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Topic: Matheology § 224
Replies: 13   Last Post: Apr 12, 2013 7:27 PM

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Alan Smaill

Posts: 757
Registered: 1/29/05
Re: Matheology § 224
Posted: Apr 8, 2013 10:30 AM
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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 All-mighty-formal-system, proving all arithmetic
> true formulas.
>
> We'd be simply change the name "All-mighty-formal-system"
> to "All-mighty-language-structure". But it's still an Incompleteness
> (of the 2nd kind) that we'd encounter: the Incompleteness of language
> structure interpretation of the abstract (non-logical) 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



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