cousin_it comments on No one knows what Peano arithmetic doesn't know - Less Wrong

17 Post author: cousin_it 16 December 2011 09:36PM

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Comment author: cousin_it 18 December 2011 05:06:31PM 2 points [-]

More powerful formal systems are not more powerful because they know more stuff. They're more powerful because they have more confidence.

That's an awesome way of putting it, thanks!

PA proves that PA+Con(PA) proves Con(PA)

Duh, PA proves that PA+X proves X for any X, because X is one of the axioms of PA+X. Did you mean some less trivial example?

Comment author: Will_Sawin 18 December 2011 05:10:47PM 1 point [-]

No. I meant to include a trivial example. I believed that it would help clarify the point.

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