Its only still a paradox if you are attempting to stay within the bounds of first order logic.
The solutions to Gödel and Russell’s Paradox and Friege’s Basic Law V (axiom schema of unrestricted comprehension) are the same solutions but shown in different ways.
A relaxing of naive set theory leads you to at the very least, Monadic second order logic which allows for quantification over sets.
Computing is one of the most fascinating of the possibilities opened up by moving to this.
Church’s Lambda Calculus did it by removing All identity completely.
Turing did it by introducing Time (or rather Steps). Church and Turing map perfectly to one another.
Shannon tied it to entropy. (Information lacks identity in the same way that the lambda lacks identity I think) and became Information Theory.
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