I am not sure if the question/answer is philosophically important, and fairly certain it is scientifically unanswerable/nonprovable.
In terms of importance, I refer you to Leonard Peikoff’s description of infinity:
“There is a use of [the concept] “infinity” which is valid, as Aristotle observed, and that is the mathematical use. It is valid only when used to indicate a potentiality, never an actuality. Take the number series as an example. You can say it is infinite in the sense that, no matter how many numbers you count, there is always another number. You can always keep on counting; there’s no end. In that sense it is infinite—as a potential. But notice that, actually, however many numbers you count, wherever you stop, you only reached that point, you only got so far. . . . That’s Aristotle’s point that the actual is always finite. Infinity exists only in the form of the ability of certain series to be extended indefinitely; but however much they are extended, in actual fact, wherever you stop it is finite.” ~ Infinity, Ayn Rand Lexicon
In the Weak vs Strong Emergence topic, Grames cited an interesting science article (post #39) which concludes:
“… The critical point is that quantum field processes have no existence that is independent of their configurations: quantum fields are processes, and can only exist in various patterns. Those patterns come in many sizes, of many different physical and temporal scales, some as large as a human person, or a social institution – but they are all equally patterns of processes. There is no ‘bottoming out’ level in quantum field theory – it is patterns of process all the way down, and all the way up…”
The implication being (unless I’m mistaken) that current science suggests an infinite scale to the universe and everything it contains, while logic dictates the actual universe is finite. If this is the case, then we are caught between two credible positive assertions that draw contradictory conclusions. In terms of importance, one would have to determine whatever influence one assertion has to the other. Should the scientific claim be discarded, for example, because it’s not logically possible? Or should the logical claim be revised to admit the possibility of an infinite universe??