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Re: Antifoundation axiom
Posted:
Mar 13, 2013 1:14 PM


K_h wrote: > > "CharlieBoo" wrote in message > news:60eb0d021d73401199cf4b30f376a718@9g2000yqy.googlegroups.com... > > > > > Do you consider relationships besides sets (relations)? Right now we > > have: > > > > A. Everything is a set. > > B. x ~e x is not a set. > > This is not a correct characterization of set theory. In the generally > accepted approach, not everything is a set and no collection can be a member > of itself. Collections are bifurcated into two types and they are sets and > proper classes. So "Everything is a set" just isn't part of modern theory.
In ZF, "everything is a set" is usually true in as much as there is just one type (or is the word "sort"?) of variable and they range over sets and nothing else. I write "usually" because Suppes' set theory is ZF, but he has "things" (those are scare quotes, I'm not quoting Suppes) only some of which are sets. I don't know if Suppes calls his set theory ZF because I don't have the book to hand at the moment.
 When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting



