Date: Oct 12, 2012 8:37 PM Author: camgirls@hush.com Subject: Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ? On Oct 13, 9:39 am, George Greene <gree...@email.unc.edu> wrote:

> On Oct 12, 5:49 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:

>

> > deductive system is a list of formulas,

> > each of which is a logical axiom

>

> NO, a deductive system IS NOT a list of formulas.

>

> JEEzus.

That's a quote from WIKI

>

> > there is no decision procedure

> > that determines whether arbitrary formulas are logically valid

>

> THERE IS, however, an algorithm that CONFIRMS that a formula is

> logically valid WHEN IT IS.

so why can't you do brute force lexicographically on ALL formulas and

output

VALID

NOT VALID

> The consequence relation for standard classical first-order logic IS

> SEMI-decidable.

> The reason it is not a decision procedure is that there is no

> algorithm that can confirm

> (in the general case) that a first-order wff is NOT valid when it's

> NOT (although that is also

> confirmable SOMEtimes -- every confirmation that a wff IS valid is

> also a confirmation&proof

> that its denial is not).

>

> > So much for your ALGORITHMIC proof that

>

> > ~E(r) xer <-> ~xex

>

> > is a part of ZFC AUTOMATICALLY.

>

> NO, DUMBASS -- THERE IS a proof -- so, therefore, there is, also, by

> definition, AN ALGORITHM that CONFIRMS

> the existence of a proof -- that

> ~Er[ xer <--> ~xex ] is valid.

> If you had any sense you would just PRESENT THIS PROOF YOURSELF.

I don't present proofs.

I enter them into proof software and claim the theorem is true as far

as the axioms and consistency of the proof software is concerned.

>

> BECAUSE this proof depends ON NO axioms -- LOGICAL OR OTHERWISE --

> this sentence is necessarily valid

> and necessarily a theorem OF ALL first-order formal theories in which

> IT CAN BE STATED AT ALL, i.e., in which

> a binary predicate e is in THE FIRST-ORDER LANGUAGE in which the

> theory is being phrased.

> All those theories "have" or "contain" (a theory is a set of sentences

> that is closed under logical consequence)

> all the first-order validities PLUS their axioms PLUS the theorems

> THAT FOLLOW FROM their axioms.

..because you say so.

Where on EARTH have you guys been HIDING this

******************************************************

*PLATONIC WORLD OF ABSOLUTE TRUTHS*

******************************************************

FOR THE LAST 10 YEARS YOU'VE BEEN DENYING

1 SINGLE FORMULA IS BONA FIDE TRUE#.

As far as MATHS AND LOGIC is CONCERNED

#TRUE = W.R.T. STATED AXIOMS

I have not SEEN a FORMAL PROOF BY RESOLUTION ONCE on SCI.LOGIC.

I wan't born with

T |- formula & ~formula

->

! (T |- formula )

&

T |- ~EXIST(formula)

embedded into my AXIOMLESS AUTOMATIC Thought Processes!!

Last chance George, put up THEOREM 1 of your AXIOMLESS LOGIC THEORY or

SHUT UP!

Herc