Kurt Godel - the religion of mathamatics
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Godel states that for any system, there exist statements which must be taken on faith - in other words cannot be proven. There exist uncomputable operations in artificial life structures such as the game of Life. Since there is no systematic way to decide in advance whether a given mathematical problem is decidable or undecidable by the operation of a Turing machine, i.e. the fate of the machine cannot be known in advance. Therefore, the fate of cellular automata patterns cannot be systematically known in advance, even though all such patterns are strictly deterministic. Randomness and uncertainty are built into the Universe due to the restrictions of logic itself, as soon as systems become complex enough to engage in self-reference. Is God hidden in the details - as uncle Albert always predicted? Does this not "prove" that a faith based system such as religion is logically correct and that for any complex system a deterministic outcome is impossible ? But if an outcome is impossible to predict does this not also say that "God" cannot be omnipotent at the same time ? I need some coffee !!! Richard "He who joyfully marches in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice. --Albert Einstein
Richard Stringer wrote: Godel states that for any system, there exist statements which must be taken on faith - in other words cannot be proven. These are not equivalent statements. If something cannot be proven, then one option is to neither believe it nor disbelieve it --- to say you don't know. Richard Stringer wrote: Does this not "prove" that a faith based system such as religion is logically correct Do religions claim that there are certain propositions that are logically indecidable and which happen to coincide with their major tenets? How would they know they are logically indecidable if "there is no systematic way to decide in advance whether a given mathematical problem is decidable or undecidable by the operation of a Turing machine, i.e. the fate of the machine cannot be known in advance"? You seem to be engaging in the loose thinking all too characteristic of religious belief. John Carson "I believe in an America where the separation of church and state is absolute--where no Catholic prelate would tell the President (should he be Catholic) how to act, and no Protestant minister would tell his parishoners for whom to vote ... and where no man is denied public office merely because his religion differs from the President who might appoint him or the people who might elect him. - John F. Kennedy
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Richard Stringer wrote: Is God hidden in the details On the contrary, God should be as obvious as looking at the make up of your own body(liver, heart, blood flowing all over, etc…), or just looking out the window(trees, insects, rain,…). I am familiar with Godel's Theorems, specifically his Incompleteness Theorem, but approaching the topic through this way is unnecessary and usually fruitless, because of a) its not accessible by the majority. b) people tend to philosophize way too much. c) people talk a lot, but they just don’t know what they are talking about… On another note just observing your everyday routine, while being truthful to yourself, will lead you to the obvious. Just look at your food, at your respiratory system, at sleep, just contemplate where everything came from… you get the idea. Quran [translation of the meaning]:
2:[164] Behold! In the creation of the heavens and the earth; in the
alternation of the Night and the Day; in the sailing of the ships through the
Ocean for the profit of mankind; in the rain which Allah sends down from the
skies, and the life which He gives therewith to an earth that is dead; in the
beasts of all kinds that He scatters through the earth; in the change of the
winds and the clouds which they trail like their slaves between the sky and
the earth, (here) indeed are Signs for a people that are wise.3:[190] Behold! in the creation of the heavens and the earth, and the
alternation of Night and Day, there are indeed Signs for men of
understanding.3:[191] Men who celebrate the praises of Allah, standing, sitting, and lying
down on their sides, and contemplate the (wonders of) creation in the heavens
and the earth, (with the thought): "Our Lord! not for naught hast thou
created (all) this! Glory to Thee! Give us salvation from the Penalty of the
Fire.A.A. wrote: On the contrary, God should be as obvious as looking at the make up of your own body(liver, heart, blood flowing all over, etc…), or just looking out the window(trees, insects, rain,…). Sure, given something remarkable, it is quite natural to believe that it was created by an unobservable being using an unknown mechanism for which no evidence exists. A perfectly common sense conclusion indeed. John Carson "I believe in an America where the separation of church and state is absolute--where no Catholic prelate would tell the President (should he be Catholic) how to act, and no Protestant minister would tell his parishoners for whom to vote ... and where no man is denied public office merely because his religion differs from the President who might appoint him or the people who might elect him. - John F. Kennedy
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Richard Stringer wrote: Godel states that for any system, there exist statements which must be taken on faith - in other words cannot be proven. These are not equivalent statements. If something cannot be proven, then one option is to neither believe it nor disbelieve it --- to say you don't know. Richard Stringer wrote: Does this not "prove" that a faith based system such as religion is logically correct Do religions claim that there are certain propositions that are logically indecidable and which happen to coincide with their major tenets? How would they know they are logically indecidable if "there is no systematic way to decide in advance whether a given mathematical problem is decidable or undecidable by the operation of a Turing machine, i.e. the fate of the machine cannot be known in advance"? You seem to be engaging in the loose thinking all too characteristic of religious belief. John Carson "I believe in an America where the separation of church and state is absolute--where no Catholic prelate would tell the President (should he be Catholic) how to act, and no Protestant minister would tell his parishoners for whom to vote ... and where no man is denied public office merely because his religion differs from the President who might appoint him or the people who might elect him. - John F. Kennedy
John Carson wrote: These are not equivalent statements. If something cannot be proven, then one option is to neither believe it nor disbelieve it --- to say you don't know. Syntaxally they may not be equivalent ( although I can argue either side ) but mathmatically they are the same thing. Consider the old paradox: Person 1: Person 2 cannot tell the truth. Person 2: Person 1 is correct. Which statement is correct ? Express your answer in boolean terms or any other construct you can devise . John Carson wrote: You seem to be engaging in the loose thinking all too characteristic of religious belief. I was attempting, in my own crude mannher, to express an idea that God could be represented in terms of a mathmatical construct. The "God" I was referring to is not a religious type of construct such as Jehova or Alla or Jesus which in MHO are basically attempts to humanize somrthingt we cannot quite understand but in terms of an artifical object that can have various meanings that cannot be determined in a deterministic manner. Richard "He who joyfully marches in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice. --Albert Einstein
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Richard Stringer wrote: Is God hidden in the details On the contrary, God should be as obvious as looking at the make up of your own body(liver, heart, blood flowing all over, etc…), or just looking out the window(trees, insects, rain,…). I am familiar with Godel's Theorems, specifically his Incompleteness Theorem, but approaching the topic through this way is unnecessary and usually fruitless, because of a) its not accessible by the majority. b) people tend to philosophize way too much. c) people talk a lot, but they just don’t know what they are talking about… On another note just observing your everyday routine, while being truthful to yourself, will lead you to the obvious. Just look at your food, at your respiratory system, at sleep, just contemplate where everything came from… you get the idea. Quran [translation of the meaning]:
2:[164] Behold! In the creation of the heavens and the earth; in the
alternation of the Night and the Day; in the sailing of the ships through the
Ocean for the profit of mankind; in the rain which Allah sends down from the
skies, and the life which He gives therewith to an earth that is dead; in the
beasts of all kinds that He scatters through the earth; in the change of the
winds and the clouds which they trail like their slaves between the sky and
the earth, (here) indeed are Signs for a people that are wise.3:[190] Behold! in the creation of the heavens and the earth, and the
alternation of Night and Day, there are indeed Signs for men of
understanding.3:[191] Men who celebrate the praises of Allah, standing, sitting, and lying
down on their sides, and contemplate the (wonders of) creation in the heavens
and the earth, (with the thought): "Our Lord! not for naught hast thou
created (all) this! Glory to Thee! Give us salvation from the Penalty of the
Fire.A.A. wrote: On the contrary, God should be as obvious as looking at the make up of your own body(liver, heart, blood flowing all over, etc…), or just looking out the window(trees, insects, rain Can you prove any of this drivel? A.A. wrote: On another note just observing your everyday routine, while being truthful to yourself, will lead you to the obvious. Just look at your food, at your respiratory system, at sleep, just contemplate where everything came from… you get the idea. The closer we get to the beginning the simplier everthing gets. Your kind of concept of God must mean that he/she is simple indeed. No philosophy - just an obervation. Richard "He who joyfully marches in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice. --Albert Einstein
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John Carson wrote: These are not equivalent statements. If something cannot be proven, then one option is to neither believe it nor disbelieve it --- to say you don't know. Syntaxally they may not be equivalent ( although I can argue either side ) but mathmatically they are the same thing. Consider the old paradox: Person 1: Person 2 cannot tell the truth. Person 2: Person 1 is correct. Which statement is correct ? Express your answer in boolean terms or any other construct you can devise . John Carson wrote: You seem to be engaging in the loose thinking all too characteristic of religious belief. I was attempting, in my own crude mannher, to express an idea that God could be represented in terms of a mathmatical construct. The "God" I was referring to is not a religious type of construct such as Jehova or Alla or Jesus which in MHO are basically attempts to humanize somrthingt we cannot quite understand but in terms of an artifical object that can have various meanings that cannot be determined in a deterministic manner. Richard "He who joyfully marches in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice. --Albert Einstein
Richard Stringer wrote: Syntaxally they may not be equivalent ( although I can argue either side ) but mathmatically they are the same thing. COnsider the old paradox: Person 1: Person 2 cannot tell the truth. Person 2: Person 1 is correct. Which statement is correct ? Express your answer in boolean terms or any6 other construct you can devise. My point was that "taking something on faith" is normally interpreted to mean that you actually believe that the proposition is true. Confronted with an undecidable proposition (if indeed one can be so confronted), then believing the proposition to be true is not the only option. John Carson "I believe in an America where the separation of church and state is absolute--where no Catholic prelate would tell the President (should he be Catholic) how to act, and no Protestant minister would tell his parishoners for whom to vote ... and where no man is denied public office merely because his religion differs from the President who might appoint him or the people who might elect him. - John F. Kennedy
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Godel states that for any system, there exist statements which must be taken on faith - in other words cannot be proven. There exist uncomputable operations in artificial life structures such as the game of Life. Since there is no systematic way to decide in advance whether a given mathematical problem is decidable or undecidable by the operation of a Turing machine, i.e. the fate of the machine cannot be known in advance. Therefore, the fate of cellular automata patterns cannot be systematically known in advance, even though all such patterns are strictly deterministic. Randomness and uncertainty are built into the Universe due to the restrictions of logic itself, as soon as systems become complex enough to engage in self-reference. Is God hidden in the details - as uncle Albert always predicted? Does this not "prove" that a faith based system such as religion is logically correct and that for any complex system a deterministic outcome is impossible ? But if an outcome is impossible to predict does this not also say that "God" cannot be omnipotent at the same time ? I need some coffee !!! Richard "He who joyfully marches in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice. --Albert Einstein
Richard Stringer wrote: Does this not "prove" that a faith based system such as religion is logically correct In my view, all our knowledge has a degree of certainty ranging from 0% to 100%. Virtually everything that we regard as "proven" is not actually at 100% certainty. People often make hidden assumptions (many of these are generally good assumptions), but the upshot of these assumptions is that we can't reach 100% certainty on anything. There is one exception. I think that "I think therefore I am" proves (100%) that I exist. Beyond that, things fall to 99.9% certainty or something similar. Is the earth a sphere? I think that's at 99.9+% certainty. Maybe all the pictures are fakes. Maybe there is some strange space-warp which makes the earth look like a sphere. I highly doubt any alternative hypothesis, and I'm comfortable with saying that anything at 99% certainty is "certain" or "proved". I'm also comfortable with looking at people strangely when they say something contrary (e.g. "the earth is flat"). Every idea with a probability less than 100% (absolutely proven) and greater than 0% (absolutely disproven) isn't the same. What are the odds that tin foil hats protect you from the mind-reading devices of UFOs? Not likely, but it's not 0% either. It's low enough that I can look at you funny if you believe that. In spite of the fact that "spherical earth" and "tin foil hats" ideas are both less than 100% certain and greater than 0% certain, I'm guessing that we both agree that believing in the spherical earth and tin foil hats is not the same. Now, when people start talking about faith in God, they tend to smooth over the differences between 99% certain and 1% certain and just say "it all has a degree of uncertainty - and therefore a degree of faith". I disagree with that. Some people argue that "We can't be certain that the laws of physics won't change tomorrow, it's faith - just like my faith in God". Well, I don't buy that argument. It's true that I don't know that the laws of physics won't change tomorrow, but I've gone through quite a few mornings and have yet to see one where the laws of physics seem different. Based on my experience of repetition, I'm going to say that "laws of physics remaining the same tomorrow" is above 99.9%. The odds of God existing are a bit lower. The odds of a particular God existing (as described in the Bible, Koran, etc) are quite a bit lower - although I won't go into my arguments right now. The problem with "faith
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Richard Stringer wrote: Is God hidden in the details On the contrary, God should be as obvious as looking at the make up of your own body(liver, heart, blood flowing all over, etc…), or just looking out the window(trees, insects, rain,…). I am familiar with Godel's Theorems, specifically his Incompleteness Theorem, but approaching the topic through this way is unnecessary and usually fruitless, because of a) its not accessible by the majority. b) people tend to philosophize way too much. c) people talk a lot, but they just don’t know what they are talking about… On another note just observing your everyday routine, while being truthful to yourself, will lead you to the obvious. Just look at your food, at your respiratory system, at sleep, just contemplate where everything came from… you get the idea. Quran [translation of the meaning]:
2:[164] Behold! In the creation of the heavens and the earth; in the
alternation of the Night and the Day; in the sailing of the ships through the
Ocean for the profit of mankind; in the rain which Allah sends down from the
skies, and the life which He gives therewith to an earth that is dead; in the
beasts of all kinds that He scatters through the earth; in the change of the
winds and the clouds which they trail like their slaves between the sky and
the earth, (here) indeed are Signs for a people that are wise.3:[190] Behold! in the creation of the heavens and the earth, and the
alternation of Night and Day, there are indeed Signs for men of
understanding.3:[191] Men who celebrate the praises of Allah, standing, sitting, and lying
down on their sides, and contemplate the (wonders of) creation in the heavens
and the earth, (with the thought): "Our Lord! not for naught hast thou
created (all) this! Glory to Thee! Give us salvation from the Penalty of the
Fire.A.A. wrote: On the contrary, God should be as obvious as looking at the make up of your own body(liver, heart, blood flowing all over, etc…), or just looking out the window(trees, insects, rain,…). I refer you to my signature (the text here is edited, but the full quote is in the linked article). Oh, and I recommend reading Dawkins book "The Blind Watchmaker". The Design Argument for God (which is at least implied by your statement here) is a pretty poor one, I have to say, and thoroughly refuted there. I see no god there, but the emergent behaviour of the rules our universe intrinsically has. It's both wonderful and liberating to get that inkling.
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Godel states that for any system, there exist statements which must be taken on faith - in other words cannot be proven. There exist uncomputable operations in artificial life structures such as the game of Life. Since there is no systematic way to decide in advance whether a given mathematical problem is decidable or undecidable by the operation of a Turing machine, i.e. the fate of the machine cannot be known in advance. Therefore, the fate of cellular automata patterns cannot be systematically known in advance, even though all such patterns are strictly deterministic. Randomness and uncertainty are built into the Universe due to the restrictions of logic itself, as soon as systems become complex enough to engage in self-reference. Is God hidden in the details - as uncle Albert always predicted? Does this not "prove" that a faith based system such as religion is logically correct and that for any complex system a deterministic outcome is impossible ? But if an outcome is impossible to predict does this not also say that "God" cannot be omnipotent at the same time ? I need some coffee !!! Richard "He who joyfully marches in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice. --Albert Einstein
All it really proves is my oft stated thesis that human beings will instinctively turn anything into a religion, given sufficient time to work out the details... "In the final analysis, secularism is little more than another religion the first amendment should be protecting the American people against."
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All it really proves is my oft stated thesis that human beings will instinctively turn anything into a religion, given sufficient time to work out the details... "In the final analysis, secularism is little more than another religion the first amendment should be protecting the American people against."
I bet (and hope) you didn't earn a title because of that thesis. -- Booohoo!
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I bet (and hope) you didn't earn a title because of that thesis. -- Booohoo!
Not yet! "In the final analysis, secularism is little more than another religion the first amendment should be protecting the American people against."
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Godel states that for any system, there exist statements which must be taken on faith - in other words cannot be proven. There exist uncomputable operations in artificial life structures such as the game of Life. Since there is no systematic way to decide in advance whether a given mathematical problem is decidable or undecidable by the operation of a Turing machine, i.e. the fate of the machine cannot be known in advance. Therefore, the fate of cellular automata patterns cannot be systematically known in advance, even though all such patterns are strictly deterministic. Randomness and uncertainty are built into the Universe due to the restrictions of logic itself, as soon as systems become complex enough to engage in self-reference. Is God hidden in the details - as uncle Albert always predicted? Does this not "prove" that a faith based system such as religion is logically correct and that for any complex system a deterministic outcome is impossible ? But if an outcome is impossible to predict does this not also say that "God" cannot be omnipotent at the same time ? I need some coffee !!! Richard "He who joyfully marches in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice. --Albert Einstein
Richard Stringer wrote: Is God hidden in the details - as uncle Albert always predicted? Why "hidden", and why "details"? Though you can't call me religous as such, some kind of miracle in plain sight everywhere (though somethimes I think it really was a woman with PMS). Richard Stringer wrote: Does this not "prove" that a faith based system such as religion is logically correct Yes, it does not proof that any faith based system is right. or wrong. Or better or worse than a system excluding faith. The difference between axioms and faith might only be quantity - but that's a lot here: Math demands that as an axiomatic system only the bare minimum is taken which is required to describe the world you look at, and cannot be proven. Whereas faith (by design) stands beyond proof or un-proof. P.S. I liked your previous sig better
we are here to help each other get through this thing, whatever it is Vonnegut jr.
sighist || Agile Programming | doxygen -
I bet (and hope) you didn't earn a title because of that thesis. -- Booohoo!
Jörgen Sigvardsson wrote: I bet (and hope) you didn't earn a title because of that thesis. No, but Stan is sort of right. Only it looks increasingly like religion is an evolved behaviour of humans that provided a survival benefit early on in our species existence, rather than because of any inherent truth. I wonder how your average theist would feel if I mentioned that their religion is really just the current result of thousands of years of evolving belief by monkeys and monkey-descendents in God :-) Plus this[^] :-)