In metaphysics it is important to keep in mind that our object of study is a totally unique phenomenon. If we forget this then we may fall into confusion on many issues. One such issue would be the problem of the size of the universe. If by ‘universe’ we mean ‘the world as a whole’, all possible mental and corporeal phenomena as well as the container that contains them, or the ‘multiverse’ and whatever contains that, then this question may seem to present us with an intractable paradox.
The universe appears to be extended in space and time. In this case, it must be finitely or infinitely extended. To say that it is finitely extended, like a football, is to say that it is not, after all, the world as whole. This idea must be rejected. To say that it is infinitely extended is possible, mainly because the idea is so confusing, but it would directly contradict the scientific evidence and explain exactly nothing.
The root of this topological problem is our idea of extension. This seems a harmless enough concept in our everyday classical or Newtonian universe, but it unravels in quantum mechanics and metaphysics. If the ‘world as a whole’ means what it says, then the idea that it is extended in space and time is incoherent. Then space would be extended in space and time would extended in time. It would be unsurprising if this idea caused paradoxes and contradictions. If we remember that in metaphysics we are dealing with a unique phenomenon, a phenomenon that encompasses all other phenomena, and thus adopting an ultimate perspective on the world, we can avoid this paradox. To think of the universe as a giant football or as infinitely extended is to make it incomprehensible. For an ultimate level of analysis our everyday Newtonian idea of extension would have to be abandoned.
The mathematician Hermann Weyl wrote much that is relevant to this topic. I discuss his thoughts in a previous post. He concludes that the idea of an extended continuum is paradoxical and has no empirical support. https://theworldknot.wordpress.com/tag/weyl/