Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: A HARD FLAW in Godel's Proof
Replies: 7   Last Post: Dec 8, 2012 2:27 PM

 Messages: [ Previous | Next ]
 Posts: 822 Registered: 9/1/10
' (97 (97d (97Errors (97iEmany (in .~~ .cisco ~ ~(97e
CCCIDDD Contacts Desktop Documents Downloads een e'en elev ELw end f~ittin Fa
(WAS RE: Re: A HARD FLAW in Godel's Proof)

Posted: Nov 19, 2012 6:55 AM

On Nov 17, 8:55 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Nov 18, 1:10 pm, "INFINITY POWER" <infin...@limited.com> wrote:
>
>
>
>
>
>
>
>
>

> > THINKING CAPS ON!
> > ARGUE LOGICALLY!
> > ASSUME ANYTHING!
> > ROLLBACK ASSUMPTIONS LATER ON <<!

>
> > STEP 1:  DEFINE a 2 parameter predicate DERIVE(THEOREM, DERIVATION)
>
> > DERIVE(T,D) is TRUE IFF
> >   D contains a sequence of inference rules and substitutions
> >   and the final formula T in D is logically implied from the Axioms.

>
> > - - - - - - - - - - - - - -
>
> > STEP 2:  DEFINE a Godel Statement.
>
> > i.e.  Godel Statement named G =
> >     ALL(M)  ~DERIVE(G,M)

>
> > - - - - - - - - - - - - - -
>
> > STEP 3:  IS G A THEOREM?
>
> > ASSUME: YES G IS A THEOREM
> >     DERIVE(   G:ALL(M)~DERIVE(G,M)  , D )

>
> > - - - - - - - - - - - - - -
>
> > STEP 4:  UNIFY THE QUERY TO THE AXIOMS TO GET THE ANSWER
>
> >   GOAL :       DERIVE(  G:ALL(M)~DERIVE(G,M)   , D )
> >   SUBGOAL :    G:ALL(M)~DERIVE(G,M)

>
> >   (SUBGOALs are a Derivation Process that calculate reverse D in the trace)
>
> > - - - - - - - - - - - - - - -
>
> > STEP 5:  REMOVE THE QUANTIFIER
>
> >   G:~EXIST(M)DERIVE(G,M)
> >   G: ~DERIVE(G,M)

>
> > M is a variable and Existential by Double Variable Instantiation Rule of
> > UNIFY().

>
> > - - - - - - - - - - - - - - -
>
> INSERT  A STEP:
>
> STEP 6a
>
> G: ~DERIVE(G,  [G | M] )
>
> G is the HEAD of M by definition.  (either 1st or last element)
> M are the REMAINING TAIL of deductions back to the axioms.
>
> [G <- <M>]
> [G <- N <- <O>]
> ...
> [G <- N <- P <- ... <- AXIOMS ]
>
> Now M is strictly FREE as it doesn't contain G as an element in it's
> deduction list.
>
> and 6a reduces to 6 below.
>
>
>
>
>
>
>
>
>

> > STEP 6:  M IS A FREE VARIABLE
>
> >   G: ~DERIVE(G,M)
>
> > is a null statement that will return
'
(97
(97d
(97Errors
(97iEmany
(in
.~~
.cisco
~
~(97e
'~urif
000
100
128
als
Blaauw-bezien.W
CCCIDDD
Contacts
Desktop
Documents
een
e'en
elev
ELw
end
f~ittin
Favorites
filenames.txt
for
ful.crd
gtmp
gtmpgPa
ID
iff
information
isaccording
iseen
Ke~'
Kruid
''loathsome.al
m.crd
Martin
Money
Musatov.txt
Music
new 2.mak
oin
'Phalve
Pictures
r
S~tal-l,tter
Saved Games
Searches
Semis
so
TA
''Theft
Videos
'vochtig
Windows[1]
with
x.16
Y.Y.Y.Y.53
Y~(97g
>
> > SUBGOAL:  M?
>
> > i.e. When parsed by a clever logic compiler, Godel's Statement will return a
> > Query in response

>
> > [PROVER]- "Why is sentence G not derivable?"
>
> > Herc
>
> > --
> > if( if(t(S),f(R)) , if(t(R),f(S)) ).
> >     if it's sunny then it's not raining
> > ergo
> >        if it's raining then it's not sunny

'
(97
(97d
(97Errors
(97iEmany
(in
.~~
.cisco
~
~(97e
'~urif
000
100
128
als
Blaauw-bezien.W
CCCIDDD
Contacts
Desktop
Documents
een
e'en
elev
ELw
end
f~ittin
Favorites
filenames.txt
for
ful.crd
gtmp
gtmpgPa
ID
iff
information
isaccording
iseen
Ke~'
Kruid
''loathsome.al
m.crd
Martin
Money
Musatov.txt
Music
new 2.mak
oin
'Phalve
Pictures
r
S~tal-l,tter
Saved Games
Searches
Semis
so
TA
''Theft
Videos
'vochtig
Windows[1]
with
x.16
Y.Y.Y.Y.53
Y~(97g

Date Subject Author
11/17/12 INFINITY POWER
11/17/12 Graham Cooper
11/19/12
11/18/12 Graham Cooper
11/18/12 Graham Cooper
12/8/12 Graham Cooper