Just ignore the fact that logic can't say what is the truth:
Two scientists have formalized a theorem regarding the existence of God penned by mathematician Kurt Gödel. But the God angle is somewhat of a red herring -- the real step forward is the example it sets of how computers can make scientific progress simpler.
As headlines go, it's certainly an eye-catching one. "Scientists Prove Existence of God," German daily Die Welt wrote last week.
But unsurprisingly, there is a rather significant caveat to that claim. In fact, what the researchers in question say they have actually proven is a theorem put forward by renowned Austrian mathematician Kurt Gödel -- and the real news isn't about a Supreme Being, but rather what can now be achieved in scientific fields using superior technology.
When Gödel died in 1978, he left behind a tantalizing theory based on principles of modal logic -- that a higher being must exist. The details of the mathematics involved in Gödel's ontological proof are complicated, but in essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.
Even at the time, the argument was not exactly a new one. For centuries, many have tried to use this kind of abstract reasoning to prove the possibility or necessity of the existence of God. But the mathematical model composed by Gödel proposed a proof of the idea. Its theorems and axioms -- assumptions which cannot be proven -- can be expressed as mathematical equations. And that means they can be proven. This is the flaw---theorems and axioms cannot be proven just because they can be expressed as mathematical equations because they are assumptions. It's also a non sequitur in logic.
Proving God's Existence with a MacBook
That is where Christoph Benzmüller of Berlin's Free University and his colleague, Bruno Woltzenlogel Paleo of the Technical University in Vienna, come in. Using an ordinary MacBook computer, they have shown that Gödel's proof was correct -- at least on a mathematical level -- by way of higher modal Just because it is new doesn't automatically make it prove anything about the truth.logic. Their initial submission on the arXiv.org research article server is called "Formalization, Mechanization and Automation of Gödel's Proof of God's Existence."
The fact that formalizing such complicated theorems can be left to computers opens up all kinds of possibilities, Benzmüller told SPIEGEL ONLINE. "It's totally amazing that from this argument led by Gödel, all this stuff can be proven automatically in a few seconds or even less on a standard notebook," he said.
The name Gödel may not mean much to some, but among scientists he enjoys a reputation similar to the likes of Albert Einstein -- who was a close friend. Born in 1906 in what was then Austria-Hungary and is now the Czech city of Brno, Gödel later studied in Vienna before moving to the United States after World War II broke out to work at Princeton, where Einstein was also based. The first version of this ontological proof is from notes dated around 1941, but it was not until the early 1970s, when Gödel feared that he might die, that it first became public.
Scientists have "proven" God's existence, at least in theory, by plugging in mathematician Kurt Godel's philosophy on their MacBooks. As noted by Spiegel Online, however, what the two computer scientists did was more of display of what can be achieved in scientific fields by using greater technology rather than verify the existence of a Supreme Being. The story, however, has become a sensation with headlines like "Scientist Prove Existence of God," going viral on the Web.
Godel was an Austrian mathematician who, in 1978, left behind a theory, This is a conjecture and not a scientific theory! which essentially says that a higher being must exist if people believe He does. So there you are---unicorns, flying saucers, all the gods of history, all the stories in Scripture, astrology all are facts now since there are people that believe they are true. :roll: Though the mathematics are much more complex, God exists as a concept, than he can exist in reality. So every concept anyone has, even the insane, actually exists. Is there any kind of logic that is dumber than this? Yes, they exist, in a persons mind, that doesn't mean it exists outside of it in the world of reality we live in. All this so-called proof of God shows is that the belief in God is imaginary and a delusional belief. It actually proves God or gods don't exist accept in people's minds. :roll: :lol:
According to CNET via the Inquisitr, the complication theorems and axioms boil down to this: "God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist."
It's not the first attempt at rationalizing the abstract idea, but computer scientists Christoph Benzmüller of Berlin's Free University and his colleague, Bruno Woltzenlogel Paleo of the Technical University in Vienna, put a new spin on it, Spiegel Online wrote.
Armed with their MacBooks, the scientific duo showed Godel's proof was correct. "It's totally amazing that from this argument led by Gödel, all this stuff can be proven automatically in a few seconds or even less on a standard notebook," Benzmüller told Spiegel Online.
The original purpose of Benzmüller's work was to show how advanced computers have become. He added: "I didn't know it would create such a huge public interest but [Gödel's ontological proof] was definitely a better example than something inaccessible in mathematics or artificial intelligence. ... It's a very small, crisp thing, because we are just dealing with six axioms in a little theorem. ... There might be other things that use similar logic. Can we develop computer systems to check each single step and make sure they are now right?"
:roll: :rollin: :rollin: :rollin: Solitary
the obvious of course is "which god is proven" and the answer of course is "none of them". I would like to suggest my answer to this conundrum to the xian argument. They would hold to the principle that no greater can be conceived. However the simplicity of the counter argument is often overlooked. We CAN conceive of a greater. How? BY a god that is NOT jealous, NOT envious, NOT angry, NOT homophobic. Why do humans champion the behavior in a god that we detest in human behavior? Because we think that because humans are "flawed" a god has a right to be all the lesser of human behavior, which is the best reason that a god is not a god.
Even beyond conceiving of better gods than any of the currently known ones, it's perfectly possible to conceive of things that cannot possibly exist in reality that are still greater than any current understanding of god.
I do not understand how something that is by definition limited by the laws of reality could be the greatest conceivable thing, when there is a huge playing field where we aren't bothered by silly laws of reality to conceive things in.
Are you going on about Gödel's incompleteness theorem again?
All Godel's theorem says is that a given mathematical system is based on a number of axioms, that is, statements that are given as true, or so called unproven truths. If one wants to prove any of those unproven truths then one must enlarge the systen with new, unproven truths. Therefore, no mathematical system is ever complete.
Now, this is about mathematical systems, not life, not the universe, and therefore, to go from this to prove the existence of God is utterly ridiculous.
Quote from: "Solitary"When Gödel died in 1978, he left behind a tantalizing theory based on principles of modal logic -- that a higher being must exist. The details of the mathematics involved in Gödel's ontological proof are complicated, but in essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.
WTF? This origin of the ontological argument was Anselm of Canturbury nearly a thousand years ago, not Gödel in the 20th century. I doubt very much Gödel would want credit for that steaming pile of crap.
Quote from: "josephpalazzo"All Godel's theorem says is that a given mathematical system is based on a number of axioms, that is, statements that are given as true, or so called unproven truths. If one wants to prove any of those unproven truths then one must enlarge the systen with new, unproven truths. Therefore, no mathematical system is ever complete.
I think the article Solitary quoted (add me to the list of people that would like to see the link to quoted articles) is about Gödel's modal ontological argument not about Gödel's Incompleteness theorems:
http://en.wikipedia.org/wiki/G%C3%B6del ... ical_proof (http://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof)
Quote from: "josephpalazzo"Now, this is about mathematical systems, not life, not the universe, and therefore, to go from this to prove the existence of God is utterly ridiculous.
Yep, that's pretty much the case. It doesn't matter whether or not Gödel's modal ontological argument can be expressed as a mathematical equation or not - it still depends on accepting premises. An analysis of the premises of Gödel's modal ontological argument can get very complicated, usually delving deeply into the logical modal operator "necessary" or "necessarily". Ultimately, the I think it boils down to just what you suggest - why should defining something in such a way that it is a logical necessity imply anything about physical reality (and that's assuming that you accept the premise that "God" is defined in such a way that it is a logical necessity - which is itself a very debatable assumption).
Quote from: "aileron"Quote from: "Solitary"When Gödel died in 1978, he left behind a tantalizing theory based on principles of modal logic -- that a higher being must exist. The details of the mathematics involved in Gödel's ontological proof are complicated, but in essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.
WTF? This origin of the ontological argument was Anselm of Canturbury nearly a thousand years ago, not Gödel in the 20th century. I doubt very much Gödel would want credit for that steaming pile of crap.
I'm pretty sure what the author is saying is that Gödel formulated the ontological argument in modal logic terms. I don't think Anselm or the other formulators of ontological arguments had done that - but the author should have made that more clear.
It was the putting of the argument into modal logic terms that made it possible for the scientists to translate it into a mathematical equation.
Quote from: "aitm"the obvious of course is "which god is proven" and the answer of course is "none of them". I would like to suggest my answer to this conundrum to the xian argument. They would hold to the principle that no greater can be conceived. However the simplicity of the counter argument is often overlooked. We CAN conceive of a greater. How? BY a god that is NOT jealous, NOT envious, NOT angry, NOT homophobic. Why do humans champion the behavior in a god that we detest in human behavior? Because we think that because humans are "flawed" a god has a right to be all the lesser of human behavior, which is the best reason that a god is not a god.
On top of the "which god" they are still stuck with infinite regress.
Quote from: "Solitary"in essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.
I utterly fail to grasp how the above works. However:
Quote from: "josephpalazzo"All Godel's theorem says is that a given mathematical system is based on a number of axioms, that is, statements that are given as true, or so called unproven truths. If one wants to prove any of those unproven truths then one must enlarge the systen with new, unproven truths. Therefore, no mathematical system is ever complete.
Now, this is about mathematical systems, not life, not the universe, and therefore, to go from this to prove the existence of God is utterly ridiculous.
This makes it somewhat more lucid to me.
Gerard
http://en.wikipedia.org/wiki/Existence_of_God (http://en.wikipedia.org/wiki/Existence_of_God)
(//http://upload.wikimedia.org/math/a/b/4/ab47f643c7918fda58089c7f5129a183.png)
"Consideration of the axioms, especially ... [Axiom 2], may tend to dampen one's confidence in ... [Axiom 3] and ... [Axiom 4] — that is, if one harbors any real doubt about self-consistency. I don't say that the argument begs the questions of ... [God's possible existence]; the charge is too difficult to establish. but observe that one cannot just tell by scrutinizing a property what it entails; one might be surprised at a consequence."
http://en.wikipedia.org/wiki/C._Anthony_Anderson (http://en.wikipedia.org/wiki/C._Anthony_Anderson)
QuoteMerci pour ces informations interessantes.
Comme l'affirme lui-meme Van Gogh :
« N'oublions pas que les petites emotions sont les grands capitaines de nos vies et qu'a celles-la nous y obeissons sans le savoir. »
Translation:
QuoteThank you for this interesting information. As the asserted itself Van Gogh: " Do not forget that the small emotions are the great captains of our lives and that has those-the we obey without knowing it. "
Welcome. You might want to try using a translator if you want to be taken seriously.
So, essentially, this formula was for making scientific processes easier, and some people made a claim that this proves the existence of god? But couldn't I hypothetically make a formula and claim the same thing, or even the opposite? Hasn't it already been established across the board that numbers and mathematics only has significance if we choose to assign value to those specific numbers and formula? In that case, someone made up a formula, knowing that, just to say "this is proof god exists"? It sounds to me like something a 4 year old kid would do.
Quote from: "Jaded"http://en.wikipedia.org/wiki/Existence_of_God
[ Image (//http://upload.wikimedia.org/math/a/b/4/ab47f643c7918fda58089c7f5129a183.png) ]
"Consideration of the axioms, especially ... [Axiom 2], may tend to dampen one's confidence in ... [Axiom 3] and ... [Axiom 4] — that is, if one harbors any real doubt about self-consistency. I don't say that the argument begs the questions of ... [God's possible existence]; the charge is too difficult to establish. but observe that one cannot just tell by scrutinizing a property what it entails; one might be surprised at a consequence."
http://en.wikipedia.org/wiki/C._Anthony_Anderson (http://en.wikipedia.org/wiki/C._Anthony_Anderson)
Just to prove the point that anyone can copy/paste, :twisted: :
QuoteTo formalize the argument sketched above, the following definitions and axioms are needed:
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 2: If a property is positive, then its negation is not positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is a positive property
Axiom 1 assumes that it is possible to single out positive properties from among all properties. Gödel comments that "Positive means positive in the moral aesthetic sense (independently of the accidental structure of the world)... It may also mean pure attribution as opposed to privation (or containing privation)." (Gödel 1995). Axioms 2, 3 and 4 can be summarized by saying that positive properties form a principal ultrafilter.
From these axioms and definitions and a few other axioms from modal logic, the following theorems can be proved:
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.
I would appreciate if someone were to answer the other post I had in this thread. I want to know if I got it all wrong or if what I said is really what is going on here. If what I said truly applies here than that is a childish and disgraceful misuse of mathematics.
Quote from: "frosty"So, essentially, this formula was for making scientific processes easier, and some people made a claim that this proves the existence of god? But couldn't I hypothetically make a formula and claim the same thing, or even the opposite? Hasn't it already been established across the board that numbers and mathematics only has significance if we choose to assign value to those specific numbers and formula? In that case, someone made up a formula, knowing that, just to say "this is proof god exists"? It sounds to me like something a 4 year old kid would do.
Quote from: "frosty"I would appreciate if someone were to answer the other post I had in this thread. I want to know if I got it all wrong or if what I said is really what is going on here. If what I said truly applies here than that is a childish and disgraceful misuse of mathematics.
Yes, your earlier post was pretty much spot on. That's why math is not considered a science. It is a language, and like any language it can be useful if used properly. Unfortunately, it follows that it could also be used childishly. And using it to prove the existence of a deity would fall in that category.
Wow, now I feel sorry for that guy in high school that got suspended because he argued with a teacher about how math in general is an accepted human creation. Never question anything outside the box in a Catholic high school, they will go Medieval on your ass in a heartbeat.