On the freeways of los angeles county, there are some big clunky old electronic signs that are supposed to give drivers a heads up about trouble further down the road, with messages like "105 East jammed - Take 91". One time I saw a message that said "This is a test message." I remember from logic that there are problems with self referencing assertions, such as the assertion "This statement is false", which in a naive way can appear to be "provable" as neither true or false, using the method of proof by contradiction (if I remember all that correctly).
I think the freeway statement, which I think may be in the same general category of assertions, is "apparently" paradoxical. It appears to be an entity which contains it's own definition. But if that's true, then its definition contains it's definition. Then its definition must contain its definition which must contain its definition. Since this leds to a definition of infinite length, then that means there's no defintion attainable for the message, which means no one can know what it means. They should replace it with e.g. "The following is a test message: Little Miss Muffet...sat on a tuffet...eating her curds and whey... Along came a spider...and sat down beside her...and said 'What's in the bowl, biitch?' - ADC" - right?
I think the freeway statement, which I think may be in the same general category of assertions, is "apparently" paradoxical. It appears to be an entity which contains it's own definition. But if that's true, then its definition contains it's definition. Then its definition must contain its definition which must contain its definition. Since this leds to a definition of infinite length, then that means there's no defintion attainable for the message, which means no one can know what it means. They should replace it with e.g. "The following is a test message: Little Miss Muffet...sat on a tuffet...eating her curds and whey... Along came a spider...and sat down beside her...and said 'What's in the bowl, biitch?' - ADC" - right?
