On Oct 28, 2:36 am, Nam Nguyen <namducngu...
> >> - Therefore a theory that can carry out basic arithmetic operations
> >> is a consistent theory.
> > G del never says any such thing.
> Not literally word for word of course. No more than he said
> that his informal proof can be "formalized" by PRA 80 years
> later, word for word.
SCI.MATH and SCI.LOGIC seem to think FORMAL means it's got A, E, ~,
( ) in it!
Common mistake by beginners to assume their language is formal because
it looks rigorous but it's actually a lot of work to construct an
actual formal system.
On Oct 27, 11:28 am, George Greene <gree...@email.unc.edu> wrote:
> EVERYthing is formal and algorithmic. In particular, first-order
> INFERENCE AND PROOF are formal and algorithmic.
This is just LINE BY LINE level of automation, not a formal system.
Same MEGA-MISTAKE by Godel and Tarski.
The FORMAL SYSTEM enumerates the sentences, you don't CONSTRUCT
"We can CONSTRUCT *A* sentence" L<->~Tr(#L)
"We can CONSTRUCT *ANY* sentence" L<->~Tr(#L)
F&~F |- W
From a Contradiction Anything Follows!
You cannot prove anything about Axiomatic Systems this way!