But what is more "self evident" just might be what's more apparently obvious. Some people would say that X=X is more apparently obvious.
That is called major brain fog...
at1with0 wrote:I'm confused. I thought khan was suggesting that it is not self-evident that X=X.
at1with0 wrote:Physical reality can be seen as a set.
Tegmark's response in  (sec VI.A.1) is to offer a new hypothesis "that only Godel-complete (fully decidable) mathematical structures have physical existence".
Axiomatic set theory
I will informally list the undefined notions, the axioms, and two of the ``schemes'' of set theory, along the lines of Bourbaki's account. The axioms are closer to the von Neumann-Bernays-Gödel model than to the equivalent ZFC model. (But some of the axioms are identical to some in ZFC; see the entry ZermeloFraenkelAxioms.) The intention here is just to give an idea of the level and scope of these fundamental things.
...There are three undefined notions:
1. the relation of equality of two sets
2. the relation of membership of one set in another (xy )
3. the notion of an ordered pair, which is a set comprised from two other sets, in a specific order.