I’m reading a book that Phil bought me a couple of Christmas’s ago. It is called “Godel, Escher, Bach: an Eternal Golden Braid”, and it is so dense that my mind is just in a state of goo. But it is really good, and I’m learning a lot.
But the point of this is that I wanted to share with you a passage from it so you could see what I’m going through right now.
“Most sets, it would seem, are not members of themselves – for example, the set of walruses is not a walrus, and the set containing only Joan of Arc is not Joan of Arc (a set is not a person) -and so on. In this respect, most sets are rather “run-of-the-mill”. However, some “self-swallowing” sets do contain themselves as members, such as the set of all sets, or the set of all things except Joan of Arc, and so on. Clearly, every set is either run-of-the-mill or self-swallowing, and no one set can be both. Now nothing prevents us from inventing R: the set of all run-of-the-mill sets. At first, R might seem a rather run-of-the-mill invention – but that opinion must be revised when you ask yourself, “Is R itself a run of the mill set or a self-swallowing set?” You will find that the answer is: “R is neither run-of-the-mill nor self-swallowing, for either choice leads to a paradox.”
And I’m reading this for fun…