Fil Albuquerque wrote:
...when pretentiously mentioning a final set of all sets we are saying nothing at all...not that there is n´t a final set of all sets but simply that we cannot define it nor containing it if not allusively...any set but specially a final set of all sets does not belong nor can it be informed to any of its parts...
Apparently set theory arose out of a need to deal with the idea of infinity... to make it available to reason? The idea of convergent progressions arose from it? I think I'm running before I can walk here, but I keep coming back to this issue: you can relate an entity (numbers are a simple example) to its immediate neighbors . You can't relate a specific number to infinity, though. All numbers become equivalent when you do that. It's because infinity is a negative idea: it's a lack of limitation. It's not a positive thing
that's available for relationship... except as a concept it's related negatively with the idea of limitation. That's why it's convenient (and only possible?) to talk about infinite progressions as sets. A single member of the progression can relate to the set
because the set
is closed or limited even though the number of members isn't.
I think we're loitering around the difference between a thing and its definition. A set is like a club that requires entities to meet certain qualifications for membership. A set is really nothing but criteria. It's when you think of criteria
as a bucket capable of holding things
that exhibit that criteria... that's when things get weird. You can end up with an infinitely large bucket. I have a suspicion we didn't really escape from the basic problem by introducing set theory. I've bought a book about the history of set theory.. maybe I won't sound so silly after I read it.
Fil Albuquerque wrote:
Being "there" and not "here" is a property of any bit of information which distinguishes it from any other...talking about sets is talking about locations as much is talking about patterns...
Right. Each member implies all the other members and implies the set itself. Location can't be identified by any absolute coordinates... as you said, location is talking about an observer/observed relationship. Man.. it's complicated. Confused is a good place to be, I suppose.