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Penrose: Mathematicians view mathematics as discovered

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  • Nils K.
    Dear All! Dear Stan! Stan, you said that most mathematicians believe maths is invented. But Roger Penrose (mathematician and superphysicist) says that the
    Message 1 of 5 , Jan 20, 2013
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      Dear All! Dear Stan!

      Stan, you said that most mathematicians believe maths is invented.
      But Roger Penrose (mathematician and superphysicist) says
      that the opposite is the case.

      [Quote from "my" message "Roger Penrose: Mathematics is discovered":]

      "Certainly," he [Penrose]says, "mathematicians view mathematics
      as something out there, which seems to have a reality independent of the
      ordinary kind of reality of things like chairs, which we normally think of as real. It's sometimes referred to as a `Platonic world,' a Platonic reality. …

      [Unquote]

      Do you know about gallup/poll results here?
      Who is right, Stan or Roger?

      By the way: Interestingly, Penrose views maths as a kind of reality, just like NKO and Plato, and also views maths as independent of "ordinary" reality, just as NKO and Plato.

      Lastly, by the way, I consider this philosophical debate as relevant EP stuff. It's about human thinking and reasoning. I believe there are at least two distinct genotypes here, namely discoverists and inventists.

      Best
      NKO
    • mark hubey
      I hate to say this but these words do not do justice to the process because the words were invented for different purposes e.g. everyday ordinary humdrum
      Message 2 of 5 , Jan 20, 2013
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        I hate to say this but these words do not do justice to the process because the words were invented for different purposes e.g. everyday ordinary humdrum things. See below.


        On Sun, Jan 20, 2013 at 11:00 AM, Nils K. <n-oeij@...> wrote:
         

        Dear All! Dear Stan!

        Stan, you said that most mathematicians believe maths is invented.
        But Roger Penrose (mathematician and superphysicist) says
        that the opposite is the case.

        [Quote from "my" message "Roger Penrose: Mathematics is discovered":]

        "Certainly," he [Penrose]says, "mathematicians view mathematics
        as something out there, which seems to have a reality independent of the
        ordinary kind of reality of things like chairs, which we normally think of as real. It's sometimes referred to as a `Platonic world,' a Platonic reality. …


        They see things as something out there because of what Wigner wrote (e.g. Unreasonable Effectivenes...).

        If something was arbitrarily created out of thin air why does it fit so perfectly into the real world phenomena?

         


        By the way: Interestingly, Penrose views maths as a kind of reality, just like NKO and Plato, and also views maths as independent of "ordinary" reality, just as NKO and Plato.


        That word, "reality" is one of the buzzword, fogwords, or weasel words of philosophers, (still premedieval) and it only
        confuses them.

        "Reality" is like "existence"; it means too many things. Numbers do not exist in the same sense as bananas. 


        Lastly, by the way, I consider this philosophical debate as relevant EP stuff. It's about human thinking and reasoning. I believe there are at least two distinct genotypes here, namely discoverists and inventists.

        Best
        NKO




        --
        Regards,
        Mark Hubey

        "Learning to think in mathematical terms is an essential part of becoming a liberally educated person. "
        -- Kenyon College Math Department Web Page 

      • Stan Franklin
        NKO, I don t have statistics about how many mathematicians come down on the invented vs the discovered side of the controversy. I based by earlier assertion on
        Message 3 of 5 , Jan 21, 2013
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          NKO,

          I don't have statistics about how many mathematicians come down on the invented vs the discovered side of the controversy. I based by earlier assertion on my perception that there has been no argument among mathematicians as to the validity of the work of Goedal and that of Cohen that, together, demonstrate the independence of the continuum hypothesis with respect to the axioms of set theory. Were mathematics to have some sort of separate reality, such an independence result couldn't exist. The continuum hypothesis would have to be either true or false.

          Stan


          On Sun, Jan 20, 2013 at 10:00 AM, Nils K. <n-oeij@...> wrote:
           

          Dear All! Dear Stan!

          Stan, you said that most mathematicians believe maths is invented.
          But Roger Penrose (mathematician and superphysicist) says
          that the opposite is the case.

          [Quote from "my" message "Roger Penrose: Mathematics is discovered":]

          "Certainly," he [Penrose]says, "mathematicians view mathematics
          as something out there, which seems to have a reality independent of the
          ordinary kind of reality of things like chairs, which we normally think of as real. It's sometimes referred to as a `Platonic world,' a Platonic reality. …

          [Unquote]

          Do you know about gallup/poll results here?
          Who is right, Stan or Roger?

          By the way: Interestingly, Penrose views maths as a kind of reality, just like NKO and Plato, and also views maths as independent of "ordinary" reality, just as NKO and Plato.

          Lastly, by the way, I consider this philosophical debate as relevant EP stuff. It's about human thinking and reasoning. I believe there are at least two distinct genotypes here, namely discoverists and inventists.

          Best
          NKO




          --
          Stan Franklin   Professor   Computer Science
          W. Harry  Feinstone  Interdisciplinary  Research   Professor
          Institute for Intelligent Systems        
          FedEx Institute of Technology              
          The University of Memphis
          Memphis, TN 38152 USA  
          901-678-1341
          <http://ccrg.cs.memphis.edu/~franklin/>  
          lab <http://ccrg.cs.memphis.edu/>

        • Nils K.
          Dear Stan, dear All! ... I don t have statistics about how many mathematicians come down on the invented vs the discovered side of the controversy. I based by
          Message 4 of 5 , Jan 24, 2013
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            Dear Stan, dear All!

            --- In evolutionary-psychology@yahoogroups.com, Stan Franklin wrote:

            I don't have statistics about how many mathematicians come down on the
            invented vs the discovered side of the controversy. I based by earlier
            assertion on my perception that there has been no argument among
            mathematicians as to the validity of the work of Goedal and that of Cohen that, together, demonstrate the independence of the continuum hypothesis with respect to the axioms of set theory. Were mathematics to have some sort of separate reality, such an independence result couldn't exist. The continuum hypothesis would have to be either true or false.

            NKO:
            This (above) is outside my capacity in the philosophy and logic of
            mathematics. I'm check mate here and now. But not totally silent.
            I will try to come up with some comments, not necessarily going
            against your conclusions above.

            I will focus on "independence" and "independence result", core words
            in your reasoning.

            Independence (just as randomness) is main facts and mechanisms in
            physics and biology. It's beyond human understanding that our
            (enormous number of) genes are so extremely independent, and thereby
            making evolutionary change possible. Both genetics, physiology, and
            anatomy are modular, and each of the unlimited numbers of modules can
            be changed a lot without changing other modules. Even human behavior
            is modular, having no goverment, it's largely a "war" among behavior
            modules (human instincts).

            In physics waves are entangled. Entanglement is perhaps the most
            crazy in quantum mechanics. Nevertheless waves are at the same time
            independent, which is also crazy. As if this was not enough, we have
            the double picture of the physical world: Waves and particles, which
            Bohr and Einstein claimed is impossible for humans to understand.

            But now I was talking about the physical world, but some of us are
            claiming math be non-physical and absolutely independent of the
            physical world. But, nevertheless, I find it strange that
            INDEPENDENCE is ruled out in mathematics. I also find it strange that
            mathematics is a branch of biology (i.e. only existing in human
            brains), as the inventists are concluding. (Are they concluding so?)

            I do think we cannot rule out that the specific INDEPENDENCE you,
            Stan, talked about above, could be a integrated part of the non-
            physical world of mathematics, in the same manner as the wave picture
            is independent of the particle picture in physics. These pictures
            depend on how we ask questions to nature. We can ask questions to
            math as well. So?

            Best,
            NKO
          • Stan Franklin
            NKO, Sorry, I should have said what independent meant in this technical context. It means that there are two sets of reasonable axioms for set theory (the
            Message 5 of 5 , Jan 25, 2013
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              NKO,

              Sorry, I should have said what independent meant in this technical context. It means that there are two sets of reasonable axioms for set theory (the underlying primitive basis for mathematics) under one of which the continuum hypothesis is true, and under the other it's false. You can have it either way depending on the axioms you start with.

              Hope this helps.

              Stan


              On Thu, Jan 24, 2013 at 9:09 AM, Nils K. <n-oeij@...> wrote:
               



              Dear Stan, dear All!



              --- In evolutionary-psychology@yahoogroups.com, Stan Franklin wrote:

              I don't have statistics about how many mathematicians come down on the
              invented vs the discovered side of the controversy. I based by earlier
              assertion on my perception that there has been no argument among
              mathematicians as to the validity of the work of Goedal and that of Cohen that, together, demonstrate the independence of the continuum hypothesis with respect to the axioms of set theory. Were mathematics to have some sort of separate reality, such an independence result couldn't exist. The continuum hypothesis would have to be either true or false.

              NKO:
              This (above) is outside my capacity in the philosophy and logic of
              mathematics. I'm check mate here and now. But not totally silent.
              I will try to come up with some comments, not necessarily going
              against your conclusions above.

              I will focus on "independence" and "independence result", core words
              in your reasoning.

              Independence (just as randomness) is main facts and mechanisms in
              physics and biology. It's beyond human understanding that our
              (enormous number of) genes are so extremely independent, and thereby
              making evolutionary change possible. Both genetics, physiology, and
              anatomy are modular, and each of the unlimited numbers of modules can
              be changed a lot without changing other modules. Even human behavior
              is modular, having no goverment, it's largely a "war" among behavior
              modules (human instincts).

              In physics waves are entangled. Entanglement is perhaps the most
              crazy in quantum mechanics. Nevertheless waves are at the same time
              independent, which is also crazy. As if this was not enough, we have
              the double picture of the physical world: Waves and particles, which
              Bohr and Einstein claimed is impossible for humans to understand.

              But now I was talking about the physical world, but some of us are
              claiming math be non-physical and absolutely independent of the
              physical world. But, nevertheless, I find it strange that
              INDEPENDENCE is ruled out in mathematics. I also find it strange that
              mathematics is a branch of biology (i.e. only existing in human
              brains), as the inventists are concluding. (Are they concluding so?)

              I do think we cannot rule out that the specific INDEPENDENCE you,
              Stan, talked about above, could be a integrated part of the non-
              physical world of mathematics, in the same manner as the wave picture
              is independent of the particle picture in physics. These pictures
              depend on how we ask questions to nature. We can ask questions to
              math as well. So?

              Best,
              NKO




              --
              Stan Franklin   Professor   Computer Science
              W. Harry  Feinstone  Interdisciplinary  Research   Professor
              Institute for Intelligent Systems        
              FedEx Institute of Technology              
              The University of Memphis
              Memphis, TN 38152 USA  
              901-678-1341
              <http://ccrg.cs.memphis.edu/~franklin/>  
              lab <http://ccrg.cs.memphis.edu/>

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