Is there a school of logic that explores the patterns that seem to be created by the logic in statements? I wonder about if statements that seem to be simple can actually create (or have hidden within them) intricately complex patterns, mechanisms, or paradoxes. For example: Two people are in an argument and each accuses the other with the phrase “You say that I am wrong. But I say that it is you who is truly wrong as you say that.” This phrase seems logically self-defeating when it is said by either person, because each side’s accusation does the very thing it accuses in the other. At first glance, the two arguers’ accusations seem to simply cancel each other out (like -1+1=0), or make a zigzag that goes on forever. But, because of what the two arguers together end up saying about this phrase that they both use and repeat to each other, does their back-and-forth actually produce other, more complicated patterns? For instance, might their back-and-forth end up creating a tessellation or a fractal (like a dragon curve?)? Or maybe even a 3-dimensional figure? Instead of a zigzag, might their back-and-forth be better represented in its logic by a Mobius strip? Or by something like the motions of a "Jacob’s ladder" toy? And then what such patterns could mean for the two arguers is not merely do their accusations cancel each other out, but paradoxes might happen like each is inadvertently saying to the other “you are right and I am wrong?” What discipline in logic (or is it an area in mathematics?) might explore this kind of thinking? Many thanks and best wishes for continued success for askphilosophers.org.

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