boolean functions return true or false or never halt: bool x() { return !x(); }and algorithms can't always decide which of the 3 it is: bool x() {return !returnsTrue("x()"); } Halting Problem |
propositions can be proven true or false or can't be proven: x := ¬xand math can't always prove which of the 3 it is: x := ¬provable("x")Gödel's Proof |
statements can be reasoned true or false or can't be reasoned: this statement is falseand humans can't always reason which of the 3 it is: this statement is not trueStrengthened Liar |