Prove this statement; The universe is infinite. Possible or impossible? Cosmological minds want to know!
Also, measurement seems to be at the core of this question. What, exactly, may be measured? At this point allow me to introduce to you theology, the philosophy of the immeasurable. It just may be that all that is reasonable, or even rational, may not be measurable.

Many moons hath reason
And some, not her own
Reflect in her seas
Confounding her astronomers
But, Oh!, delighting me!