On Mon, Feb 19, 2018 at 3:55 PM, Brent Meeker <meeke...@verizon.net> wrote:

​> ​
> Is there a non-constructive way to determine whether an axiomatic system
> (axioms+inference rules) must be Goedel incomplete?  Must one show that
> arithmetic is a model or is there some simpler method?


​
Any
​
axiomatic system
​
powerful enough to do arithmetic (and its not much use if it isn't) can't
be both self consistent (that is to say there is not a proof
​in the system​
 that something is true and also a proof that the same thing is false) and
complete
​ (there are true statements that have no proof).
 And if
​the system​
 is self consistent there is no way to prove it is so while remaining in
the system.

 ​John K Clark​

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