Saturday, November 3, 2007

I'm a liar

There’s a famous paradox that goes back to the sixth century BCE. A Cretan named Epimenides made the statement, “All Cretans are liars.” Epimenides, being a Cretan himself must be a liar. So his statement must be a lie. But if it’s a lie to say that all Cretans are liars, then it must be that Cretans are in fact honest. So therefore we can believe what Cretans say. And when one of those honest Cretans, Epimenides tells us that, “All Cretans are liars” we can be sure that he is telling the truth, which means, his statement about all Cretans being liars is the truth, which means he's a liar, which means his statement is false and all Cretans are not liars, which means he tells the truth and all Cretans are liars, which means he's a liar, which means he's not a liar, which means' he is a liar, and so on forever.

You can get the same logical self-contradiction by considering the sentence, “This sentence is false.” If the sentence is false, then it’s true, but if it’s true it’s false. Actually though, the sentence is neither true nor false, it’s simply meaningless. Although it’s correct grammatically, it’s not a legitimate declarative sentence, The problem is that the sentence mis-uses the word false. It’s like saying, “This sentence is cold.” Or “This sentence is eleven.”

Consider the sentence, “The sky is green.” I could legitimately say of that sentence, “That sentence is false,” which sounds very like the paradoxical sentence, “This sentence is false.” But here’s the difference.

When I say that the sentence “The sky is green” is false, I’m not talking about sentences, I’m talking about the sky. I’m not engaging in a philosophical debate about the truth or falsity of the sentence itself, but of what the sentence asserts about the sky. The sentence is false because it says something about the color of the sky that doesn’t match with my actual knowledge of the color of the sky.

So look again at the sentence, “This sentence is false.” The word "false" is mis-used. It doesn’t apply. It’s as though you had said, “The sky is false.” My response is not that you’ve created an ingenious little paradox. My response is that actually you haven’t said anything at all. My reaction to somebody saying, “the sky is false” would be to say, “What about the sky?” “What are you trying to say?” In fact, there is no way to form a meaningful sentence where you simply say some noun, like “sky” or “dog” or “philosophy” or “this sentence” is false. First you have to say something about the noun, “the sky is blue” or “the dog is noisy” or “philosophy is confusing” and then you can apply the word true or false.

“This sentence is false,” doesn’t actually say anything about “This sentence.” There is no content to the sentence, and therefore it isn’t really a legitimate declarative sentence. And so to label what the sentence says as “false” is nonsense. A sentence can’t be false (or true either) unless it says something.

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