I Emergent space-time from what?

[JRB]

I understand Demystifier and others this is my first post on a physics forum and I thought later I shouldn't have said that! :)

 

[JRB]

Yes thanks for that nomadreid its contained and yes I am thinking of Cantor's Absolute, apparently he called it the infinity of infinities. Its paradoxical to talk about bounded infinities even if mathematically they can be tamed but I am thinking from the perspective of the absolute. Does it make any sense to say the infinite hierarchy exists within it, yet the absolute is something beyond, more or different to the hierarchy and so in some sense it does end there, as there is nothing more or beyond the absolute?

 

[nomadreid]

Its paradoxical to talk about bounded infinities

The "paradox" disappears quickly, for example, when you consider that an infinite set is just a set which can be put into one-to-one correspondence with a proper subset. If you are interpreting the word "infinite" as "unattainable" (not to use the word "inaccessible", which is the name of one type of infinite set), then you just need to remember that it is only unattainable using a certain collection of axioms, but is perfectly attainable when you add an appropriate axiom. Also, you may be getting "finite" mixed up with "bounded", which is not the same. A finite set is bounded, but a bounded set need not be finite: bounded will mean that there is something which it is less than, and interpreting "less than" as set membership, since an infinite set can be a member of another set, it is easy to see that an infinite set can be bounded.

yes I am thinking of Cantor's Absolute

That is a problem, since Cantor's Absolute turned out to be rather non-mathematical. There is of course always a kind of absolute from the point of view of a particular theory-model pair, to wit, the universe of that model, but this "relative absolute" was not what Cantor had in mind. For example, the fact that there is no such thing as a greatest ordinal, or Löwenheim-Skolem's upward theorem, and other technicalities made Cantor's idea untenable in mathematics. Of course, the other side of his idea, associating this concept with a divinity, is also outside the realm of mathematics.

Does it make any sense to say

The rest of your questions assume the existence of this Absolute, so since this Absolute is not a tenable notion in mathematics, the answer to those questions is that those assertions do not make mathematical sense. Whether they make some kind of metaphysical sense is not something I would touch upon here.