. If autological means “to mean itself”, and heterological means “to not mean itself”, then answering the question whether the term “heterological” is heterological seems to produce a paradox, where it oscillates between being heterological and autological. For a logician this is a tragedy, but for us it’s a useful primitive, so we name this property of oscillating “autoheterological”.
Interestingly, if you assume “autoheterological” is autoheterological then implies it’s autological. If it’s autological that must mean it’s heterological, and if it’s heterological then it’s still heterological. Meaning that it sort of decays through multiple steps. If you wanted to give a name to a term that goes through a process of decay like this you might call it multiautoheterological, is that enough prefixes?
Autoheterologicality is a property that’s critical for designing self-stabilizing systems. Here’s a cute example of an autoheterological property that leads to a self-stabilizing system.
In this example the autoheterological part is the the parameter that measures the distance from the contact point to the base of the cup.
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