Date: Apr 12, 2013 7:31 PM
Author: Frederick Williams
Subject: Re: Matheology § 224

Nam Nguyen wrote:

> In any rate, "proved true in all [formal] systems" is a mixed-up
> of technical terminologies: formal systems prove syntactical theorems,
> truths are verified in language structures. The two paradigms are
> different and _independent_ : proving in one doesn't logical equate
> to the other.

G\"odel's completeness theorem shows that they aren't independent.

When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting