Axioms n beyond

OK so axioms and logic do seem to have some value in this. The consciousness conundrum can be formulated very simply ... this is informal I'll spend some time to make it precise later...

If we postulate that there are things, and then use those things to explain how we came to postulate that there are things then we have a theory in terms of the thing we were trying to explain. It would be impossible to have a theory not in terms of things so we can't replace that original postulate.

More generally a theory must be in terms of what it is not, otherwise we are taking it as an starting assumption... an axiom. We can't prove an axiom we can only show that it is consistent with other axioms.

The question then of how we arrive at axioms is beyond axioms then. It must be accepted by reason that we can generate propositions as a fact. That cannot be the work of the brain!

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Set theory again. On a table let us take some red beads and put them in a box and some yellow beads and put them in a box we have 2 boxes which might be described as the red box and the yellow box. The red box is not actually red, and the yellow box is not actually yellow. Our table universe (U1) has only 2 entities, namely the two boxes.

Now if we were to think about the box of boxes; in the analogy, we would create a big box for the two boxes and then we would have a new universe (U2) with 1 box (namely the box of boxes of universe U1). What we obviously can't do in the physical world is to put the big box in itself.

Now in set theory it is assumed that all subsets of a set already exist, so set theory says that in universe U1 the set of boxes {red box, yellow box} exists automatically which is the same as U1. However it is not an actual box.

When we actually build that box we get a new universe with 1 member. Only once that set is constructed does is actually exist, but to make it a member of its own construction is a problem.

If it didn't exist then it would bring its own constrcution down. If it does exist then it makes itself exist. The existence of the set depends upon itself. e.g. if T = {T} then T needs to exist to create T (so it doesn't really exist). If T does not exist then T = {} which exists.

Now we can create sets simply by chosing our ontology, and we can change subject to make sets disappear. Now with T = {T} what ontology do we have? or what universe is that a member of? To create T we must already have T.

The set of all Universes which have "blue" as a member. Which universe is T in?

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Having shown to myself today (almost like Descartes) that there is a "just is" feature of experience that at the root our experiences just are, I'm now ledt thinking how far does "just is" go. Obviously the arrangement of things in my room can be changed, it is not "just is". So what rule divides that which "just is" and that which can be investigated, understood and changed?