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God and Gödel

Eiron
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Posted 05/17/09 - 03:13 PM:	#21
I want to thank everyone for their posts to my question. It is inspiring to know there are people out there with such knowledge and who are willing to communicate with each other and help someone out. I expected more "are you a nitwit?" kind of answers. I see I have a lot to learn. Now, where do I find the knowledge to decipher what to hell most of you were talking about? ;O) Edited by Eiron on 05/17/09 - 08:32 PM. Reason: I was not Just joking!

HenrikO
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Posted 05/26/09 - 11:53 AM:	#22
A good book on the subject is "Gödel's Theorem: An Incomplete Guide to Its Use and Abuse" by Torkel Franzén.

endless nameless
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Posted 06/08/09 - 07:09 AM:	#23
treysuttle wrote: A I know Godel actually worked on versions of the ontological argument...although presumably never believing in God he enjoyed the argument as a kind of hobby, but I am not sure what his incompleteness theorem has to do with the existence of God. Really? Wikipedia seems to suggest otherwise: http://en.wikipedia.org/wiki/Kurt_G%C3%B6del#cite_note-10 Gödel was a convinced theist and a lifelong Christian. He rejected the notion that God was impersonal, as Einstein believed. He believed firmly in an afterlife, stating: “I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife." Assuming that this isn't fallacious, what do we make of it?

saprofit
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Posted 06/09/09 - 05:18 AM:	#24
what about any philosophical system? If certain philosophical system (e.g. Plato's) is logically coherent and complete, doesn't gödel's theorems implicate that it has some false statements?

7
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Posted 06/10/09 - 05:24 AM:	#25
endless nameless wrote: Really? Wikipedia seems to suggest otherwise: http://en.wikipedia.org/wiki/Kurt_G%C3%B6del#cite_note-10 Gödel was a convinced theist and a lifelong Christian. He rejected the notion that God was impersonal, as Einstein believed. He believed firmly in an afterlife, stating: “I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife." Assuming that this isn't fallacious, what do we make of it? He was Christian.

7
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Posted 06/10/09 - 05:26 AM:	#26
saprofit wrote: what about any philosophical system? If certain philosophical system (e.g. Plato's) is logically coherent and complete, doesn't gödel's theorems implicate that it has some false statements? Plato never said that arithmetic is complete. Mathematicians of his day weren't even aware of thse issues.

7
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Posted 06/10/09 - 05:31 AM:	#27
HenrikO wrote: A good book on the subject is "Gödel's Theorem: An Incomplete Guide to Its Use and Abuse" by Torkel Franzén. Peter Smith's is more thorough and he does not expect readers to be knowledgeable about logic, either. It's more mathematically demanding than the one you mentioned, but anyone can read it. It has many interesting philosophical comments, too. The Franzén doesn't attempt to present a rigorous proof.

saprofit
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Posted 06/12/09 - 03:38 AM:	#28
7 wrote: Plato never said that arithmetic is complete. Mathematicians of his day weren't even aware of thse issues. I'm not talking about mathematics but the logical possibility of any philosophical system. Someone told me that Gödel's theorems implicate that there cannot be ca oherent and final system, with all truth statements. One predicate will always be excluded. If a system is coherent and has all true statements then it can't be final. Is this true? Edited by Benkei on 06/12/09 - 04:02 AM

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Posted 06/16/09 - 02:26 AM:	#29
saprofit wrote: I'm not talking about mathematics but the logical possibility of any philosophical system. Someone told me that Gödel's theorems implicate that there cannot be ca oherent and final system, with all truth statements. One predicate will always be excluded. If a system is coherent and has all true statements then it can't be final. Is this true? Goedel's 1st theorem basically says that there cannot be a complete axiomatization of arithmetic that is consistent. There will always be arithmetic statements that slip through the cracks (they cannot be proved and their negations cannot be proved). If an axiomatization of arithmetic is complete, then it is inconsistent. However, Plato didn't try to axiomatize arithmetic and I don't believe he said anything implying that there exists a complete, consistent axiomatization of arithmetic. WRT philosophical systems in general, if a given system is able to prove for every statement either the statement or its negation, then it is inconsistent. A philosophical system is unlikely to fall victim to this difficulty because it doesn't address this issue; it does not attempt to give formal axioms. Edited by 7 on 06/16/09 - 02:32 AM

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