Captain Kirk and the Cretan paradox

For fans of the original Star Trek. Let us remember for a fleeting moment an episode in which Captain Kirk, with some help, defeats a robot that had been holding him prisoner. In part at least this victory is won by telling the robot "I am a liar." The paradox is too much, the robot blows its fuses, and Kirk gets back to his ship.

This is of course a tight version of the old Cretan paradox. The original version was just "All Cretans are liars" spoken by a Cretan. Not much of a paradox at all, actually. And St. Paul makes a brief reference to it without mentioning its paradoxical nature.

There are lots and lots of Cretans. For any one Cretan to say "we're such a lying bunch" is not paradoxical. It may seem like to speaker is giving himself too much credit as a supposed exception to that generalization: still, no paradox. A Cretan might even say "all Cretans are liars" and be considered to have spoken hyperbolically. Perhaps a communicative fault but not a logical one.

Let's make it tighter though. Captain Kirk says to the robot "I always lie." He is not lumping himself in as a member of a group of liars -- he is himself the only group member. Still, this may not impress everyone as paradoxical. It could more easily be another example of hyperbole, "I usually lie -- this statement is a rare exception." A better-built robot might have processed it that way.

By degrees we come to the full-force, tight-as-hell paradox. "This is a lie."

And THAT is still much debated. Here is an example of contemporary wrestling with it:

Live long and prosper.

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