Doron Posted November 21, 2004 Report Posted November 21, 2004 In order to define a framework that is researched and manipulated by a formal language, we first have to define the limitations of the formal language itself. Since any language cannot work without information, we first define what are the minimal and maximal conditions that cannot give us any information, when we try to research them. The minimal concept that cannot be researched is Emptiness, because no information can be found in it. The maximal concept that cannot be researched is Fullness, because it is beyond measurement or manipulation of information. So, formal language can work, if and only if we can measure or manipulate information by our rigorous and consistent logical/gremial rules of our framework. It is obvious that this information can be found only within the middle domain that exists between Emptiness and Fullness, where Emptiness and Fullness concepts, are included in the middle domain only as its non-reached (permanent unexplored) limitations. By this basic approach, which comes before any formal method, we achieve 3 fundamental conditions that must exist in the basis of any consistent framework: 1) We clearly define its operational domain. 2) Any measureable element that can be found in the middle-domain, cannot be but a consistent element of the middle-domain, because it is based on a non-destructive associations between the limits of the middle-domain. 3) Our framework is symmetrical by default, because it is based on constructive associations between opposites. These initial conditions are so comprehensive until they can use concepts like Redundancy and Uncertainty as first-order conditions of our framework. It means that we not just use information, but also first define the full range of the information concept itself, before it is used by some logical/gremial rules. This approach is deeper than any formal logical/gremial rules, and exposes new abilities of the language of Mathematics, which are beyond the Standard formal method. (Urelement: http://mathworld.wolfram.com/Urelement.html ) Empty set is {}. Full set is {__}. Point is {.}. Segment is {._.} The difference between Sgment' edge and a point, can be found in: http://www.geocities.com/complementarytheory/SegPoint.pdf a) There is no urelement between {} and {.}. B) There is no urelement between {.} and {._.}. c) There is no urelement between {._.} and {__}. By {} <--x(={.}) we mean that {.} is a potential {}. By x(={._.}--> {__}} we mean that {._.} is a potential {__}. The least useful input cannot be anything but a combination of {.} AND {._.} forms; therefore x is at least both {.} AND {._.} information form. Now we can write ({},{__}):={x|{} <--x(={.}) AND x(={._.})--> {__}} Some examples that are based on this approach: ------------------------------------------------------------------------------A proof that cannot be accomplished by using standard N members: Theorem: 1*5 not= 1+1+1+1+1 Proof: 1*5 = {1,1,1,1,1} not= {{{{1},1},1},1},1} = 1+1+1+1+1 To understand this proof, please read at least page 13 of http://www.geocities.com/complementarytheory/ONN2.pdf ------------------------------------------------------------------------------A test that shows the advantage of - and + operations in an included-middle logical reasoning framework, can be found in pages 22-29 of <a target=_blank class=ftalternatingbarlinklarge href="http://www.geocities.com/complementarytheory/My-first-axioms.pdf">http://www.geocities.com/co
Tormod Posted November 21, 2004 Report Posted November 21, 2004 Thanks for your post, Doron. At first I wondered why it was posted in the mathematics group but it is obvious after reading it - although it seems more of a "logic" discussion than a physics/maths discussion to me. Originally posted by: DoronThe minimal concept that cannot be researched is Emptiness, because no information can be found in it. The maximal concept that cannot be researched is Fullness, because it is beyond measurement or manipulation of information. I have problems with statements like this. "the minimal concept that cannot be researched"...do you mean "minimum"? And then you go on to state the term "emptiness". This makes me question your approach. It see1ms to me you try to define the limits of knowledge by finding what we can't know at two ends, the nothing end and the too much end. But I disagree with this approach because when you state that something is a concept (ie, "emptiness") then it is also possible to know something about it (ie, it is a definition of something - but of what?). What kind of emptiness? Vacuum? Numberless? Dimensionless? Nothingness? It is ambiguous and therefore not something you can base a logic language on. The same goes for "Fullness". It is even harder to accept because fullness is just a word. Full of what? Do you mean a system that is saturated an thus so full of info that nothing meaningful can be extracted from it? But even such a system is then defined as a concept and concepts we can know something about.
Tim_Lou Posted November 21, 2004 Report Posted November 21, 2004 i think fullness and emptiness are basically the same thing. emptiness means nothing, nothing can get in.fullnes means its full, nothing can get in, since its full.
Tim_Lou Posted November 21, 2004 Report Posted November 21, 2004 i would like to see, if this theory can explain something full of emptiness... : )
Tim_Lou Posted November 21, 2004 Report Posted November 21, 2004 hmm... i think that the world is either fullness or emptiness. think about an object, it consists of atoms, subatomic particles... lets say we take a quark, and see its "structure"if its full, that means its fundamental, since its full, so there is no internal structure.if its not full, then there is space, which is emptiness, and maybe some "fullness" stuff in the emptiness.and when we go deeper into the fullness object, it repeats itself back to the first part. but when talking about fullness, does it mean infinite density, since nothing can squeeze in? so the volume it takes would be zero, and zero is emptiness?
Doron Posted November 21, 2004 Author Report Posted November 21, 2004 Dear Tormod and Tim_Lou, First, thank you for your reply. Since my language is Hebrew, then if you do not understand something, maybe a part of the reason is that I do not express myself correctly in English, so please forgive me. Emptiness and Fullness concepts are used as the weakest and strongest information forms that cannot be manipulated by any mathematical tool. It means that thay are the weakest and the strongest non-composed information forms, which are used as the limits of any formal or informal language. By using the set concept we can distinguish between emptiness and fullness, because: |{}| = 0 where |{__}| = The one, where "The One" is a non-composed element, which is different from "one of many". By using these limitations, we first clearly distinguish between actual infinity (Emptiness and Fullness) and potential infinity, which is any collection of infinitely many elements. In short, potential infinity is the composed form of infinity that cannot reach the state of the non-composed actual infinity. Please look at this diagram, in order to understand better my idea: http://www.geocities.com/complementarytheory/RiemannsLimits.pdf As for symmetry: (If {} then {__}) AND (if {__} then {}) = 1 By this proposition we get the true value, which is based on a symmetry between opposite concepts. The logical basis of Emptiness is: oo …E nor E nor E … oo = 1 The logical basis of Fullness is: oo …F and F and F … oo = 1 For more detailes please see pages 4,5,6 of http://www.geocities.com/complementarytheory/CompLogic.pdf Thank you, Doron
Bo Posted November 22, 2004 Report Posted November 22, 2004 3) Our framework is symmetrical by default, because it is based on constructive associations between opposites. But the 2 opposites are not the same, so in the limiting case to the opposites, we have no symmetry. And we can of course define O{full}=O{empty} (where O is any operator in our language), but this is a big constraint on our language. the rest of the links all look quite interesting; when i have more time i will look at them more clearly Bo
Doron Posted November 22, 2004 Author Report Posted November 22, 2004 [Q by Bo]But the 2 opposites are not the same Complementary associations between opposites is the strongest possible symmetry, because the symmetrical source of the associations is deeper then the opposites, so in the external level there are opposites, but they are indistinguishable in their symmetrical internal level. Without this source of symmetry, there cannot be constructive associations between opposites. Please look at Complementary Logic paper: http://www.geocities.com/complementarytheory/CompLogic.pdf
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