Andrew Coppin:
How come the set of all sets doesn't exist?
... Felipe Almeida Lessa cites a relevant page
Ouch. Clearly, set theory is way more complicated than people make out. (I always thought a "set" was just a collection of objects...)
You are right. A set is a collection of objects, nothing more, provided you know what is a collection, what is an object, and what is the meaning of the verb "is". Since this is a café chat, I'll tell you a Zen story. A young apprentice thinks that an apple is just an apple. But then, he starts studying. One day he gets his enlightment, and learns that an apple is a terribly complicated entity. There are concrete apples, there is also an idea of an apple, a "universal apple". He knows then that his apple is a symbol which hides inside the secret of the structure of our knowledge about things. He feels humble facing his apple, and yet happy that he could grasp some of its mysteries. The question "what is an apple" is an infinite source of other questions which lead him to the Wisdom. Seeral years later he becomes a Master. Now, he sees clearly that an apple holds also the knowledge about the structuration of the Unverse. His apple allows him to ask questions about, say, limit of things: where this apple begins? What does it mean "inside"? How to distinguish an apple from a non-apple? Can we ask where there are two identical apples? ... When the Master gets older, he sees also that apples hold the secrets of life and death. They symbolize - if one wants to see it - the Eternal Ring of perpetuation of things. You must destroy your apple in order to let grow new ones. ... et caetera. ++ Finally, our hero becomes a Great Master, a true one. He looks at the universe below him, and he sees, as clearly as never before, that an apple is just an apple... Jerzy Karczmarczuk