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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 ]
 Charlie-Boo Posts: 1,635 Registered: 2/27/06
Re: I Bet \$25 to your \$1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent

Posted: Mar 15, 2013 2:42 PM

On Mar 15, 12:14 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Mar 15, 3:34 am, Charlie-Boo <shymath...@gmail.com> wrote:
>

> > On Mar 13, 5:57 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > -------------
>
> >  >  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 ...
>
> JUST ANSWER 1 QUESTION STRAIGHT!
>
> How many CHARACTER SYMBOLS are in CBL?

All of CBL uses only the 128 ASCII characters (punctuation, lower and
upper case letters, digits) as symbols so that I can program it
directly.

CBL is basically Predicate Calculus plus (1) input and output
variables [like Lambda Expressions], (2) operators (separated by
commas) # / , / , - , = , ~ and comma.

The most developed part in terms of having implemented it on a
computer are # , = , ~ and functions used to prove Recursion Theory
theorems. The most developed part of the theory is Representability
in which all references to Relationships are of the form
P(a,b,b,b, . . .) i.e. all of the components past the first are the
same, and each reference to a Relationship is treated as a Proposition
as in Propositional Calculus with no quantifiers.

The popular system closest to CBL is the Kleene Arithmetic Hierarchy.
I apply the same logic to CBL expressions but with a big difference:
Instead of a linear hierarchy, I have a set of ?bases? which are
Relationships where Diagonalization is used to show what is not
representable by a particular base.

How Axiomatic Systems Stack Up Regarding Diagionalization &
Incompleteness

1. ZF and Frege Logic have 2 bases (SET and CLASS, CONCEPT and SET)
2. KAH (Kleene) has an infinite list of bases (A0=E0=Recursive,
A1=~r.e., E1=r.e., etc.)
3. CBL treats any Relationship as a base. Q is the base in P/Q.

# / Tertiary infix predicate operator over Individuals x Relationships
+Functions x Relationships
/ Binary infix predicate operator over Relationships x Relationships
= Binary infix predicate operator over Individuals (EQUALITY)
~ Binary infix predicate operator over Individuals (EQUIVALENCE)
- Unary leading infix predicate operator (GENERAL NEGATION)
, Repetitive infix predicate operator over Relationships

~ ^ v => == e a ( ) Formulas (wffs) with special use of ~ operator as
NEGATION

Variables - single letter plus index:

Individuals: M , N , O , M4 , M5 , . . .
Quantified: A , B , C , A4 , A5 , . . .
Input: I , J , K , I4 , I5 , . . .
Output: x , y , z , x4 , x5 , . . .
Relationships: P , Q , R , P4 , P5 , . . .
Sets: S , T , U , S4 , S5 , . . .
Components: a , b , c , a4 , a5 , . . .
Functions: f , g , h , f4 , f5 , . . .
Expressions: E , F , G , E4 , E5 , . . .

(Abbreviations A1 = A , A2 = B , A3 = C , M1 = M , M2 = N , M3 =
O . . . )

Individuals, Quantifieds, Inputs and Outputs range over the universal
set TRUE. Sets are total predicate functions over anything x
anything. Relationships are partial predicate functions over anything
x anything. Components, Functions and Expressions are as in
mathematics.

Constants (multiple letters):

PR The set of provable sentences
TW The set of true sentences.
DIS The set of refutable sentences.
SELF A relationship for which SELF / SELF
NOTX A relationship for which ~ P / NOTX whenever P / NOTX.

Family of Functions

s-i(I,J) Relationship I with J substituted for its i-th component

M # P / Q means P = Q(M): (all x )P(x,x,. . .) == Q(M,x,x,. . .)
P / Q means (exists M)M # P / Q

Syntax (variable name) Convention: F(a,b) iff f(a)=b (f is the Frege
epsilon of F)

HLC: Higher Level CBL (Propositional Calculus): P in HLC is
P(a,b,b, . . .) in CBL

Axiom: There exists a SELF and there exists a NOTX.
In other words: SELF/SELFand P/NOTX => ~P/NOTX

Godel (relation bew) and Turing (Universal Turing Machine) proved
there exists a SELF. ZF is attempting to prove there exists a NOTX.
These are the only 2 bases in Mathematics besides superficial
limitations of subsets.

I am one of the earliest proponents of CBL.

C-B

> ====================================
>
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
> .
>
> You can't!   The answer is TYPE: NUM!
>
>
> because IT RUNS!
>
> Here is 1 of 9 MODULES of BLOCKPROLOG
>
> Check function ATERM and AVAR
>
> TERM
> a-z, 0-9, % and *
>
> VAR
> A-Z, @
>
> That's 26 + 10 + 2 + 26 + 1 = 65 CHARACTERS!
>
> CBL has how many?
>
> What is   | {ALPHABET(CBL)} |  ?
>
> <?
>
> //**********************************
> //**********************************
>
>
> function aterm(\$ch)
> {
>         \$good = false;
>         if ((\$ch>="a") & (\$ch<="z"))
>         {
>                 \$good = true;
>         }
>         if ((\$ch>="0") & (\$ch<="9"))
>         {
>                 \$good = true;
>         }
>         if ((\$ch=="!") | (\$ch=="%"))
>         {
>                 \$good = true;
>         }
>         return \$good;
>
> }
>
> function avar(\$ch)
> {
>                 return (((\$ch>="A") & (\$ch<="Z")) | (\$ch="@"));
>
> }
>
> {
>
>   if (\$id == 0)
>   {
>         \$id = 1;
>     \$sql1 = "SELECT MAX(id) AS MID FROM HEADS";
>     \$result1 = mysql_query(\$sql1);
>     if (\$row = mysql_fetch_array(\$result1))
>     {
>         \$id = \$row['MID'] + 1;
>     }
>   }
>
>   //echo "<br>STORE:" . \$id ." : ". \$ref ." : ". \$term;
>
>   if (avar(\$term[0]))   //A B C
>   {
>      \$sql1="INSERT INTO
>      VALUES(\$id, '\$ref', '*', '\$term')";
>   }
>   else                  //a b c
>   {
>      \$sql1="INSERT INTO
>      VALUES(\$id, '\$ref', '\$term', '')";
>   }
>
>     \$result1=mysql_query(\$sql1);
>
> //    echo "<br>DEBUG10 FID:" . mysql_insert_id();
>     return \$id;
>
> }
>
> function tableTails(\$id, \$ref, \$term, \$tail)
> {
>
> }
>
> function tableQuery(\$ref, \$term)
> {
>   //echo "<br>QUERY: ". \$ref ." : ". \$term;
>
>   global \$pushes;
>
>   if (aterm(\$term[0]))
>   {
>     \$sql1="INSERT INTO
>     QUERY(ref, term, buds)
>     VALUES('\$ref', '\$term', 0)";
>     \$result1=mysql_query(\$sql1);
>   }
>   else
>   {
>                 pushvr(\$term, \$ref);
>                 \$pushes++;
>   }
>
> }
>
> {
>
> // \$strng = 'a  [b  c]  [d  e]'
>
> // +----+-----+------+-----+
> // | id | ref | term | var |
> // +----+-----+------+-----+
> // |  1 |  1  |  f   |     |
> // |  1 |  21 |  g   |     |
> // |  1 |  22 |  a   |     |
>
> // SQL TABLE TAILS
> // +----+-----+------+-----+------+
> // | id | ref | term | var | tail |
> // +----+-----+------+-----+------+
> // |  1 |  1  |  t   |     |   1  |
> // |  1 |  21 |  x   |     |   1  |
> // |  1 |  22 |  y   |     |   1  |
>
> //    f [g a]                  BLoCKPROLOG
> //      t [x y].
> //
> //    f(g(a)) :- t(x(y)).      PROLOG
>
>   //echo "<br><br>DEBUG:add-facts " . \$strng;
>
>   \$i = 0;
>   \$lentail = strlen(\$strng);
>   \$bc = 0;            // bracket count
>   \$tc[0] = 1;         // term count
>   \$ec = 0;            // ] count
>   \$charmode = false;
>   \$term = "";
>   \$sym = "*";
>   \$hid = 0;
>
>   while (\$i < \$lentail)
>   {
>         \$ch = \$strng[\$i];
>         \$ischar = false;
>         \$isvar = false;
>         \$gotterm = false;
>         \$gotsym = false;
>
>         if (aterm(\$ch))
>         {
>                 \$ischar = true;
>         }
>         if ((\$ch>="A") & (\$ch<="Z"))
>         {
>                 \$ischar = true;
>                 \$isvar = true;
>         }
>
>         if (\$ischar)
>         {
>           if ((!\$charmode) & (\$sym!="*"))
>           {
>                 \$gotsym = true;
>                 \$thesym = \$sym;
>           }
>                 \$term = \$term . \$ch;
>                 \$charmode = true;
>                 \$sym = "";
>         }
>         else
>         {
>
>     //check for  '['  ']'  ' '
>
>         if (\$ch == "[")
>         {
>          \$sym = "[";
>           }
>           if (\$ch == "]")
>           {
>         \$sym = "]";
>         \$ec++;
>           }
>           if ((\$ch == " ") & (\$sym == ""))
>           {
>         \$sym = " ";
>           }
>           if (\$charmode)
>           {
>                 \$gotterm = true;
>           }
>           \$charmode = false;  //ignore consecutive spaces
>         }
>
>         if (\$gotterm)
>         {
>                         // add to table when character stream ends
>
>         \$ref = "";
>         for (\$r=0;\$r<=\$bc;\$r++)
>         {
>           \$ref = \$ref . \$tc[\$r];
>         }
>
>         if (\$tail == 0)
>         {
>           \$hid = tableHeads( \$hid, \$ref, \$term);
>                         }
>         if (\$tail > 0)
>         {
>           \$hid = tableTails( \$hid, \$ref, \$term, \$tail);
>                         }
>         if (\$tail < 0)
>         {
>           \$hid = tableQuery( \$ref, \$term);
>                         }
>
>                         \$term = "";
>     }
>
>     if (\$gotsym)
>     {
>                         //if (\$thesym == "]")
>                   //{
>                         while (\$ec>0)   //multiple end brackets    ]]][
>                         {
>                           \$bc--;
>                           \$ec--;
>                           if ((\$thesym != "[") | (\$ec > 0))
>                           {
>                           \$tc[\$bc]++;
>                         }
>                         }
>                   //}
>                         if (\$thesym == "[")
>                   {
>                         \$tc[\$bc]++;
>                         \$bc++;
>                         \$tc[\$bc]=1;
>                   }
>                   else
>                   {
>                         if (\$thesym == " ")
>                   {
>                         \$tc[\$bc]++;
>                     }
>                   }
>
>                   \$gotsym = false;
>     }
>
>         \$i++;
>         }
>
>    return \$hid;
>
> }
>
> ?>
>
> .
> .
> .
> .
> .
> .
> .
>
> That's the INPUT PARSER that detects what level of BRACKETS have been
> entered before each  TERM.
>
> EACH TERM of EACH LINE has to be PROCESSED by a PARSER.
>
> COPY AND PASTE-ABLE <=/=>  MACHINE PARSABLE PROOF
>
> That's 1 of 9 MODULES called by the INDEX.PHP
>
> <?
>
> //**********************************
> //**            INDEX             **
> //**********************************
>
>
> //SETUP INSTRUCTIONS IN BP-CONFIG.PHP
>
>
> include "bp-config.php";
> include "bp-init.php";
> include "bp-query.php";
> include "bp-command.php";
> include "bp-routines.php";
> include "bp-main.php";
>
> main(htmlentities(\$_POST['text1']));
>
> include "bp-footer.html";
>
> ?>
>
> 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