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

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• ... 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@...>:
> 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

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
>
>
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--
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.
http://www.earthtreasury.org/
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