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Frege's Concept - Script (Begriffsschrift)

  1. Mar 18, 2004 #1
    "Frege's main goal was to improve the foundations of mathematics and scientific work in general. In attaining this goal he invented a artificial language (Begriffsschrift), which were itself a milestone in human intellectual history.

    The Begriffsschrift makes use of a logical notation that makes it possible to express sentences of larger complexity than Aristotle's logic did. Indeed, we are talking a revolution in logic (it was published in 1879)."
    ( http://www.findlink.dk/frege/frege.htm )


    Some examples of Frege's Concept-Script (Begriffsschrift) logical notations can be found here:

    http://mailbox.univie.ac.at/Frank.Hartmann/Vorlesung/ws07.htm

    http://www.stephenwolfram.com/publications/talks/mathml/Images/Frege.jpg

    An example of 7 steps thet translates his notations to the modern linear way, can bo shown here:
    http://www.roman-eisele.de/phil/stuff/logik/BaumZuBegriffsschrift.pdf

    And a full text of him in modern notations, can be shown here:
    http://comet.lehman.cuny.edu/mendel/papers/Adobe Versions/AdobeNewBGForms.pdf

    Frege's method gives us a good opportunity to examine the general information structure that standing in the basis of well defined notations and their relations.

    Most mathematicians of his time did not understand his work because he used a non-conventional way to address his remarkable ideas.

    His unique representation was left behind, and the insights of it where never learned by the community of modern mathematicians.

    For the last 20 years I am (on and off) in a private journey for my own pleasure that tries to find the information structures that maybe standing in the basis of any information system.

    By this approach I hope to find a general method that can order these information structures by their symmetry degrees, and then to define a common and simple basis to any information system, which gives us the ability to find deeper relations between so called different areas of information systems.

    Shortly speaking, I hope to find an organic and dynamic structure that can enrich the ways that self aware systems in infinity many levels of awareness, can communicate among them, without destroying or blocking each other’s opportunities to flourish.

    Lately I discovered Frege’s work and I think that there is a deep connection between his representation method and my goal.

    If we examine Frege’s structural forms we can find that they are private cases of broken symmetries that appearing in my ordered information structures, for example please open the attached pdf file in page 4 (in the paper, not in the acrobat screen):

    http://www.geocities.com/complementarytheory/ET.pdf

    Also you can see that these ordered information structures, can be represented in variety ways, but still all these different representations are based on the same symmetry transformation between its most symmetrical form and most broken form, which are limited by a given finite quantity.

    The old-new way that I have started here cannot be done by a one person, so if you find my work useful to you I’ll be glad to share my best in a common research with you.

    A general view of my work can be found here:

    http://www.geocities.com/complementarytheory/CATpage.html


    Yours,

    Organic.
     
    Last edited: Mar 18, 2004
  2. jcsd
  3. Mar 18, 2004 #2

    matt grime

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    So you simlutaneously want 'well defined notation' and use without explanation the following non-standard terms:

    standing in the basis of
    information system
    symmetry degree
    ordered information structure

    You also cite the work of a man whose contributions were overlooked (allegedly) because he didn't use conventional notation. You might want to ponder on that the next time you write binary tree for something that isn't a tree (in the mathematical sense).

    Given your repeated indications that you think mathematicians are 'wrong' and closed minded about your ideas, who do you think is going to come and help you?
     
  4. Mar 18, 2004 #3
    I can find persons that can understand my ideas, and these persons do not afraid to open themselves and their methods to the complexity of the real life, for example:

    Code (Text):

    -----Original Message-----
    From: Dr. A.M.Selvam [mailto:amselvam@eth.net]
    Sent: Monday, March 01, 2004 10:04 AM
    To: Shadmy Doron
    Subject: A new approach for the definition of a NUMBER

    1 March 2004

    Dear Doron  Shadmi

     I am indebted to you for your email dated
    16 February giving references of your valuable
    research work.
     
     I find your original research work very valuable
    for developing a simple unified theory with ramifications
    in the numerical modeling of nonlinear dynamical
    systems/processes.

     Your research work would benefit many of the scientists
    particularly those who are working in the area of
    numerical modeling.

                                       with best regards
                                        yours sincerely
                                  Dr. (Mrs.) A. Mary Selvam
     
    Papers of Dr. (Mrs.) A. Mary Selvam can be found here:

    http://www.geocities.com/CapeCanaveral/Lab/5833/pub11.html
     
  5. Mar 18, 2004 #4
    Matt,

    Let us try to work together.
    Let F be a finite integer which its tree-like structure can be ordered by its symmetry degree, where symmetry degree means transformation between complete parallel branches to complete nested branches.

    Please take these informal definitions and try to address them in a rigorous way.

    Thank you.

    Organic
     
    Last edited: Mar 18, 2004
  6. Mar 18, 2004 #5

    matt grime

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    Why would I be remotely qualified to offer a rigorous definition of the objects in your head? You aren't Witten, sorry to have to break that to you, we don't have to decide what you mean. You do. You've also, as ever, just introduced yet more undefined terms into it. Remember you are the one that wanted 'well defined notation'.

    I've read some of her papers. Not knowing what 'quantum chaoslike' means (despite knowing what quantum chaos is) I don't feel qualified to offer an opinion on her merits. Presumably you checked all her papers carefully, and understood them all. Also her statements about occurences of things in DNA patterns has to be up there in the 'stating the bleeding obvious' category, but then she is a meteorologist.
     
  7. Mar 18, 2004 #6
    Matt,

    All I asked is to work together with you, but since you don't find my ideas understood by you, then let's forget my offer.

    I have noticed that you never opened a thread of your own, can you tell us why?

    I think that's the reason why she can understand me and you don't, because your community trying to avoid reality influence.
     
    Last edited: Mar 18, 2004
  8. Mar 18, 2004 #7

    matt grime

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    Offer me a simple clear definition of any of the things you use and we can see.

    Why would I bother starting a thread in TD? I've no need to, or interest in so doing. My research is available to those who need it. Somehow I don't think asking in General Math whether the homotopy colimit in the stable category is naturally isomorphic to the first corner in the triangle of the Bousfield localization wrt the f.g modules will get any responses worth considering. If i come across anything that requires posting I'll be the first to ask.
     
  9. Mar 19, 2004 #8
    Can you take this transformation and address in your way?

    Code (Text):
    [b]
    A set is only a framework to explore our ideas.

    The concept of an oredered set does not depend on the quantity concept as shown here:

    By Complementary Logic multiplication is noncommutative,
    but another interesting result is the fact that multiplication
    and addition are complementary opreations that can be ordered
    by different symmetry degrees where quantity remains unchanged
    for example:

    A Number is anything that exists in ({},{__})

    Or in more formal definition:

    ({},{_}):={x|{} <-- x(={.}) AND x(={._.})--> {_}}

    Where -->(or <--) is ASPIRATING(= approaching, but cannot become closer to).

    If x=4 then number 4 example is:

    Number 4 is a fading transition between multiplication 1*4 and
    addition ((((+1)+1)+1)+1) ,and vice versa.

    This fading can be represented as:
     

    (1*4)              ={1,1,1,1} <------------- Maximum symmetry-degree,
    ((1*2)+1*2)        ={{1,1},1,1}              Minimum information's
    (((+1)+1)+1*2)     ={{{1},1},1,1}            clarity-degree
    ((1*2)+(1*2))      ={{1,1},{1,1}}            (no uniqueness)
    (((+1)+1)+(1*2))   ={{{1},1},{1,1}}
    (((+1)+1)+((+1)+1))={{{1},1},{{1},1}}
    ((1*3)+1)          ={{1,1,1},1}
    (((1*2)+1)+1)      ={{{1,1},1},1}
    ((((+1)+1)+1)+1)   ={{{{1},1},1},1} <------ Minimum symmetry-degree,
                                                Maximum information's  
                                                clarity-degree                                            
                                                (uniqueness)


    ============>>>

                    Uncertainty
      <-Redundancy->^
        3  3  3  3  |          3  3             3  3
        2  2  2  2  |          2  2             2  2
        1  1  1  1  |    1  1  1  1             1  1       1  1  1  1
       {0, 0, 0, 0} V   {0, 0, 0, 0}     {0, 1, 0, 0}     {0, 0, 0, 0}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |  |  |  |       |__|_ |  |       |__|  |  |       |__|_ |__|_
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |__|__|__|_      |_____|__|_      |_____|__|_      |_____|____
        |                |                |                |
        (1*4)            ((1*2)+1*2)      (((+1)+1)+1*2)   ((1*2)+(1*2))
     
     4 =                                  2  2  2
              1  1                        1  1  1          1  1
       {0, 1, 0, 0}     {0, 1, 0, 1}     {0, 0, 0, 3}     {0, 0, 2, 3}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |__|  |__|_      |__|  |__|       |  |  |  |       |__|_ |  |
        |     |          |     |          |  |  |  |       |     |  |
        |     |          |     |          |__|__|_ |       |_____|  |
        |     |          |     |          |        |       |        |
        |_____|____      |_____|____      |________|       |________|
        |                |                |                |
    (((+1)+1)+(1*2)) (((+1)+1)+((+1)+1))  ((1*3)+1)        (((1*2)+1)+1)

       {0, 1, 2, 3}
        .  .  .  .
        |  |  |  |
        |__|  |  |
        |     |  | <--(Standard Math language uses only this
        |_____|  |     [i]no-redundancy_no-uncertainty_symmetry[/i])
        |        |
        |________|
        |    
        ((((+1)+1)+1)+1)
     

    Multiplication can be operated only among objects with structural identity,
    where addition can be operated among identical and non-identical
    (by structure) objects.

    Also multiplication is noncommutative, for example:

    2*3 = ( (1,1),(1,1),(1,1) ) , ( ((1),1),((1),1),((1),1) )

    3*2 = ( (1,1,1),(1,1,1) ) , ( ((1,1),1),((1,1),1) ) , ( (((1),1),1),(((1),1),1) )
    [/b]
     
    Last edited: Mar 19, 2004
  10. Mar 19, 2004 #9

    matt grime

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    No, because I shouldn't have to tell you what the definitions are of the objects in your own theory, and more importantly I think calling it a multiplication on N is a misleading thing to do. Even allowing for your defintion of elements of n, the product of two of them is not another element of N. What is 2*3, because it's not an integer. As lots of people have pointed out you are defining some not uninteresting combinatorial constructions on certain kinds of trees, probably making it something akin to a groupoid, or monoid. Some elements get labels in N, some do not.

    A reasonable mutliplication takes pairs of elements in N and assigns another element in N (closure), we might also ask that it distributes over addition, and that m*n = m*(n-1) +m or that m*1=1*m=m

    We don't have to do that, but all the structures you are describing are known and studied (rings, division algebras, algebras, domains, fields, rigs rngs, monads, groups, groupoids).

    In fact the reason why we identify copies of the integers inside these structure is exactly because given a multiplicative identity where mulitplication distributes over addition (ie a ring structure) then we either get a copy of Z in the ring, ro we get some ring of integers modulo M for some M.

    If we don't require associativity etc then we get other well known objects.
     
    Last edited: Mar 19, 2004
  11. Mar 19, 2004 #10
    I take these structures as general representation of information, which is ordered by its symmetry levels that are
    connected to information's clarity degrees, based on uncertainty AND redundancy.

    Can you show me some mathematical research that using multiplication and addition from this point of view?

    Shortly speaking, can you show me this?:

    Code (Text):

    (1*4)              ={1,1,1,1} <------------- Maximum symmetry-degree,
    ((1*2)+1*2)        ={{1,1},1,1}              Minimum information's
    (((+1)+1)+1*2)     ={{{1},1},1,1}            clarity-degree
    ((1*2)+(1*2))      ={{1,1},{1,1}}            (no uniqueness)
    (((+1)+1)+(1*2))   ={{{1},1},{1,1}}
    (((+1)+1)+((+1)+1))={{{1},1},{{1},1}}
    ((1*3)+1)          ={{1,1,1},1}
    (((1*2)+1)+1)      ={{{1,1},1},1}
    ((((+1)+1)+1)+1)   ={{{{1},1},1},1} <------ Minimum symmetry-degree,
                                                Maximum information's  
                                                clarity-degree                                            
                                                (uniqueness)
     


    Let us say that we have here a transformation between super set {1,1,1,1} to "normal" set {{{{1},1},1},1}
    and vise versa.
     
    Last edited: Mar 19, 2004
  12. Mar 19, 2004 #11

    matt grime

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    Seeing as you haven't told anyone what 'clarity degree' 'symmetry degree' 'redundancy' 'uncertainty' mean to you, then the answer is trivially 'of course I can't show you any of that, because no one knows what to show you'.

    Show me a snark, or a boodjum, something gambolling in the mimsy wabe.

    Try looking up, oh, I don't know, theory of non-associative algebras, monads or something.
     
  13. Mar 19, 2004 #12
    This is what it means to me:
    Code (Text):
     
                  Uncertainty
      <-Redundancy->^
        3  3  3  3  |
        2  2  2  2  |
        1  1  1  1  |
       {0, 0, 0, 0} V
        .  .  .  .
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |__|__|__|_
        |
        (1*4)


       {0, 1, 2, 3}
        .  .  .  .
        |  |  |  |
        |__|  |  |
        |     |  | <--(Standard Math language uses only this
        |_____|  |     no-redundancy_no-uncertainty_symmetry)
        |        |
        |________|
        |
        ((((+1)+1)+1)+1)
     
    Is it understood?
     
  14. Mar 19, 2004 #13

    matt grime

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    No. That is an example in one particular case.

    Is redundancy the number of columns, the labels on the columns, the shape of the columns (same for uncertainty as in all that follows)

    it doesn't say why there is no redundancy in the second diagram.

    it doesn't tell me what the redundancy of another diagram might be.

    it doesn't tell me if redundancy is something only attributable to trees, or if other objects may have it, whatever 'it' is.

    i don't know how to 'measure' redundancy, is ti a numerical qunatity like the order of an element of a group.

    so tell us what constitutes redundancy.
     
  15. Mar 19, 2004 #14

    matt grime

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    Here's an example. Pick some meaningful word. Solid, and hence solidity. They sound as though they may have vaguely mathematical meanings.

    Let me now associate to them some proper definition of my own that I will refuse to explain. Ok, done it. R is solid, Q is not solid. Question: is N solid?
     
  16. Mar 19, 2004 #15
    Let us get back to set and super set:

    Let us say that we have here a transformation between super set {x,x,x,x} to "normal" set {{{{x},x},x},x}
    and vise versa.

    Let a,b,c,d stends for uniquness, then we get:


    Code (Text):
     
                  Uncertainty
      <-Redundancy->^
        d  d  d  d  |
        c  c  c  c  |
        b  b  b  b  |
       {a, a, a, a} V
        .  .  .  .
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |__|__|__|_
        |
        ={x,x,x,x}


       {a, b, c, d}
        .  .  .  .
        |  |  |  |
        |__|  |  |
        |     |  | <--(Standard Math language uses only this
        |_____|  |     no-redundancy_no-uncertainty_symmetry)
        |        |
        |________|
        |
        ={{{{x},x},x},x}

    [b]
    ============>>>

                    Uncertainty
      <-Redundancy->^
        d  d  d  d  |          d  d             d  d
        c  c  c  c  |          c  c             c  c
        b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
       {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |  |  |  |       |__|_ |  |       |__|  |  |       |__|_ |__|_
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |__|__|__|_      |_____|__|_      |_____|__|_      |_____|____
        |                |                |                |
        {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}    
     
                                          c  c  c
              b  b                        b  b  b          b  b
       {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |__|  |__|_      |__|  |__|       |  |  |  |       |__|_ |  |
        |     |          |     |          |  |  |  |       |     |  |
        |     |          |     |          |__|__|_ |       |_____|  |
        |     |          |     |          |        |       |        |
        |_____|____      |_____|____      |________|       |________|
        |                |                |                |
        {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x}

        a, b, c, d}
        .  .  .  .
        |  |  |  |
        |__|  |  |
        |     |  | <--(Standard Math language uses only this
        |_____|  |     no-redundancy_no-uncertainty_symmetry)
        |        |
        |________|
        |    
        {{{{x},x},x},x}
    [/b]                
     
     
    Last edited: Mar 25, 2004
  17. Mar 19, 2004 #16

    matt grime

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    Still doesn't explain what it is and how to find it. Firstly I doubt if ever learned the rules that allow you to assign the letters abc and d to those patterns. Secondly the last picture has no redundancy or uncertainty in it, an the first one does. but what about the others? All you need to say is that the diagram has redundancy if ..... blah, where that's some description, perhaps only for the n=4 case, youi can generalize later.

    Is it perhaps that the diagram is 'certain' iff there is one row of letters when you label it? If so why didn't you just say so. Can you give an equivalent statement that telss me when a diagram as redundancy.

    Note I don't need to know what redundancy *means*, only the criteria for noting its existence.

    For instance one doesn't need to understand the meaning of the *word* chaos to know that a dynamical system is chaotic if it has topological transitivity and sensitive dependence on initial conditions, all of which are well defined.


    Have you deicded if N is solid yet?
     
  18. Mar 19, 2004 #17
    Matt,

    There is an algorithm for this, which is based on Cartesian product.

    You can see it here:

    http://cyborg2000.xpert.com/ctheory/

    Please don't go beyond 6 or 7.

    The cartesian pruduct results adding left-right combinations that can be ignored.
     
  19. Mar 19, 2004 #18

    matt grime

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    So are you actually going to say what you mean by redundancy and uncertainty or not? Come on, Organic, it's your requirement to have things well defined.

    Figured out if N is solid or not
     
  20. Mar 19, 2004 #19
    Let us say that we have here a transformation between
    super set {x,x,x,x} to "normal" set {{{{x},x},x},x} and vise versa.


    Let XOR be #

    Let a,b,c,d stends for uniquness, then we get:

    Code (Text):
     
                  Uncertainty
      <-Redundancy->^
        d  d  d  d  |
        #  #  #  #  |
        c  c  c  c  |
        #  #  #  #  |
        b  b  b  b  |
        #  #  #  #  |
       {a, a, a, a} V
        .  .  .  .
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |  |  |  |
        |__|__|__|_
        |
        ={x,x,x,x}


       {a, b, c, d}
        .  .  .  .
        |  |  |  |
        |__|  |  |
        |     |  | <--(Standard Math language uses only this
        |_____|  |     no-redundancy_no-uncertainty_symmetry)
        |        |
        |________|
        |
        ={{{{x},x},x},x}

    [b]
    ============>>>

                    Uncertainty
      <-Redundancy->^
        d  d  d  d  |          d  d             d  d
        #  #  #  #  |          #  #             #  #        
        c  c  c  c  |          c  c             c  c
        #  #  #  #  |          #  #             #  #  
        b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
        #  #  #  #  |    #  #  #  #             #  #       #  #  #  #  
       {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |  |  |  |       |__|_ |  |       |__|  |  |       |__|_ |__|_
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |  |  |  |       |     |  |       |     |  |       |     |
        |__|__|__|_      |_____|__|_      |_____|__|_      |_____|____
        |                |                |                |
        {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}    
     
                                          c  c  c
                                          #  #  #      
              b  b                        b  b  b          b  b
              #  #                        #  #  #          #  #        
       {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
        .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
        |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
        |__|  |__|_      |__|  |__|       |  |  |  |       |__|_ |  |
        |     |          |     |          |  |  |  |       |     |  |
        |     |          |     |          |__|__|_ |       |_____|  |
        |     |          |     |          |        |       |        |
        |_____|____      |_____|____      |________|       |________|
        |                |                |                |
        {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x}

        a, b, c, d}
        .  .  .  .
        |  |  |  |
        |__|  |  |
        |     |  | <--(Standard Math language uses only this
        |_____|  |     no-redundancy_no-uncertainty_symmetry)
        |        |
        |________|
        |    
        {{{{x},x},x},x}
    [/b]                
     
    For clearer picture please read this:
    http://www.geocities.com/complementarytheory/HelpIsNeeded.pdf

    No input has solid form.
     
    Last edited: Mar 25, 2004
  21. Mar 20, 2004 #20

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Nope, you keep drawing the same pictures, but you still won't tell us about redundancy and uncertainty.


    How can you state no input has solid form. I haven't told you what the definition of 'solid' is. You're presuming that it is something to do with the ordinary meaning of the word solid. It isn't really. Here's a hint:

    N, Z, R, C are 'solid', Q is not, neither is the set {1/n | n in N}, the cantor set is 'solid' surprisingly.

    So is the set of finite groups solid?
     
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