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BoS:Logics of Boxes

(previously Box operating System)
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"H. Finalis [2oo4, with Deborah Caron ("D.C.!", r.i.p. 2oo6...)]" -->

Russell's paradox is an illusion

(see below for syntax code,it's easy)
*Q:Q={X|X/Q}
*Q:*X:X/Q<>X/Q
*Q:#X:X/Q<>X/X
*Q:!*X:!(X/Q<>X/X)
*Q:!*X:X/Q<>!X/X
*Q:!Q={X|!X/X}
(See appendix for another proof)

New entities for Set Theory: locatives, zones and 'Sigma's.

*Q:Q'={X|Q/X}
*Q:X/Q <> Q/X
*Q,X: X//Q <>(X/Q & X%Q)

Complete and computable system with all basic Axioms and Theorems.

And, foremost, uncountable new mysteries and problems.

This is part of Metaphysics. It is useful describing all kind of networks, and the structure of reality, including mind.

This theory is new-born and is still in its baby-shoes. Help might help.

The author is a single person with friends many, most artists.

Since this site is on x.eu the standard language is choosen as (pidgin) english. This should be a x.be site, but since our country is hesitating about it's own existance... Anyway Our Nation's Capital is Brussels. For this reason; x.eu .

'Solyans' is a middle-age name, useable in Latin; for example: HIC EST LOCVS SOLYANTIS. (The 'Y' is pronounced like the french 'U'. 'H' is pronounced while taking air. 'SOLYANTIS' is the genitive form of Solyans. 'V' is the same as 'u', pronounced like the french 'Ou') Since Latin is an European standard language (should be/was), *Solyans* seems a logic choice.

I think XXth's century's 'positivism' is a philosophical dead-end. XXth's science is mere an illusion to go beyond. What response has science about consciousness? None. Maybe because they're wrong. Psychiatry, although so popular is wrong and mostly bad. (Most untold, anybody knows)

The author of this notes is 34 years old in 2oo8, male and not married. He's waiting for his fellow mates regarding their critics and mostly their esthetic help for this site. They seem to be quite lazy. Me too. Call me Jasper if you want to; this is my name when talking dutch (not ducky, duck!) We don't have any private internet connections.

The purpose of Logics is universal truth in Space AND Time. Personal matters do not matter; ergo :
SoSo2oo8 proudly presents

BoS

(c)SoSo2oo8,2007-2008, all rights reserved. It be so.

Since I decided to use the most standard typefaces and symbols the usual symbols of logics are replaced by ASCII-standard symbols, also available on typewriters. This is the conversion table of ASCII-symbol and classic mathematical symbols:

! negation
!! True
* for each, for all
# exists
@ (no use)
== statement equivalency
<>,<=> if and only if
=> then
/ is an element of
% is a subset(part) of

Al Alpha
Be Beta
Ga Gamma
De Delta
Si Sigma
Pi Pi
Om Omega
0 Omicron
(list is not complete yet)

Example: Some major statements written with classic symbols:
(NOT YET AVAILABLE!)

Note: future syntax improvements are possible and even probable

Back to begin

This is a first draw for the theory of boxes. All theorems, including the most obvious ones are proven. Each statement in the list is true; each statements follows from others by equivalence or consequence. The first two statements are axioms. They declare the existence of two essential sets, which are: Om (OMEGA) the set of all sets and 0 (ZERO, NULL or OMICRON), the empty set. Both have a very simple definition.

#Om={X|!!}
#0={X|!!!}
*X:X/Om<>!!
[X|X/Om==!!]
*X:X/Om
*X:X/0<>!!!
*X:!X/0<>!!
[X|!X/0==!!]
*X:!X/0
Om/Om
0/Om
!Om/0
!0/0
#X:X/X
#X:!X/X
#Q:*X:X/Q
#Q:*X:!X/Q

*Q:#Om={X|!!}
*Q:#M={X|!!}
*Q:#M:*X:X/M<>!!
*Q:#M:*X:X/M
*Q:#M:Q/M
*Q:#X:Q/X
\QED

*Q:#O:*X:X/O<>!
*Q:#O:*X:!X/O
*Q:#O:!Q/O
*Q:#X:!Q/X
\QED

[A,B,X|A%B == *X:X/A=>X/B]
[A,B|A=B == A%B & B%A]
*Q:#-Q:-Q={X|!X/Q}
*Q:#-Q={X|!X/Q}
*Q:*X:X/-Q<>!X/Q
*Q,X:X/-Q<>!X/Q
[Q,X|X/-Q==!X/Q]
*Q:#Q'={X|Q/X}
*Q:*X:X/Q'<>Q/X
*Q,X;X/Q'<>Q/X
[Q,X|X/Q'==Q/X]
*A,B:A%B <> *X:X/A=>X/B
*A,B:A=B <>(A%B & B%A)
*A,B:A=B <>(*X:X/A=>X/B & *X:X/B=>X/A)

*A,B:A=B <> *X:X/A<>X/B
#-Om={X|!X/Om}
*X:X/-Om<>!X/Om
*X:!X/-Om<>X/Om
*X:!X/-Om<>!!
*X:!X/-Om
*X:!X/0 & *X:!X/-Om
*X:!X/0 & !X/-Om
*X:!X/0 <> !X/-Om
*X:X/0 <> X/-Om
0=-Om <> *X:X/0<>X/-Om
0=-Om <> !!
0=-Om
*A,B:A=-B <> *X:X/A<>X/-B
*A,B:A=-B <> *X:X/A<>!X/B
*A,B:A=-B <> *X:!X/A<>X/B
*A,B:A=-B <> *X:X/-A<>X/B
*A,B:-A=B <> *X:X/-A<>X/B
[A,B|A=-B==*X:X/-A<>X/B]
[A,B|-A=B==*X:X/-A<>X/B]
[A,B|A=-B==-A=B]
*A,B:A=-B <> -A=B
*A,B:A=B <> A%B&B;%A
*A,B:A=B <> B%A&A;%B
*A,B:B=A <> B%A&A;%B
*A,B:B=A <> A=B
[A,B|B=A == A=B]
-0=Om
Om=-0
-Om=0

Listing v0.0 (manual) - To Be Continued...


Previous is not a very good BoS-listing, it's demonstrative and not so essential. The interpreter-program is far from finished. Many statements will follow. Be sure for now it's easy to prove that:


*Q:Q/Om <> Q%Om

With this theorem one can easily demonstrate a big bang of an infinite number of sets in Om, all singular unlike undifferentiated points... A chaos into which it's hard to find and keep order... It's often though, but lovely.
Here's the proof, although nothing was said about BoS-metalogics yet;

#Om={X|!!}
#0={X|!}
*X:X/Om<>!!
[X|X/Om == !!]
*X:X/Om
Om/Om
0/Om
*X:X/0<>!
*X:!X/0<>!!
[X|!X/0 == !!]
*X:!X/0
!Om/0
!0/0
*A,B:A%B <> *X:X/A=>X/B
*A,B:A=B <>(A%B & B%A)
*Q:Q%Om <> *X:X/Q=>X/Om
*Q:Q%Om <> *X:X/Q=>!!
*Q:Q%Om <> *X:!!
*Q:Q%Om <> !!
*Q:Q%Om
*X:X%Om
(*X:X/Om) & (*X:X%Om)
*X:X/Om & X%Om
*X:X/Om <> X%Om
\QED
0/Om => {0}%Om
\ERGO; {0}%Om => {0}/Om => {0,{0}}%Om => {0,{0}}/Om => ...ad infinitum

This made me wonder.
?

More listings will be added with next updates. (One cannot just downcopy data written with a mechanical typewriter)

\>The problem i'm thinking about now: "Is there a co-set for each set?"
? *Q:#-Q={X|!X/Q}
\> elseway said;
? *Q:#P:P={X|!X/Q}
\> the inversed of this;
? #Q:*P:!P={X|!X/Q}
\> I wonder if there is a proof to this or if this is an axiom, a random truth...
\> TO BE CONTINUED!

Last update (8th): 1.IIX-2oo8AD[modified 28.X-2o1oAD]

New Online start date:31.XII'17
Version 1.9 17th of I 2o18

'Smoking dude' drawing: (c)Franquin,...

Everything else: (c)G.Lowie [Gent/Bruxelles]

Appendix: another proof about Russell's non existance:

Back to begin

Personal note:
"This feels strange, because it says that certain sets, how obvious they might seem, just don't exist. So one has to be careful when defining new sets... The paradox doesn't break the basic set theory, but one has to admit it is impossible to create a Russell set. This must have some philosophical meaning. Accepting this, although, makes logics feel more pure and less academic. It adds beauty."



De Muren zijn zo sterk, Zo hard.
Alle handen die me reikten
wilden, stierven of gaven op.
Mijn tranen bereiken de bewoonde wereld niet.
Het is Ik en de muren.
D.C.

The Walls are so strong, so hard.
All the hands that for me
reached, died or gave up.
My tears don't reach a living soul.
It's but Me with the walls. (translated)
D.C.

Les Murs sont si forts, si durs
Toutes les mains vers moi
tendues, mortes ou abandonn饳
Pas un chat qui entende mes larmes
C'est Moi et les murs. (traduit)
D.C.

The walls are So strong, So hard...



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