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The Liar Paradox is famous because it seems to break the foundational tenant of classical that all statements are either true or false. Your example is also in
by kyleschiller 9y ago
The Liar Paradox is famous because it seems to break the foundational tenant of classical that all statements are either true or false.
Your example is also interesting, but doesn't really break things in the same way.
I don't necessarily agree with this, I think there are plenty of important things to consider with both, but that's why one became famous without the other.
- kazinator 9y agoIt does break things in the same way, because the tenet is that all statements are either true exclusive or false. If we can follow sound reasoning such that some statement can be either true or false, based on the exact steps we take, that is exactly the same problem: a contradiction somewhere. "This sentence is true" doesn't contradict itself, but two different ways of evaluating it contradict each other. Researcher A assumes the sentence is true and comes to the conclusion that it is. Researcher B assumes that it is false, substitutes in the value and also concludes that it is correct. Neither has found a contradiction in isolation, but A and B's findings contradict each other. In terms of electronics-based intuition, "this sentence is false" is like an unstable circuit: e.g. an inverter feeding its own output to its output. This might result in oscillation. "This sentence is true" is like bistable feedback: it gives us a flip-flop which "latches" whichever value we inject.