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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

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Charlie-Boo

Posts: 1,588
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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.? ?
>
> >http://groups.google.com/group/sci.logic/msg/3bc441b51ffe6455?hl=en
>
> > 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!
>
> I could answer that Question about MY SET THEORY
>
> 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)} |  ?
>
> <?
>
> //**********************************
> //**             ADD              **
> //**********************************
>
> //Copyright 2013 (c) BLOCKPROLOG.COM
>
> 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")) | ($ch="@"));
>
> }
>
> function tableHeads($id, $ref, $term)
> {
>   global $factadded;
>
>   if ($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
>   {
>      $sql1="INSERT INTO
>      HEADS(id, ref, term, var)
>      VALUES($id, '$ref', '*', '$term')";
>   }
>   else                  //a b c
>   {
>      $sql1="INSERT INTO
>      HEADS(id, ref, term, var)
>      VALUES($id, '$ref', '$term', '')";
>   }
>
>     $result1=mysql_query($sql1);
>     $factadded = true;
>
> //    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);
>                 $pushes++;
>   }
>
> }
>
> function add1line($strng, $tail)
> {
>
> // $strng = 'a  [b  c]  [d  e]'
>
> // SQL TABLE HEADS
> // +----+-----+------+-----+
> // | 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 $hid;
>
> }
>
> ?>
>
> .
> .
> .
> .
> .
> .
> .
>
> That's the INPUT PARSER that detects what level of BRACKETS have been
> entered before each  TERM.
>
> EACH TERM of EACH LINE has to be PROCESSED by a PARSER.
>
> COPY AND PASTE-ABLE <=/=>  MACHINE PARSABLE PROOF
>
> That's 1 of 9 MODULES called by the INDEX.PHP
>
> <?
>
> //**********************************
> //**            INDEX             **
> //**********************************
>
> //Copyright 2013 (c) BLOCKPROLOG.COM
>
> //SETUP INSTRUCTIONS IN BP-CONFIG.PHP
>
> include "bp-header.html";
>
> include "bp-config.php";
> include "bp-init.php";
> include "bp-add.php";
> include "bp-query.php";
> include "bp-command.php";
> include "bp-routines.php";
> include "bp-main.php";
>
> main(htmlentities($_POST['text1']));
>
> include "bp-footer.html";
>
> ?>
>
> Herc
> --www.BLoCKPROLOG.com




Date Subject Author
3/13/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/13/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/14/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/14/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/14/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/14/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/14/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/14/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/14/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/15/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/19/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/19/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/19/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/15/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/15/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo
3/15/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Graham Cooper
3/19/13
Read Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Charlie-Boo

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