
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted:
Oct 12, 2012 8:37 PM


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 firstorder logic IS > SEMIdecidable. > The reason it is not a decision procedure is that there is no > algorithm that can confirm > (in the general case) that a firstorder 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 firstorder formal theories in which > IT CAN BE STATED AT ALL, i.e., in which > a binary predicate e is in THE FIRSTORDER 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 firstorder 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

