| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| Full Idea: Zermelo assumes that not every predicate has an extension but rather that given a set we may separate out from it those of its members satisfying the predicate. This is called 'separation' (Aussonderung). | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3 |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 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. | |
| From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.4 | |
| 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! |
| 13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
| Full Idea: There are set theories that countenance exceptions to the Principle of Separation in exchange for a universal set. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) |