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rhollerith_dot_com comments on No coinductive datatype of integers - Less Wrong
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I still do not see how first-order logic relates in any way to cousin_it's statement in grandparent of grandparent.
Just because second-order logic is incomplete does not mean we must restrict ourselves to first-order logic.
I think I recall reading somewhere that you only need first-order logic to define Turing machines and computer programs in general, which seems to suggest that "not expressible in first order logic" means "uncomputable"... I could just be really confused about this though...
Anyway, for some reason or other I had the impression that "not expressible in first order logic" is a property that might have something in common with "hard to explain to a machine".
ADDED. relates -> supports or helps to illuminate