A very large book
SupraRef refers to its index every book that does NOT refer to itself in the index.
Does SupraRef refer to itself in the index? Provide valid reasoning for your answer.
This is a recasting of Russell's Paradox: "Is the set of sets that are not members of themselves a member of itself?" It remains a paradox and remains a refutation to the idea that once the elements of a set are defined, a candidate element is then unambiguously either
in or
not in the set.
Note: this uses Frege's definition of sets which allows for improper subsets, i.e, subsets containing the set itself, just as SupraRef may reference SupraRef.
Edited on June 6, 2023, 3:19 pm
It is unresolvable.