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Re: Definition of Mathematics
Posted:
Feb 28, 2012 9:37 PM
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Has anyone actually learned how to parse Godel's sentence? What if he means that there exists a G that is not provable in T? But, I already know that axioms are not provable. If axioms are provable, they are not axioms anymore. So, if G is just an element not provable in T, just make that G an axiom if it is that important. If that G is not important, then my theory is fine without it provable. So what?
So, what do you mean by consistency anyway? There exists not a G in T such that G is both true and false? Then, not only do we need to define all axioms, but we also have to define all rules of composition, which involve substitution. Are you ready to write down the complete set of all your grammars as a starting point?
If not, we can't even write a compiler for your theory, not to mention the ability to check its consistency!
If we cannot even get past this point of discussion, then our understanding of consistency is fairly shallow if not incorrect.
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