Is there any Mathematician in the house…
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I didn't follow that thread, but just looking at the posts around your link, I'm confused that Teacup would ask how you prove that a point or a line "exists". They were originally conceived as concepts known not to exist in the real world. I think Euclid defined a line as "length without breadth". It's a definition, not the study of something that "exists".
Red Stateler wrote:
It's a definition, not the study of something that "exists".
This is very relevant in that Axioms themselves are a given and not something we seek to prove.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
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Red Stateler wrote:
It's a definition, not the study of something that "exists".
This is very relevant in that Axioms themselves are a given and not something we seek to prove.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
A.A. wrote:
This is very relevant in that Axioms themselves are a given and not something we seek to prove.
Did you actually read what I wrote in the threads you referenced? Or did you just read my reply immediately below, realize you were wrong, and go about pretending that you were right?
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Look, it's simple. Godel's theorem implies that certain axioms must be taken as true without there being the possibility of being able to prove them true. That's incompleteness. Godel says that you CAN'T develop a system based on axioms that can be shown definitively to be either true or false. More specifically, there are statements regarding the natural numbers which are true, but you cannot prove this. If you think otherwise, then that's your opinion, however the rest of the scientific and mathematical community disagrees with you. But don't let that stop you from trying to develop a proof of the contrary. Feel free.
Come and see the violence inherent in the system! Help! Help! I'm being repressed!
The Apocalyptic Teacup wrote:
Godel's theorem implies that certain axioms must be taken as true without there being the possibility of being able to prove them true.
No it doesn't.
The Apocalyptic Teacup wrote:
That's incompleteness.
No it's not. Your getting a bit closer with the other parts, though what is available on Wikipedia is a good resource, it might not be presented in a way that is easily approachable.
The Apocalyptic Teacup wrote:
however the rest of the scientific and mathematical community disagrees with you.
You'd be surprised.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
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The Apocalyptic Teacup wrote:
Godel's theorem implies that certain axioms must be taken as true without there being the possibility of being able to prove them true.
No it doesn't.
The Apocalyptic Teacup wrote:
That's incompleteness.
No it's not. Your getting a bit closer with the other parts, though what is available on Wikipedia is a good resource, it might not be presented in a way that is easily approachable.
The Apocalyptic Teacup wrote:
however the rest of the scientific and mathematical community disagrees with you.
You'd be surprised.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
A.A. wrote:
No it doesn't.
:laugh: Oh man, you're clueless... Here, from the University of Hawaii, "Godel's First Incompleteness Theorem. Any adequate axiomatizable theory is incomplete. In particular the sentence "This sentence is not provable" is true but not provable in the theory." Like I said, you're wrong.
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Or anyone with a strong Logic background who wants to provide some benefit to the SB community (I have seen several variations of the theme here). If so reconfirm that the theorem referenced here is not implying what he thinks its implying.[^]
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
My mathematical reasoning leads me to conclude that the Teacup is probably the wrong guy to challange on math.
Modern liberalism has never achieved anything other than giving Secularists something to feel morally superior about
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Exactly. He fails to understand this.
Come and see the violence inherent in the system! Help! Help! I'm being repressed!
The Apocalyptic Teacup wrote:
He fails to understand this.
So do I. Why would you need a mathematical proof of the dictionary definition of a "definition"?
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A.A. wrote:
No it doesn't.
:laugh: Oh man, you're clueless... Here, from the University of Hawaii, "Godel's First Incompleteness Theorem. Any adequate axiomatizable theory is incomplete. In particular the sentence "This sentence is not provable" is true but not provable in the theory." Like I said, you're wrong.
First a piece of advice: Calm down when your discussing a topic, where your understanding of the basics is shaky at best...
The Apocalyptic Teacup wrote:
"Godel's First Incompleteness Theorem. Any adequate axiomatizable theory is incomplete. In particular the sentence "This sentence is not provable" is true but not provable in the theory."
I would tell you to read that carefully, but you need some basic background to understand what is being expressed...
The Apocalyptic Teacup wrote:
Like I said, you're wrong.
I hope your not responding just to be argumentative.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
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First a piece of advice: Calm down when your discussing a topic, where your understanding of the basics is shaky at best...
The Apocalyptic Teacup wrote:
"Godel's First Incompleteness Theorem. Any adequate axiomatizable theory is incomplete. In particular the sentence "This sentence is not provable" is true but not provable in the theory."
I would tell you to read that carefully, but you need some basic background to understand what is being expressed...
The Apocalyptic Teacup wrote:
Like I said, you're wrong.
I hope your not responding just to be argumentative.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
You're like Ilion, you never actually respond. Fortunately, I've created a thread above for you.
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Or anyone with a strong Logic background who wants to provide some benefit to the SB community (I have seen several variations of the theme here). If so reconfirm that the theorem referenced here is not implying what he thinks its implying.[^]
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
If you want to discuss what Godel does or doesn't mean (and can do so in a civilized fashion), there's a whole forum devoted to math type stuff here.
-- CleaKO The sad part about this instance is that none of the users ever said anything [about the problem]. Pete O`Hanlon Doesn't that just tell you everything you need to know about users?
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The Apocalyptic Teacup wrote:
He fails to understand this.
So do I. Why would you need a mathematical proof of the dictionary definition of a "definition"?
Red Stateler wrote:
So do I. Why would you need a mathematical proof of the dictionary definition of a "definition"?
Because in mathematics there is a classification of theories that includes theories which are "complete" and theories that are "incomplete". Incomplete theories can contain statements which are true but those statements are not provably true within the context of the theory.
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The Apocalyptic Teacup wrote:
He fails to understand this.
So do I. Why would you need a mathematical proof of the dictionary definition of a "definition"?
Red Stateler wrote:
Why would you need a mathematical proof of the dictionary definition of a "definition"?
You don't and to put it very simply: Logic as it applies to Mathematics makes no attempt to do that.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
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The Apocalyptic Teacup wrote:
Godel's theorem implies that certain axioms must be taken as true without there being the possibility of being able to prove them true.
No it doesn't.
The Apocalyptic Teacup wrote:
That's incompleteness.
No it's not. Your getting a bit closer with the other parts, though what is available on Wikipedia is a good resource, it might not be presented in a way that is easily approachable.
The Apocalyptic Teacup wrote:
however the rest of the scientific and mathematical community disagrees with you.
You'd be surprised.
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
John is correct in his interpretation.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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Or anyone with a strong Logic background who wants to provide some benefit to the SB community (I have seen several variations of the theme here). If so reconfirm that the theorem referenced here is not implying what he thinks its implying.[^]
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
If the "he' you're referring to is Teacup, I would say he has one of the stronger mathematical backgrounds available on CP (so you already have your answer: Teacup's right). If you were referring to the Negus as "he", then my previous statement still applies...
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John is correct in his interpretation.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
Andy Brummer wrote:
John is correct in his interpretation.
First thanks for the input... If by interpertation you mean "Godel's theorem implies that certain axioms must be taken as true without there being the possibility of being able to prove them true." then it is clearly not the case. In fact I fail to see how one remotely familiar with the subject can possibly come to this conclusion, in which case I must ask, what do you think an axiom actually is?
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
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Andy Brummer wrote:
John is correct in his interpretation.
First thanks for the input... If by interpertation you mean "Godel's theorem implies that certain axioms must be taken as true without there being the possibility of being able to prove them true." then it is clearly not the case. In fact I fail to see how one remotely familiar with the subject can possibly come to this conclusion, in which case I must ask, what do you think an axiom actually is?
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
Ah, my bad. If you replace axiom with theorem in that statement then it becomes true, since the result Goedel's theorem is about theorems not axioms. However he did prove that adding additional axioms even an infinite number of axioms will not affect the results of Godel's theorem. You can't complexify yourself out of the problem. Anyway as far as your Goedel's theorem => God idea goes. That's completely bogus. You are making a number of wild assumptions to get there. First our universe is nothing but a logic system. When you do that you are confusing physics models with the real world. The models do a good job predicting observations, but it doesn't mean that the real world is a physics model. That's the main fallacy that many religious people fall into and feel they need to attack science over. Just because a model has a good fit with experiment, it doesn't mean that reality is an implementation of that model. Another issue with that assumption is that another solution to the problems introduced with Goedel's theorem is to abandon the law of excluded middle and accept statements that have partial truth values. Given that at the lowest levels nature is best modeled with quantum mechanics, trying to cram truth into a simple boolean state might be the real problem.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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Ah, my bad. If you replace axiom with theorem in that statement then it becomes true, since the result Goedel's theorem is about theorems not axioms. However he did prove that adding additional axioms even an infinite number of axioms will not affect the results of Godel's theorem. You can't complexify yourself out of the problem. Anyway as far as your Goedel's theorem => God idea goes. That's completely bogus. You are making a number of wild assumptions to get there. First our universe is nothing but a logic system. When you do that you are confusing physics models with the real world. The models do a good job predicting observations, but it doesn't mean that the real world is a physics model. That's the main fallacy that many religious people fall into and feel they need to attack science over. Just because a model has a good fit with experiment, it doesn't mean that reality is an implementation of that model. Another issue with that assumption is that another solution to the problems introduced with Goedel's theorem is to abandon the law of excluded middle and accept statements that have partial truth values. Given that at the lowest levels nature is best modeled with quantum mechanics, trying to cram truth into a simple boolean state might be the real problem.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
Andy Brummer wrote:
Ah, my bad. If you replace axiom with theorem in that statement then it becomes true, since the result Goedel's theorem is about theorems not axioms. However he did prove that adding additional axioms even an infinite number of axioms will not affect the results of Godel's theorem. You can't complexify yourself out of the problem.
All good, I figured it would be easy to misread so decided to run it by you one more time.
Andy Brummer wrote:
Anyway as far as your Goedel's theorem => God idea goes. That's completely bogus. You are making a number of wild assumptions to get there. First our universe is nothing but a logic system. When you do that you are confusing physics models with the real world. The models do a good job predicting observations, but it doesn't mean that the real world is a physics model. That's the main fallacy that many religious people fall into and feel they need to attack science over. Just because a model has a good fit with experiment, it doesn't mean that reality is an implementation of that model.
:confused: I can only imagine what the response would have been like had I actually talked about the subject referenced here. :) You might be thinking of somebody else. ;)
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
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Andy Brummer wrote:
Ah, my bad. If you replace axiom with theorem in that statement then it becomes true, since the result Goedel's theorem is about theorems not axioms. However he did prove that adding additional axioms even an infinite number of axioms will not affect the results of Godel's theorem. You can't complexify yourself out of the problem.
All good, I figured it would be easy to misread so decided to run it by you one more time.
Andy Brummer wrote:
Anyway as far as your Goedel's theorem => God idea goes. That's completely bogus. You are making a number of wild assumptions to get there. First our universe is nothing but a logic system. When you do that you are confusing physics models with the real world. The models do a good job predicting observations, but it doesn't mean that the real world is a physics model. That's the main fallacy that many religious people fall into and feel they need to attack science over. Just because a model has a good fit with experiment, it doesn't mean that reality is an implementation of that model.
:confused: I can only imagine what the response would have been like had I actually talked about the subject referenced here. :) You might be thinking of somebody else. ;)
Belief in God Finding Allah Surah AlHaaqa(The Reality) Surah Qaf
A.A. wrote:
:confused: I can only imagine what the response would have been like had I actually talked about the subject referenced here. :) You might be thinking of somebody else. ;)
Sorry about that, I'm 0 for 2 now and I'm beginning to feel like stapler. That was Negus with the Goedel => God stuff. I don't know what I was thinking. You wouldn't have used the G word for your deity.
If evidence reaches a conclusion then it makes sense. If it doesn't, it's just lame to go on TRYING to prove a theory that you made up when all the evidence points the other way. That's how crazy is made. -espeir