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Fruitful non-excluded middle (was Re: [learningfromeachother] A sketch of physics (with John Harland))

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  • Edward Cherlin
    ... 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
    Message 1 of 1 , Apr 25, 2011
      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

      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
      > ------------------------------------
      > Each letter sent to Learning From Each Other enters the PUBLIC DOMAIN unless it explicitly states otherwise http://www.ethicalpublicdomain.org  Please be kind to our authors!Yahoo! Groups Links

      Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
      Silent Thunder is my name, and Children are my nation.
      The Cosmos is my dwelling place, the Truth my destination.
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