I know many talked about this, however I am not a professional philosopher, rather a mathematician.
In mathematics we have the concept of infinity, so we speak about infinitely big things, we compare them, we label and order different kind of infinities and we also have the "infinitely" small.
However for as much as we put our heads down, we can't really grasp the concept of infinity, but although it might sounds weird, we can instead easily and intuitively describe the order between different sizes of infinities.
Now let's talk about space. I remember in school there was someone who talked about the paradox of distances and how we can always walk half of the distance between two points and repeat it to infinity, without getting to the other point (the example was a turtle walking I guess).
I am thinking about the size of what exists. ALL OF WHICH EXISTS. I don't have a definition of existence, neither I want to talk about ontology, however suppose the first:
SPACE IS FINITE
If it is, then either it has a border or not. Now, if it has a border, then there is more space after the border, or it wouldn't be a defined border right? A border is made of two sides, one inside one outside (or not? Look at the Möbius strip) so the one outside touches some more 'space' and hence we can repeat this indefinitely - paradox.
Suppose it has no border. Then the only explanation would be a limit, in the mathematical sense, i.e. we can keep on going forward and getting closer to an imaginary border, but there is no border. Of course the distance here should be affected by it and the perception of distances would be shrank down. However if so, would it actually not be a paradox as in the physical world there seem to be no way to actually infinitely approach something without finally reaching it. Also, this would show that the space is infinite inside a finite space? If this makes sense.
Conclusion: it must be infinite.
SPACE IS INFINITE
Well if it is infinite, then there is no border and no limit! So we can always indefinitely go forward. However would this mean that the space would create itself as someone travels there? Because if it is infinite and it instantaneously exists, then how did it even start? And if it did not start, how did the things even get there in the first place? Unless it is a simulation, then something must have been moved there or created. If it is infinite, why then everything else is finite? In an infinite world, there should be infinite things!! But everything else seems finite!!
This to me looks like a contradiction. For example, why aren't there some infinitely large galaxies? It would be possible I guess in an infinite space (not according to physics, however to be entirely honest an infinite space wouldn't have much explanation either in physics!)
Hence looks like we have a paradox and therefore it must be finite!
So these things contradict themselves! So are they both true or both false? Normally two contradictive things can't have the same value, one must be true, one false or we fall in a paradox. But here only one of them cannot be correct, and so we fall again in a paradox.
What can the solution possibly be?