|Axiom: principle or rule for linking elements of a theory that is not proven within the theory. It is assumed that axioms are true and evident. Adding or eliminating axioms turns a system into another system. Accordingly, more or less statements can be constructed or derived in the new system. > System.|
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|Thiel I 341
Axioms/Zermelo/Thiel: Zermelo himself has emphasized that the question of the origin and validity domain of his set theoretical axioms remains philosophically excluded.
It will be at most possible to say that logicism has survived in the axiomatic set theory insofar as cardinal numbers are defined there as definite sets and a cardinal number arithmetic is created with them.
Philosophie und Mathematik Darmstadt 1995