The following are variations of what is known as the Epimenides paradox, a bizarre piece of mental gymnastics that I discovered in a book I’ve tried reading in the past and am now currently reading again entitled, “Godel, Escher, Bach: An Eternal Golden Braid” by Douglas R. Hofstadter. From the text,
“Epimenides was a Cretan who made one immortal statement: ‘All Cretans are liars.’ A sharper version of the statement is simply ‘I am lying’; or ‘This statement is false.’…It is a statement which rudely violates the usually assumed dichotomy of statements into true and false, because if you tentatively think it is true, then it immediately backfires on you and makes you think it is false. But once you’ve decided it is false, a similar backfiring returns you to the idea that it must be true. Try it!” (emphasis mine)
The above is an example of a one-step Strange Loop. Here’s an example of a multi-step Strange Loop:
The following sentence is false.
The preceding sentence is true.
“Taken together these sentences have the same effect as the original Epimenides paradox; yet separately, they are harmless and even potentially useful sentences. The ‘blame’ for this Strange Loop can’t be pinned on either sentence – only on the way they ‘point’ at each other.”
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{ 4 comments… read them below or add one }
Thanks for making my head hurt and giving me something else to focus on other than my work.
@ Greg,
Haha, no problem man, my head was in knots as well!
Gap in my education. I majored in Philosophy in college but never learned this one, though I always enjoyed the single step versions.
Thanks for expanding my mind… or maybe shutting it down. :>)
Marshall Jones Jr.
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It’s only a puzzle in the sense that rearranging signs on the highway creates a puzzle. Just because a sentence is gramatically correct doesn’t mean it is conceptually correct.
I can write 1=2 but that doesn’t mean it’s true. It just means I can string symbols (words are symbols) together.
However, it is exactly the same thing Escher did in many of his drawings. It takes advantage of the simplification necessary for communication. To represent a 3D image on a 2D surface we have to interpret, so there is room to trick us. To represent a concept in words we have to interpret, so there is room to trick us.
It’s also related to the way magic tricks work. I remember reading an article (in Science I think) about researchers who were using magic tricks to study how the brain works. They interviewed a street magician who explained that he could slip someone’s watch off their wrist (or whatever) while talking to them as long as he moved his hands in curves. If he moved his hands in straight lines people caught him. The scientists think that is because when something moves in a straight line the brain automatically assumes it will end up in an obvious place and can pay attention to other things (like what his other hand is doing), but when something moves in a curve the brain can’t predict where it will end up, so there is a moment where the brain can’t pay attention to anything else.