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3222Re: Fruitful non-excluded middle

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  • ms@ms.lt
    May 2, 2011
      Edward, Thank you for explaining! I've included your examples here:
      http://www.selflearners.net/ways/#992
      http://www.selflearners.net/ways/#993

      And here is a link to the semiotic square:
      http://www.selflearners.net/ways/#994

      Now I'm working on writing up a brief "general method" for "figuring
      things out". Then I'll show how I apply that to making a living.

      Andrius Kulikauskas, ms@...

      2011.04.25 20:30, Edward Cherlin rašė:
      > 2011/4/25 Andrius Kulikauskas <ms@...>:
      >> Edward, thank you for your letters! They are very helpful. I ask you
      >> also to think of examples where methods, or a kind of thinking, proved
      >> fruitful. You mention the excluded middle. For example, the Lithuanian
      >> semiotician Algirdas Julius Greimas developed the semiotic square
      >> (related to Aristotle's logical square), for example: White Black
      >> Not-Black Not-White. Where Not-White might be "colorlessness" and
      >> Not-Black might be "grey" if I remember correctly. But for my purposes,
      >> I want to document examples where such thinking was actually fruitful.
      >
      > Yale Professor Fred B. Fitch's book, Symbolic Logic presents a system
      > of logic that can be proven consistent. Dropping the law of Excluded
      > Middle was essential to the construction. Gödel's theorem depends on
      > Excluded Middle, so it doesn't apply to this proof of consistency.
      >
      > If R is the set of all sets that are not members of themselves (with
      > further precision required that does not concern us here), then R is a
      > member of R if and only if R is not a member of R. In the presence of
      > Excluded Middle, this results in contradiction. In its absence, it is
      > merely undecidable both in terms of provability and of truth.
      >
      > This idea can be followed into a realm of multiple-valued logics.
      >
      > Buddhist logic considers the possibilities
      >
      > Exists
      > Does not exist
      > Both exists and does not exist
      > Neither exists nor does not exist
      > None of the above
      >
      > as one of many ways of stating that meditation does not work the way you
      think.
      >
      >> I don't want to confuse fruitful and nonfruitful approaches! And I also
      >> want to relate each way of thinking with the kinds of results it yields.
      >>
      >> I'm always wondering how I could make a living from documenting and
      >> sharing "ways of figuring things out". Perhaps I should do that for
      >> business and economics.
      >
      > It's known as becoming a professor or a published writer.
      >
      > Separately, however, you would be welcome to contribute to our
      > analysis of business and economics for schoolchildren in developing
      > countries, where the dogmas of conventional economics are revealed to
      > be the airiest fantasies.
      >
      >> Thank you for thinking along with me!
      >>
      >> Andrius
      >>
      >> Andrius Kulikauskas
      >> http://www.selflearners.net
      >> ms@...
      >> (773) 306-3807
      >> Twitter: @selflearners
      >>
      >>
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      >>
      >
      >
      >
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