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Topic: THE ONLY -[SET THEORY]- YOU NEED IS -[SELF-CONSISTENT]- AND A -[TAUTOLOGY]-
Replies: 3   Last Post: Apr 16, 2013 10:12 PM

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Charlie-Boo

Posts: 1,585
Registered: 2/27/06
Re: THE ONLY -[SET THEORY]- YOU NEED IS -[SELF-CONSISTENT]- AND A -[TAUTOLOGY]-
Posted: Apr 2, 2013 9:27 PM
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On Feb 28, 8:54 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> A Set Exists only if that set not existing is not true!!
>
> ----PROVABLE SET THEORY------
>
>    E(S) A(X)  [XeS  <-> P(X)]
>    <->
>    ~(~E(S) A(X) [XeS <-> P(X)]  )
>
> ------------------------------------------
>
> The P.S.T. Axiom is actually a Tautology!
>
>     formula <-> ~~formula
>
> -------------------------------------------
>
> Based on NAIVE SET THEORY AXIOM
>
>    E(S) A(X)  [XeS  <-> P(X)]
>
> ------------------------------------------
>
> The is no Universe V!
>
> The Transitive Closure of P.S.T. is {}
>
> All Sets Existence must be assumed!
>
> N.S.T and Z.F.C AXIOM of SPECIFICATION
> assert Existence of Sets for certain predicates!
>
> E(S) .....
>
> ----------------------------------------
>
> P.S.T. is just a bi-conditional,  a RESTRICTION that contradicts
> THE *ASSUMPTION* OF RUSSELL'S SET!
>
>    E(S) A(X)  [XeS  <-> P(X)]
>    IFF
>    ~(~E(S) A(X)  [XeS <-> P(X)]  )
>
> -->
>
>   E(RS) A(X)  [XeRS <-> P(X)]
>   <->
>   ~(~E(RS) A(X)  [XeRS <-> P(X)] )
>
> -->
>
>   E(RS) A(X)  [XeRS <-> P(X)]
>   <->
>   ~(~E(RS) A(X)   [XeRS <-> P(X)] )
>
> -->
>
>   E(RS) A(X)  [XeRS <-> X~eX ]
>   <->
>   ~(~E(RS) A(X)   [XeRS <-> X~eX ])
>
> -->
>
>   E(RS) A(X)  [XeRS <-> X~eX ]
>   <->
>   ~(~E(RS) A(X)  [RSeRS <-> RS~eRS] )
>
> -->
>
>   E(RS) A(X)   [XeRS <-> X~eX ]
>   <->
>   ~(~E(RS)  A(X)  [f<->~f] )
>
> -->
>
>   E(RS)  A(X)  [XeRS <-> X~eX ]
>   <->
>   ~(~E(RS) A(X)  FALSE )
>
> -->
>
>   E(RS) A(X)  [XeRS <-> X~eX ]
>   <->
>   ~TRUE
>
> -->
>
>   ~E(RS) A(X)  [XeRS <-> X~eX ]
>
> ***************************
>
> Most other sets like N and U - the Set of all Sets
> can safely be assumed in P.S.T.
>
> LET
> P(x, N) <-> (x=0) v (E(z) x=S(z) & P(z, N))
>
> ASSUME
>    ~(~E(N) A(X)  [XeN <-> P(X)]  )
>
> P.S.T. AXIOM
>    E(S) A(X)  [XeS  <-> P(X)]
>    <->
>    ~(~E(S) A(X)  [XeS <-> P(X)]  )
>
> -->
>
>    E(N) [XeN  <-> P(X)]
>    <->
>    TRUE     (ASSUMPTION)
>
> -->
>
>    E(N) [XeN <-> P(X)]  )
>
> ALL SETS EXISTENCE MUST BE ASSUMED!
>
> Herc
> --www.BLoCKPROLOG.com


SUBJECT = THE ONLY -[SET THEORY]- YOU NEED IS -[SELF-CONSISTENT]- AND
A -[TAUTOLOGY]-

However, you use "tautology" only 1 time - in a question - and
"consistent" zero times. Is that as advertised?

And, as you surely know, CBL proves Russell's Paradox in 1 sentence
(and if you don't know what that means, then consult any introductory
text on logic e.g. Logic for Imbeciles) and it is in the first 10
theorems CBL generates.

C-B



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