My talk of “primitive predicates” makes sense only if you’re talking about a computational implementation.
In a truly formal logic, you do determine the definitions of the predicates purely by the axioms they are found in, including a set of axioms that are production rules, which therefore spell out execution (although order of execution is still usually ambiguous). ZF set theory is like that.
But I’ve never seen a presentation of Russell’s paradox which defined what “not” and “member-of” mean in an axiomatic way. I don’t think that had even been done for set theory at the time Russell proposed his paradox. The presentations I’ve seen always rely on your intuition about what “not” and “member of” mean.
My talk of “primitive predicates” makes sense only if you’re talking about a computational implementation.
In a truly formal logic, you do determine the definitions of the predicates purely by the axioms they are found in, including a set of axioms that are production rules, which therefore spell out execution (although order of execution is still usually ambiguous). ZF set theory is like that.
But I’ve never seen a presentation of Russell’s paradox which defined what “not” and “member-of” mean in an axiomatic way. I don’t think that had even been done for set theory at the time Russell proposed his paradox. The presentations I’ve seen always rely on your intuition about what “not” and “member of” mean.