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Topic: I Bet \$25 to your \$1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent

Replies: 20   Last Post: Mar 19, 2013 1:32 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: I Bet \$25 to your \$1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent

Posted: Mar 14, 2013 6:06 PM

>
> > YOU CANNOT SHOW US 1 SYSTEM THAT IS INCONSISTENT
>
> > by the terminology you are making up.
>
> > ----------------
>
> > If you have no USE for the word INCONSISTENT (THEORY)
>
>  >  then say so, and we can stop wasting our time discussing set
> theory
>  >  with you.
>
> With me?  That'll be the day.
>
>
>

> > -------------
>
>  >  WAGER:  I will paypal CHARLIE BOO \$25
>
>  >  if he can prove ANY theory at all is inconsistent!
>
> Didn?t I say ?CBL proves Hilbert impossible.? ?
>
>
> So you want a formal proof  in CBL that Hilbert?s Programme is
> inconsistent or some arbitrary set of typical set axioms is
> inconsistent?
>
> C-B
>

Machine parsable proof ok with you?

CBL, as far as I and anyone here can see,
is a bunch of AD-HOC guidelines on reasoning

It is the COMPLETE OPPOSITE of a Formal System.

Mentioning some VAGUE REFERENCE about MODUS PONENS used in REAL FORMAL
SYSTEMS by just making jokes is NOT substitution for CBL
functionality.

Hand waving away every argument for 3 weeks is NOT justification of
any assertion you've made here - NOTHING you've said has been backed
up COLLOQUIALLY yet alone FORMALLY.

**********

Though not complete in any sense, this is the
SMALLEST FORMAL SYSTEM possible - 12 lines of PROLOG.

tru(t).
not(f).
and(X,Y) :- tru(X),tru(Y).
and(X,not(Y)) :- tru(X),not(Y).
and(not(X),Y) :- not(X),tru(Y).
and(not(X),not(Y)) :- not(X),not(Y).
even(0).
not(and( even(X) , not(even(s(s(X)))) )).
e(A, evens) :- tru(even(A)).
tru(even(X)) :- even(X).
tru(e(A,S)) :- e(A,S).
tru(R) :- not(and(L,not(R))) , tru(L).
**************************

by using a small subset of boolean input predicates (and, not)

You can enter this command into any PROLOG software

?- tru( e( s(s(s(s(0)))) , evens )).

YES

[4 e EVENS] is a Theorem.

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

NOBODY in ANY maths department, newsgroup, book publishing house,
expert software design house, university faculty lounge, high school
maths class, fruit shop, hen house, dog house or Zuhair's scribble pad
is going to follow one single deduction in CBL, yet alone accept it as
a FORMAL PROOF.

LHS -> RHS

Try THAT 1st before you attach your initials to the word LOGIC.

Herc
--
www.BLoCKPROLOG.com

Date Subject Author
3/13/13 Graham Cooper
3/13/13 Graham Cooper
3/14/13 Charlie-Boo
3/14/13 Charlie-Boo
3/14/13 Graham Cooper
3/14/13 Charlie-Boo
3/14/13 Graham Cooper
3/14/13 Charlie-Boo
3/14/13 Graham Cooper
3/15/13 Charlie-Boo
3/19/13 Graham Cooper
3/19/13 Charlie-Boo
3/19/13 Charlie-Boo
3/15/13 Graham Cooper
3/15/13 Charlie-Boo
3/15/13 Graham Cooper
3/19/13 Charlie-Boo