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!
> > 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
> 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
> 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"
> 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
if the OPPOSITE ASSUMPTION is allowed your entire LIBRARY OF LOGIC
goes up in a puff of smoke.