2009/6/5 Torgny Tholerus <tor...@dsv.su.se>: > > Kory Heath skrev: >> On Jun 4, 2009, at 8:27 AM, Torgny Tholerus wrote: >> >>> How do you handle the Russell paradox with the set of all sets that >>> does >>> not contain itself? Does that set contain itself or not? >>> >>> My answer is that that set does not contain itself, because no set can >>> contain itself. So the set of all sets that does not contain >>> itself, is >>> the same as the set of all sets. And that set does not contain >>> itself. >>> This set is a set, but it does not contain itself. It is exactly the >>> same with the natural numbers, BIGGEST+1 is a natural number, but it >>> does not belong to the set of all natural numbers. The set of all >>> sets >>> is a set, but it does not belong to the set of all sets. >>> >> >> So you're saying that the set of all sets doesn't contain all sets. >> How is that any less paradoxical than the Russell paradox you're >> trying to avoid? >> > > The secret is the little word "all". To be able to use that word, you > have to define it.
I call that secret bullshit, and to understand that word (bullshit), you have to define it. Sorry but I think we're talking in english here, all means all not what you decide it means. Quentin. > You can define it by saying: "By 'all sets' I mean > that set and that set and that set and ...". When you have made that > definition, you are then able to create a new set, the set of all sets. > But you must be carefull with what you do with that set. That set does > not contain itself, because it was not included in your definition of > "all sets". > > If you call the set of all sets for A, then you have: > > For all x such that x is a set, then x belongs to A. > A is a set. > > But it is illegal to substitute A for x, so you can not deduce: > > A is a set, then A belongs to A. > > This deductuion is illegal, because A is not included in the definition > of "all x". > > -- > Torgny Tholerus > > > > -- All those moments will be lost in time, like tears in rain. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---