As of now, I understand classes to be introduced for us to meaningfully talk about collections of object for which describing them with sets would create problems. I have a few questions about classes to help me understand them:
Traditionally, classes can only be collections of sets, never other classes, so It seems collections of classes cannot be spoken of in NBG set theory. Is this true?
Does there exist some set theory or system which allows you talk about absolutely every collection of objects you can conceive of without contradiction?
I know these are more philosophical then usual, but thanks for the help.