Date: Nov 17, 2012 3:43 PM Author: Graham Cooper Subject: Re: SCI.LOGIC is a STAGNANT CESS PITT of LOSERS! On Nov 18, 3:11 am, George Greene <gree...@email.unc.edu> wrote:

> On Nov 17, 3:50 am, Graham Cooper <grahamcoop...@gmail.com> wrote:

>

> > FROM AXIOMS you DERIVE THEOREMS!

>

> True.

>

> > Nobody CARES if SomeModel |= 'this is not derivable from your

> > axioms"

>

> > looks TRUE!

>

> Sure they do.

>

> > IT's not DERIVABLE FROM THE AXIOMS! END OF STORY!

>

> That's NOT the end of the story!

>

> It is true that the name of the room is "sci.logic" and that WE

> therefore (even if no one else is)

> might be entitled to care about&only about what follows from the

> axioms. But the PROBLEM is

> that the primary USE for formal proof is IN *MATH*.

> THEREfore, EVEN though the sign on the door says sci.logic, it is

> MATHEMATICIANS

> who matter more.

>

> In the relevant case of models and of |= , the MOST relevant model

> around here is

> N, is THE (true&actual) NATURAL NUMBERS.

> IT DOES matter a WHOLE HECK of a lot if something that is true about N

> is NOT

> formally derivable from some decent (i.e. recursive) set of axioms.

> That is VERY important!

> PEOPLE CARE about proving things ABOUT N, *NOT* just about proving

> whatever

> follows from some axioms. For starters, how would you decide WHICH

> axioms were

> IMPORTANT? It is NEVER JUST about the axioms themselves! YOU ALWAYS

> need SOMEthing

> OUTside of logic motivating your investigation! You are always USING

> logic to help you reason

> ABOUT something ELSE!

>

> > Nothing Mathematically INCOMPLETE ABOUT IT!

>

> It is true about all these recursively enumerable formal theories that

> THEY ARE incomplete *ABOUT* N.

> You are sort of right, however, in that first-order-logic ALSO has a

> COMPLETEness theorem.

> A small and reasonable set of rules of inference REALLY IS sufficient

> to derive&prove, formally,

> EVERY theorem that is true in ALL models of the axioms.

> But there is no decent set of axioms or rules that is sufficient to

> derive&prove every (first-order) sentence that is true *in*N*,

> that is true of the natural numbers. THAT is how FOL gets to have

> BOTH a "completeness" AND an "incompleteness"

> [meta]theorem.

>

> Prolog

> just doesn't have anything to do with this. Prolog can't even do

> complete FOL.

> Prolog APPROXIMATES first-order negation-AS-failure.

>

See this is the problem.

You just BAFFLE WITH BULLSHIT every assertion made that doesn't match

your Library Of Logic Facts!

SomeModel |= this-is-not-derivable-by-axiom-set(A1)

--> A1 is incomplete.

*IF* you had any credible mathematical capacity,

you would ACKNOWLEDGE THE ARGUMENT FIRST.

Your UNPROVABLE THEORY - which is 100 YEARS OLD AND GROWING

is merely SELF-CONSISTENT that is why you ARGUE with ATTACK at the 1st

opportunity because

if the OPPOSITE ASSUMPTION is allowed your entire LIBRARY OF LOGIC

goes up in a puff of smoke.

Herc