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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: 4,227
Registered: 5/20/10
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted: Oct 7, 2012 5:48 PM
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On Oct 8, 6:38 am, George Greene <gree...@email.unc.edu> wrote:
>
> Another point that makes enumeration irrelevant is that all the new
> theorems
> that you get from the axioms were in fact already present from the
> UNDERLYING VALIDITIES that were provable FROM NO axioms,
> because every proved theorem only USES a FINITE number of the axioms.
> Thus, if the theorem was "h" and the axioms (or instances of axioms)
> used
> to prove it were a,b,c,d,f, and g, then
> a^b^c^d^f^f->h
> WAS ALREADY A THEOREM of *pure* predicate calculus, was ALREADY
> a first-order validity.  So there really is a sense in which the
> axioms merely
> highlight a subset of the validities, as opposed to adding new stuff.
> The order in which this highlighting occurs IS NOT important.
> I'm SORRY FOR YOU, HERC, that the only treatment YOU have seen
> HAPPENS to STRESS the "enumeration".  You're a victim of a lame
> education.
> Which would be easily cured if you only had sense enough to read
> ANOTHER book.



You can stick to "ENUMERABLE" if you are too clueless to WORK_OUT the
ENUMERATION.

ATLEAST THAT'S SOMETHING TANGIBLE!

BUT YOU ARE CONTRADICTING YOURSELF ALL OVER THE PLACE.

YOU SAID THE SET OF TRUTHS ARE 'AUTOMATIC' AND NOT POSSIBLE TO DERIVE
FROM AN ALGORITHM.

Herc
--

GEORGE'S SET THEORY!
*****************************

GEORGE'S RELATION ALGEBRA!
aRb

GEORGE'S INFERENCE RULES!
P -> P
~(X -> ~X)
a^b^c^d^f^g->h

GEORGE'S SET AXIOMS!
1. Extensionality:
AxAy [Az (zex <-> zey) -> x=y]
2. Regularity:
Ax [Ea (aex) <-> Ey (yex & ~Ez (zey & zex))]
3. Specification Schema:
AzAw_1...w_nEyAx [xey <-> (xez & phi)]
4. Pairing:
AxAyEz (xez & yez)
5. Union:
AfEaAyAx [(xey & yef) -> xea]
6. Replacement Schema:
AaAw_1...w_n [Ax (xea -> E!y phi) -> EbAx (xea -> Ey (yeb & phi)]
7. Infinity:
Ex [0ex & Ay (yex -> S(y)ex)]
8. Powerset:
AxEyAz [z subset x -> zey]
9. Wellordering:
AxEr (r wellorders x)

GEORGE'S VALIDATED SENTENCES!
THEOREM 1 = ..
THEOREM 2 = ..
THEOREM 3 = !E(R) XeR <-> !(XeX) *TADAAAA*


Date Subject Author
10/5/12
Read If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Frederick Williams
10/7/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Charlie-Boo
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Frederick Williams
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/7/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/8/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/9/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/11/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
camgirls@hush.com
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Richard Tobin
10/12/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
camgirls@hush.com
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
george
10/13/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/14/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Scott Berg
10/5/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Curt Welch
10/6/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Mike Terry
10/6/12
Read Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Graham Cooper

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