Nam Nguyen wrote: > > On 11/04/2013 9:38 AM, Frederick Williams wrote: > > Nam Nguyen wrote: > > > >> > >> Don't pretend I didn't have a valid reason why I refuse to technically > >> argue with you on matters related to language structure such as GIT. > > > > G\"odels' incompleteness theorem says nothing about language structures, > > its statement and its proof are wholly syntactical. > > > > So the natural numbers, underlying GIT's arguments, isn't a notion > of what we'd today refer to (or even define) as a language structure?
No, the natural numbers aren't a language structure. A language structure looks like this:
<a set U, family of relations of various arities on U, family of functions of various arities on U, distinguished elements of U>.
The details will depend on the language. U may be the set of natural numbers, indeed (for first order languages) it can always be chosen to be N so long as it isn't finite. But that has got nothing to do with your false claim that G\"odel's incompleteness theorem relates to language structure.
-- 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