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On Measures and Messages

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  • Jens Doll
    Hello Vaughan, the task of defining a measure for rationals still keeps me busy, because the meaning is getting more general than I had initially thought of.
    Message 1 of 4 , Feb 14, 2009
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      Hello Vaughan,
      the task of defining a measure for rationals still keeps me busy,
      because the meaning is getting more general than I had initially
      thought of. Have you, has anyone on this list, ever thought/read of a
      measure for (scientific) knowledge? I wonder, how such a space could
      look like and if we are/would be able to measure it ...
      Jens

      --- in December Vaughan Pratt wrote:
      > ...
      > For any vector space V over any extension K
      > of Q, just give V the weakest topology for which addition (in each
      > argument separately) and multiplication by the scalars of K are
      > continuous. V can then be reduced to a vector space V' over any
      > subfield K' of K by forgetting those scalar multipliers in K'\K.
      >...
    • A. Mani
      On Saturday 14 February 2009 21:31:28 Jens Doll wrote: the task of defining a measure for rationals still keeps me busy, because the meaning is getting
      Message 2 of 4 , Feb 16, 2009
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        On Saturday 14 February 2009 21:31:28 Jens Doll wrote:
        > the task of defining a measure for rationals still keeps me busy,
        > because the meaning is getting more general than I had initially
        > thought of. Have you, has anyone on this list, ever thought/read of a
        > measure for (scientific) knowledge? I wonder, how such a space could
        > look like and if we are/would be able to measure it ...

        If you can describe the context in more detail, then I can try to suggest
        something. The subject is quite big and it is usually a good idea to study
        enough philosophy.

        Many approaches will start from modal logic. That is almost compulsory if you
        want to deal with knowledge representation. Again you will need to pay
        attention to the philosophical motivations behind modal logic. If you are good
        in duality or canonical models, then you can always use them.

        Rough sets can be used for defining relative measures of scientific knowledge.
        See Pawlak's book or other tutorials/books for the basics. There are
        connections with concept lattices.
        But what is your concept of scientific knowledge?

        Belief revision is closely connected with non-monotonic reasoning and logics.
        It can be used for decision making, but I do not know of any good application
        to 'measure scientific knowledge'.

        Best

        A. Mani



        --
        A. Mani
        Member, Cal. Math. Soc



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      • Jens Doll
        Thank you for this firework of imaginations. I am now aware of the different types of logic, which scientific disciplines use. There seems to be only one
        Message 3 of 4 , Feb 17, 2009
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          Thank you for this firework of imaginations. I am now aware of the
          different types of logic, which scientific disciplines use. There
          seems to be only one widely used measure : lop=lines of publication.
          Maybe a different and generally accepted one can be found by search
          engines.
          Jens
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