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Re: Matheology § 224
Posted:
Apr 8, 2013 10:30 AM


Nam Nguyen <namducnguyen@shaw.ca> writes:
> Seriously, we should begin to abandon the idea that whatever is true > or false in the naturals can be structure theoretically proven, > verified. > > If we don't, we'd be in _no_ better position than where Hilbert > was with his Allmightyformalsystem, proving all arithmetic > true formulas. > > We'd be simply change the name "Allmightyformalsystem" > to "Allmightylanguagestructure". But it's still an Incompleteness > (of the 2nd kind) that we'd encounter: the Incompleteness of language > structure interpretation of the abstract (nonlogical) concept known > as the natural numbers.
But it is known structure theoretically that if we have any 2 structures that satisfy Peano axioms, then they are isomorphic: a statement is true in one if and only if it's true in the other.
 Alan Smaill



