July 9th, 2014, 11:52 AM  #11  
Senior Member Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108  Quote:
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First incompleteness theorem has been proved in Coq by Russell O'Connor in 2003 (Wikipedia).  
July 9th, 2014, 12:17 PM  #12 
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 
To bobsmith76 I'd say that the scientific method is the most powerful tool you can use to reason. Those that developed this method of reasoning acknowledged the fact that the universe is unpredictable. They had also acknowledged the fact that humans make errors. They had understood that facts we accept today may not be accepted tomorrow. All theories contain errors. That is why they are called theories. They are not absolute truths. Our scientific and mathematical theories are a work in progress. The best theories help us explain how the world works, and they make sense to us today. They may not make sense tomorrow. Better theories will emerge and some theories will be scrapped. Nothing is set in stone. Try not to attach yourself to a belief system. Keep your mind open. 
July 9th, 2014, 12:30 PM  #13  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
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I would *not* have found Aaronson's proof of the (first) incompleteness theorem on my own, though! "Easy to follow" is not the same as "easy to prove" (well, modulo P != NP... ). Quote:
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It looks like the Completeness Theorem has been proved in Isabelle here: http://afp.sourceforge.net/entries/C...nesspaper.pdf (Margetson 2004). Last edited by CRGreathouse; July 9th, 2014 at 12:34 PM.  
July 9th, 2014, 12:31 PM  #14 
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 
If you search for errors you will find them  in everything. Perfection contradicts itself. We live in a universe based on probabilities, not absolute certainties. Our universe is multidimensional, not linear. There are too many variables for us to cope with. Even our most powerful computers struggle to make accurate predictions about the future. This may be hard to accept, but nature has shown us that there is a lot to understand about this universe we inhabit. There is a lot to uncover. Logic won't provide answers to everything, and maths won't either. We are only human beings after all. 
July 9th, 2014, 12:32 PM  #15  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,664 Thanks: 2644 Math Focus: Mainly analysis and algebra  Quote:
Given the nature of your question, and the rest of the hullabaloo in this thread, I think you should explain on what basis you rest your claim rather than expecting others to justify why they believe in published, peer reviewed work.  

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