About the Universe

It all depends on your axiomatic system.

I've never heard it called that before.

So then, to put it another way:

Could the different logics in the world speak of one and the same set of theorems or of entirely different sets etc? Or else, would more than one axiomatic system derive the same theorems?

Multiple axiomatic systems can derive the same sets of theorems, or entirely different ones.

That goes without saying, though I would add that this is conditional on its strength (consistency) and scope (applicability). Also, if we are speaking of other civilizations and their capacity to derive either the same or highly advanced theorems and other deductions about the world- and it seems that my initial question has come to this- I would say that the object of study here would be the same and only the degrees would differ: the natural world and the systems created through the study of it via logic, mathematics, engineering, medicine (biochemistry) etc. This is to say that though the perspective and degree of intelligence may differ from our own, I would think that any axiomatic system from an intelligence in this universe would be founded on its surroundings (the state of affairs in its natural world) and then propagated via its understanding of the method by which it derives advanced systems.

So though it is true that multiple axiomatic systems may or may not derive entirely different theorems (given), it would seem that only the degree of understanding and thus its "axiomatic scope" would differ between civs in this universe; the object of study would differ only given the degree of its understanding- of comprehending it. Our tools used to learn about this or that in the world may be weaker or stronger than those used by others, and so studying the same thing may yield different results.

But what of the original question: is this universe a single set (though expanding and contracting- as if a living entity), or does it comprise several or many? I once glanced over an article that stated quantum physics views the universe as creating (and eliminating) "sub-universes" of all sorts and all the time.

Well, I don't believe the question is particularly meaningful. There is, of course, Russel's Paradox which shows that there is no universal set, but that's a completely different meaning of universe. As to whether the universe is one set, you could certainly consider it to be one set and if you did, I'm not sure we know enough about physics to say whether that would be inappropriate or not. You can certainly consider different subsets of the universe, and then there are the unions of those sets.

Your comments about the universe expanding/contracting as a set certainly seem reasonable from our perspective, but if you consider the Universe beyond its state at any given moment, in n physical dimensions and m time-like dimensions, however many of those there might be, you might be able to consider the universe to be one set of a single size.

Thank you for the reply- I mean that.

The image of the universe this article conjured up was akin to a balloon twisted in various knots and ties, the end result of which created five "mini" balloons connected via those knots and ties. The original balloon consisted of something like a rough sphere, but when manipulated in certain ways, the first sphere was transformed into five of them. When the knots and ties were released, the original balloon (or sphere) appeared as it was before.

Could the universe be tied up and twisted (in natural terms) to create (and eliminate) other universes? Is space-time or the very fabric of space "adjustable" enough to do this?

I once read of how enormous celestial bodies were shown to bend the space around them!

The structure of the universe is a fascinating topic in modern physics. There are some who suggest that recent astronomical discoveries suggest that the universe has elements of fractal geometry, or that it's toroidal, or that it's simply a big expanding ball.
Many scientists believe that ours is just one of a multitude of Universes and each might possess different fundamental quantities.

And thus I came to the question:

Within what are these universes contained in? Where are they?