Full Idea
The most characteristic Zermelo axiom is Separation, guided by a new rule of thumb: 'one step back from disaster' - principles of set generation should be as strong as possible short of contradiction.
Gist of Idea
The Axiom of Separation requires set generation up to one step back from contradiction
Source
report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.4
Book Reference
-: 'Journal of Symbolic Logic' [-], p.485
A Reaction
Why is there an underlying assumption that we must have as many sets as possible? We are then tempted to abolish axioms like Foundation, so that we can have even more sets!
Related Idea
Idea 18105 Replacement enforces a 'limitation of size' test for the existence of sets [Bostock]