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Thursday, May 04, 2006

Converse or contrapositive? (And what does this have to do with the price of oil?)

On NPR’s All Things Considered, Robert Siegel just interviewed New York Times columnist Thomas Friedman about his article entitled “The First Law of Petropolitics.” Friedman stated this law as follows:
There is an inverse correlation between the price of oil and the pace of freedom... As the price of oil goes up, the pace of freedom goes down.
He then went on to say, “the converse is also true.” Presumably he meant the converse of his second sentence, since the first one doesn’t have a converse. Friedman stated the converse in this way:
As the price of oil goes down, the pace of freedom goes up.
Although technically not the converse, this assertion certainly is logically equivalent to the converse, since it’s the contrapositive of the converse (as long as we believe the dichotomy that freedom and oil prices either rise or fall, rather than making a trichotomy by including the possibility that either might stay the same):
  • Statement: If price of oil rises, then pace of freedom falls.
  • Converse: If pace of freedom falls, then price of oil rises.
  • Contrapositive of the Original Statement: If pace of freedom rises, then price of oil falls.
  • Contrapositive of the Converse: If price of oil falls, then pace of freedom rises.
OK, so far so good. What Friedman called the converse is indeed logically equivalent to the converse.

But now, several minutes later in this lengthy (lengthy for radio) interview, Siegel asked, “Beyond the First Law of Petropolitics and its contrapositive, do you have any other laws?” Tut-tut: Friedman didn’t enunciate the First Law and its contrapositive (which would be vacuously equivalent to it, of course); he enunciated the First Law and the contrapositive of the converse, which is interesting precisely because it’s not equivalent to the First Law. I’m shocked, shocked...

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