AtD pg 675

[Michael J. Hußmann]

Lawrence Bryan (lebryan at speakeasy.net) wrote:

> The only thing I would add is that a simple consequence of the theorem  
> that might be easier to understand is that Godel showed that there  
> exist legitimate statements (by legitimate I mean the lexicon and  
> syntax is valid within that system) in any system that's at least as  
> rich as arithmetic whose truth cannot be determined from the axioms of  
> that system and even if the axiom system is extended there will still  
> be such unprovable statements.

I still don't see how the analogy between Gödel's theorem and Kit's
remark about n+1 dimensions being necessary would work out. After all,
you can add up vectors within an n-dimensional space just fine. This
would correspond to proving statements within a given system, which you
cannot, in the general case. Kit introduces an observer who needs to
travel in an additional dimension so he can "see" the resultant, rather
than arriving at the result by calculation. But Gödel's theorem isn't
about "seeing" a proof one could also arrive at within the system.

- Michael


Michael J. Hußmann

E-mail: michael at michael-hussmann.de
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