Ok. This sounds like a kid question made when she/he first heard about "infinite". (But is that even bad?)
So, I'll give a lecture about (cardinals) infinite numbers for some 12-15 yo kids and I wish I could make a logical proof of the statement "There are only finite-many stars in the universe"; That is, some proof without using physics/chemical properties (like the quantizable property of the matter etc.).
For example (the following is some of what I'm not looking for):
Affirmation: In a bottle of water there are only finite-many atoms
Proof: The water is all composed by smaller parts (insert physics here) of fixed size greater then some $s\in \mathbb{R}$. Suppose that there are infinite many atoms in the bottle, but that would implie that the size of the bottle is at least $\sum \limits _{i=1}^{\infty}i\cdot s$ wich do not converge for a finite number, but the bottle has a finite size; contradiction!
But how can I assume that the bottle is finite? This argument seems pretty vague when atoms in a bottle of water is changed by "stars in the universe". And I think that a proof using only logical arguments would be more interesting...
Was this clear enough? I'd be glad if anyone could help me! And if this is duplicated, I'm sorry, I couldn't find something related.
What is "our 'real' world"? If you're referring to the physical world, then it seems intuitive that you could not prove anything about it without assuming at least one physical premise (as Winther alluded to in the comments).