Tuesday, May 22, 2012

Included Middle

Filed under: General,Geometry — m759 @ 2:01 PM


"In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is.

The law is also known as the law (or principleof the excluded third (or of the excluded middle), or, in Latinprincipium tertii exclusi. Yet another Latin designation for this law is tertium non datur: 'no third (possibility) is given.'"

"Clowns to the left of me, jokers to the right"

 — Songwriter who died on January 4, 2011.

Online NY Times  on the date of the songwriter's death—

"A version of this review appeared in print
on January 4, 2011, on page C6 of the New York edition." 


"The philosopher Hubert Dreyfus and his former student
Sean Dorrance Kelly have a story to tell, and it is not
a pretty tale for us moderns. Ours is an age of nihilism,
they say, meaning not so much that we have nothing
in which to believe, but that we don’t know how to choose
among the various things to which we might commit
ourselves. Looking down from their perches at Berkeley
and Harvard, they see the 'human indecision that
plagues us all.'"

For an application of the excluded-middle law, see
Non-Euclidean Blocks and Deep Play.

Violators of the law may have trouble* distinguishing
between "Euclidean" and "non-Euclidean" phenomena
because their definition of the latter is too narrow,
based only on examples that are historically well known.

See the Non-Euclidean Blocks  footnote.

* Followers  of the excluded-middle law will avoid such
trouble by noting that "non-Euclidean" should mean
simply "not  Euclidean in some  way "— not  necessarily
in a way contradicting Euclid's parallel postulate.

But see Wikipedia's defense of the standard, illogical,
usage of the phrase "non-Euclidean."


Tertium Datur

Froebel's Third Gift

"Here I am, stuck in the middle with you."

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