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Topic: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Replies: 39   Last Post: Oct 14, 2012 11:56 PM

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 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted: Oct 14, 2012 9:21 PM

> LHS & (LHS -> (a&b->c)) -> a&b->c
>
> to derive models of backward chainable embedded theories that are
> recursively provable back to the axioms!
>

BINARY MODUS PONENS

a & b & (a&b)->c --> c

This not only WORKS! It derives all proofs!

PROOF = backward chainable binary directed acylic graph

You're still stuck on the 'CLASSIC THEOREM'!

******** 10 YEARS DEBUGGING TO FIX THIS **********

> NOT(PA |- P) & NOT(PA |- ~P).
> That is the classical theorem. Duh.
> [...]

> >> I don't see your point. The theorem says that PA can not decide a
> >> particular formula.

> > no, a particular wff (conditions apply)
> When I say "formula", I mean "WFF". I have no reason to talk about
> non-well-formed formulas.

That's why your proof is wrong.
-------------------------------------
[ERROR 1]
By WFF you mean it has a single reduction tree in predicate calculus
from sub predicates and atomic formula, giving it a unique
interpretation. So you have limited the scope of your proof to boolean
formula (true or false).
-------------------------------
[ERROR 2]
THEN: YOU START ADDING FORMULA AT WILL.
"WE CAN CONSTRUCT ANY FORMULA AND TRY TO ADD IT TO THE THEORY"
ERROR!

PA |- P
This is using an axiom-less or inconsistent theory
--------------------------------------
[VALID STEP]
Because P is "true" by some rudimentary reductions (P can't be false)
NOT( PA |- P )
NOT( PA |- ~P )
-------------------------------------
[ERROR 3]
P <-> NOT( PA |- P )
so P is TRUE (in PA)
-------------------------------------
[ERROR 4]
P is a WFF in PA
AND
P is TRUE in PA
---> P is a missing theorem of PA

You EQUATE
WFF + TRUE --> THEOREM
-------------------------------------
[ERROR 5]
Because:
(P -> Q) -> (P ^ AXIOM) -> Q
is true for 0 order terms (not formula with quantifiers)
You conclude adding AXIOMS to PA could never filter out the Godel
Statement and call it
MONOTONIC LOGIC!
--------------------------------

Herc

Date Subject Author
10/5/12 Graham Cooper
10/5/12 Frederick Williams
10/7/12 Charlie-Boo
10/5/12 Graham Cooper
10/5/12 Frederick Williams
10/5/12 Graham Cooper
10/7/12 Graham Cooper
10/8/12 Graham Cooper
10/9/12 Graham Cooper
10/11/12 Graham Cooper
10/12/12 Graham Cooper
10/12/12 Graham Cooper
10/12/12 camgirls@hush.com
10/12/12 Richard Tobin
10/12/12 camgirls@hush.com
10/13/12 george
10/13/12 Graham Cooper
10/14/12 george
10/13/12 Graham Cooper
10/13/12 george
10/13/12 george
10/13/12 Graham Cooper
10/14/12 Graham Cooper
10/14/12 Graham Cooper
10/14/12 Graham Cooper
10/5/12 Scott Berg
10/5/12 Curt Welch
10/6/12 Mike Terry
10/6/12 Graham Cooper