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Friday, November 6, 2015

Put On Your Thinking Caps


Wonderful new Brian Gallagher article in Nautilus yesterday covers some classic Ray Smullyan/George Boolos logic conundrums:

http://nautil.us/issue/30/identity/how-to-solve-the-hardest-logic-puzzle-ever?

Gives an overview of what is famously-designated "the hardest logic puzzle ever" (created by Smullyan and solved by Boolos).

Gallagher ends the piece noting the puzzle demonstrates "how essential one of the supposed fundamental laws of logic -- the law of excluded middle -- seems to be" (which assumes that "every statement is either true or false -- there is no middle ground"), or in Boolos' words, “Our ability to reason about alternative possibilities, even in everyday life, would be almost completely paralyzed were we to be denied the use of the law of excluded middle.”

A practical problem of course is that the law of the excluded middle only operates within narrow, well-defined contexts, and NOT in most of day-to-day life... language and life are far more characterized by ambiguity, continuity, and gray areas, than the discrete black-and-whiteness implied by a simplistic excluded-middle law. Thus, my own increased recent interest in so-called "fuzzy logic" (mentioned awhile back) over classic Aristotelian logic... but still, for puzzle and logic purposes, a great article.


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