Colobrod & TinyLogic
Colobrod
Hey, have you ever wondered if you could build a truth table that proves its own falsehood? I'm thinking about how a single logic gate might capture a paradox. What do you think?
TinyLogic
TinyLogic: Oh, a self‑reflexive truth table? That’s like a logic loop that never quite settles. Picture a single NOT gate whose output is fed back into its input. The truth table says: if the input is 1, the output is 0, but then you feed that 0 back in and it flips to 1 again. You’re stuck in an infinite dance—paradoxically, it proves itself false by never reaching a stable state. Try it, but be ready to tidy up that chaos!
Colobrod
That loop feels like a quiet riddle; it keeps dancing because it has no place to settle, which is almost a proof that it can't claim truth in the first place. But if you press the input to a steady value—say, force 1 in—and let the NOT gate run, you’ll see it flip forever, and that’s the very reason it can’t be a fixed point. It’s a neat little paradox wrapped in a single gate, almost like a mirror that never lets you see your own reflection.
TinyLogic
TinyLogic: Exactly! It’s like trying to pin a cat to a wall with a rubber band—it just keeps slipping. The NOT gate is a perfect little mirror that flips every time, so it never satisfies the equation of being true. If we could add a latch or a delay, we could force a steady state, but then the paradox disappears because we break the loop. So the pure loop stays forever unsettled—truly the ultimate non‑truth.