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Post  Post subject: How can Godel's theorem apply to completely defined systems?  |  Posted: Wed Aug 31, 2016 2:51 am
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Joined: Thu May 05, 2016 10:31 pm
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Location: Nebraska, USA

According to Gödel's first imcompleteness theorem, any self-consistent system has a statement that is independent of the system.
I don't understand how this is true. Take the real numbers. There are several constructions of the real numbers, and they all demonstrably describe a unique system up to isomorphism. How then can there exist a statement P about the real numbers which can be neither proven nor disproven?
Then you can invent two real number systems, one in which P is true and one in which P is false. But that can't be the case if the two real number constructions are isomorphic.

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Post  Post subject: Re: How can Godel's theorem apply to completely defined syst  |  Posted: Fri Sep 09, 2016 4:10 am
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Joined: Sat Aug 06, 2011 10:19 am
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Hope this helps.

It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence.
-W. K. Clifford-

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