The Liar’s Paradox is easy to understand, that is, it’s easy to understand why it’s hard to understand. The simplest version of the paradox is a statement about itself, “This sentence is false,” or, disguising the self-reference, “I am lying.” If the statement is true then the statement is false, get it? And if it’s false, it’s true. This is a clever language game, saying something impossible, like “I am asleep,” but where the sentence is, directly or indirectly, its own subject. In the end it’s a party trick with no use or meaning beyond itself; there is no occasion where a serious person would have to say, “This sentence is false.”
“I am a liar” is a less logically pure version of the paradox that could be heard in certain real situations. Would you believe someone who says they are a liar? Logically, if they’re telling the truth, then they may be lying.
The negation, “I am not a liar,” works differently, and you definitely hear this one in real life. A liar who says “I am not a liar” is simply lying, which is what liars do: bingo. And when a person who is not a liar says, “I am not a liar,” the statement is true and the world is a beautiful place. “I am not a liar” can be true or false but it’s not a paradox.
Logic and psychology see this differently. If someone confessed to you that they were a liar, you might believe them, because – why would someone say something bad about themselves if it were not true? But “I am a liar” sounds like someone who feels guilty, implying they aren’t very experienced at it. People who don’t lie don’t often have to deny it; on the other hand, a liar has to say “I am not a liar” so you’ll continue to believe them.
These days we have quite a few liars in the news – imagine living in a world where somebody’s job is “fact checker” – and people continue to listen to them. It turns out, attention is more important than truthfulness in deciding who we believe. An audience’s attention is what the media sell to advertisers. We listen to who’s talking, and as trusting souls we tend to believe what we’re told.
Attention likes bright things, big things, loud things, things that move. Attention likes surprises, and having its prejudices confirmed. Attention turns perceptions into memories, and beliefs. Once someone has your attention, their message gets across whether they’re lying or not; attention beats truth in any fight. And then logic hangs around to clean up the mess, creating plausible justifications and sprinkling believable explanations around so attention-getters can keep getting attention.
“I am a liar” tells you you’re dealing with an honest person, a person who knows who they are and doesn’t mind telling you. “I am not a liar” is almost always a cover for deceit. And that is the real Liar’s Paradox.