate velocity within the Lorentz transformation, and this is what I’ve done. You show that from the difference in circumferences of two circles equaling an arc length of the initial circle (the theorem is provable), that the initial radius depends on the angle taken out of the initial circle, which is not provable simply by Euclidean geometry, but true from having been proven through algebra.
I have videos of my 3D art from this univocal system at:
http://www.iphonescan.com
[quote]Since God is one and indivisible, God is not complex thus God does not have this problem. God is not a system and is not made of divisible parts. See the conversation I had with Derek about the nature of what is outside the circle.
The conclusion I have made is a logical outworking of the premises and the steps of logic. If you disagree, then identify the specific mistake I have made in my logic.[/quote]
Pretty circular reasoning…based on a man made defintion.. mate.
meant to say
I’ll tell you what it is indivisable by…a big fat ZERO.
I.e so saying that god,if it is inded 1,is indivisable is not true..ie God is indivisable by zero is true