There is a new anthology out, a collection of essays by philosophers addressing in their various ways the "Liar Paradox."
I'll discuss the paradox myself today, and then say something about the new book in tomorrow's post.
Most people, surely most people likely to be reading this blog, are familiar with most of the following material. I trust you will read on regardless.
We begin, as is conventional, with the semi-legendary Cretan seer Epimenides, who is supposed to have said "all Cretans are liars." This is a rather fuzzy non-paradoxical comment, actually. Our tendency is simply to say that even liars don't generally lie all the time. A "liar" is someone who lies out of habit, pathological need, or to take advantage of other people. There is no logical inference that every sentence from the mouth of a "liar" in the ordinary language sense be a lie. So Epimenides may well have been telling the truth.
Over the next couple of centuries, though, Epimenides' observation was sharpened into a true paradox by other thinkers. This is still called the "liar paradox" by custom, although it could more properly be called the "lie paradox" once one abstracts from the easy resolution of the above paragraph. Or even the "falsehood paradox."
The paradox, with the suitable abstraction, reads thus: "This sentence is a lie." If that sentence is a lie then, by logical implication, it must be false. If it is false, then it isn't a lie. So is it true? Then what?
But to make things even tighter, we can abstract from the notion of a "lie" and just stay within the binary of truth/falsehood. So we get, "This sentence is false."
THAT is the paradigmatic paradox. Working off the premises that (a) every well-formed sentence is either true or false and (b) that this sentence is well formed, we end up going in circles. If it is true,then what it says is true. What it says is that it is false. So it must be false. So what it says must be false. What it says IS that it is false. So (since such accuracy in description is what we mean by truth!), it is true. It is false if true, and true if false.
The paradox shows up with some regularity in pop culture. In one episode of the 1960s television show STAR TREK, "I, Mudd," Captain Kirk invoked the paradox to disable evil robots who had him in their clutches, but whose wiring went blooey as they contemplated the above points. [The title of the episode, referring to Harry Mudd, an unscrupulous adventurer who gets Kirk into a precarious position, is also of course a tribute to Isaac Asimov.] The liar has also been featured in SOUTH PARK, where Jimmy, who is apparently familiar with the history of STAR TREK, uses the same trick to save the earth from humorbots, who have come to believe that destroying the planet would be very funny.
I trust that none of my readers have blown any circuits. Not even my algorithmic readers, if I have such. And, after all, who knows?
For us humans, two obvious ways of working around the paradox suggest themselves. I mentioned two premises three paragraphs back. Either of them might be rejected.
More as promised tomorrow.
"This sentence is a lie" makes no sense, because "This sentence" does not assert a fact that can be true or false. It is like saying, "This dog is a lie."
ReplyDeleteThe sentence, "'This sentence is a lie' is a lie," also makes no sense, because "This sentence is a lie" also does not assert a fact that can be true or false. The sentence, "This sentence is a lie," is gibberish.
It isn't precisely like saying "this dog is a lie." After all, a dog is not generally a "truth bearer" in the way that well-formed sentences are. Presumably, if we were using dogs as truth bearers, one could be a lie.
DeleteFor example, if I so arranged things that a Dalmatian came to your door at 8 in the morning and sat on your porch for a few minutes (whether you happened to notice or not) if and only if you were going to receive a FedEx package later in the day, but a St Bernard came to your door at 8 AM if you were going to receive a package from some other delivery company, and no dog came to your door at all if you were going to be unpackaged: I would then be using the dogs to communicate facts.
THEN, after this practice had been well established, if the St Bernard arrived at your door, you saw this and took note, and the subsequent package was from FedEx, you could angrily say of the puppy, "THAT dog was a lie!"
Not "The dog was a liar." On the hypothesis, I am the liar -- the dog is the lie. And through some complicated convolution of this little story I suspect we could reproduce the paradigmatic paradox in canine form.
But as you'll see tomorrow, my own preferred resolution to the paradox is roughly yours, just a little more roundabout.
In exchange for your dog story, I'll tell you a cat story, which is not on point. The word "bated" in the phrase "bated breath" means holding one's breath. Some people, however, generally from ignorance of the literal meaning of the phrase, write "baited breath." "Baited breath," however, can be correct. Suppose that a cat chews some cheese and then goes up to a mouse hole and breathes into it, in the hope that a mouse, smelling the cat's breath, will exit in anticipation of a cheese dinner, but instead become the cat's dinner. The cat had baited breath.
ReplyDelete