Date: Nov 17, 2012 4:36 PM
Author: Hercules ofZeus
Subject: Re: SCI.LOGIC is a STAGNANT CESS PITT of LOSERS!

On Nov 18, 4:24 am, Frederick Williams <freddywilli...@btinternet.com>
wrote:
> Graham Cooper wrote:
>

> > FROM AXIOMS you DERIVE THEOREMS!
>
> > Nobody CARES if  SomeModel |=  'this is not derivable from your
> > axioms"

>
> > looks TRUE!
>
> > IT's not DERIVABLE FROM THE AXIOMS!   END OF STORY!
>
> How do you show that some formula (phi, let's say) is not derivable from
> the axioms?
>



You start with a naive specification of DERIVE(THEOREM)

You gave a rudimentary description of the method at one point, see how
you go!

Herc
--

TAUTOLOGIES
A B T TYPE
a a->c c Modus Ponens
d->e e->f d->f Transitivity
!(!d) TRUE d Double Negation
...
LOGIC
E(Y) Y={x|P(x)} <-> DERIVE( E(Y) Y={x|P(x)} )
DERIVE(T) <-> DERIVE(a) ^ DERIVE(b) ^ (a^b)->T
MATHEMATICS
E(Y) Y={x|P(x)} <-> PRVBLE( E(Y) Y={x|P(x)} )
PRVBLE(T) <-> NOT(DERIVE(NOT(T)))