Memories of Kurt Gödel
I know this post is aimed at laymen but this sentence is not correct."A bit more precisely, the Incompleteness Theorem shows that human beings can never formulate a correct and complete description of the set of natural numbers, {0, 1, 2, 3, . . .}."The second order Peano Axioms are categorical and thus, up to isomorphism, the only model for this axiom system are the Natural numbers {0, 1, 2, 3, ...}.  This is a complete system.  We can't happen is a recursively enumerable axiomatic description of the Natural numbers that is complete.Another way to get a complete description of the Natural numbers is to take the collection of all true statements of the Natural numbers and make that our axiomatic system.  It's just not a useful axiomatic system but it is a complete description of the Natural numbers.