# The hijack about proof theory **URL:** \ **Category:** Great Debates\ **Created:** [December 15, 2009, 4:01pm UTC](https://boards.straightdope.com/t/the-hijack-about-proof-theory/521367 "2009-12-15T16:01:28Z")\ **Posts on this page:** 1\ **Showing post:** 2
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 15, 2009, 4:44pm UTC](https://boards.straightdope.com/t/the-hijack-about-proof-theory/521367/2 "2009-12-15T16:44:47Z")
> [@Godel: are all undecidable props in consistent math systems subsets of self-referent statements?](https://boards.straightdope.com/t/godel-are-all-undecidable-props-in-consistent-math-systems-subsets-of-self-referent-statements/520559/104): > > And if Frylock continues to believe that Presburger assures us that x+x=3 is false for every domain we extend Presburger to, he’s going to have to keep denying that we can create an extension where 1.5 is a number. And that would tend to make him irrelevant for any further advancement of this thread, or my own knowledge. The statement “There is no x such that x+x = 1+1+1” is true in every extension of Presburger.\* But that _doesn’t_ mean there’s no extension where 1.5 is a number. I can make a model that satisfies Presburger in which 1.5 is a number. Namely, it’s the model just like the standard interpretation, but where we interpret the symbol “1” to refer to the number 1.5. That model satisfies the Presburger axioms, and on that interpretation there is no x where x+x = 1+1+1 (remember to interpret “1” correctly!) and on that interpretation 1.5 is an element of the domain. \*It must be, since Presburger is complete, but my proof-fu is failing me when I actually try to construct the proof. --- _[View the full topic](https://boards.straightdope.com/t/the-hijack-about-proof-theory/521367)._