“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Thursday, August 26, 2010

A brief essay on logic

While driving, I typically listen to Sirius Satellite Radio dividing my time between BBC World Service and Radio Classics (a channel devoted to the old time radio dramas and comedies). BBC is advertisement free (excepting adverts for its own programs of course) but Radio Classics has advertising for various things, including other channels, on the half-hour. One of the channels advertised is BB King's Bluesville.

During the commercial, BB King comes on and says (as close to verbatim as I can remember) "I'm the mayor. And if BB King doesn't like it, I figure no one else will either." Huh. This is, in first order predicate logic, known as an implication, i.e., if A then B, or A->B (pronounced "A implies B"). This implication is, as the saying goes (and as can be shown in a truth table), logically equivalent to | B -> | A (man, I wish I had more symbols in the Blogger interface: -> is an implication arrow; | is negation or "not" so that | B -> |A should be read "not B implies not A").

To BB's statement, this translates to "if not 'no one else will like it then not BB King doesn't like it.'" Next, "not no one else will like it" translates to "there exists someone who will like it." And "not BB King doesn't like it" translates to "BB King likes it." Thus, BB's statement is the logical equivalent of "if there exists someone who will like it then BB King likes it." There probably is no music such that there does not exist someone who will like it. Thus, there is probably no music that BB King does not like.

I'm guessing that that's not what he meant.

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