Mohsen Ravanbakhsh
>
>*Jesse,
>I definitely don't think the two systems could be complete, since 
>(handwavey
>argument follows) if you have two theorem-proving algorithms A and B, it's
>trivial to just create a new algorithm that prints out the theorems that
>either A or B could print out, and incompleteness should apply to this too*
>**
>They're not independent systems.putting that aside, I can't find the
>correspondence to my argument. It would be nice if you could clarify your
>point.

I didn't say they were independent--but each has a well-defined set of 
theorems that they will judge to be true, no? My point was just that they 
could not together be complete as you say, since the combination of the two 
can always be treated as a *single* axiomatic system or theorem-proving 
algorithm which proves every theorem in the union of the two sets A and B 
prove individually, and this must necessarily be incomplete--there must be 
true theorems of arithmetic which this single system cannot prove (meaning 
that they don't belong to the set A can prove or the set B can prove).

Jesse

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