I'm trying to find another term which means "finiteness". To me, it sounds too clumsy. Part of my mind gesticulates wildly toward a "-cy" suffix word to describe this, like "captaincy" or "valency"... but of course, "finicy" sounds a tad ridiculous and there is obviously no such word.
Even if I did use "finiteness", I feel it would suggest too strongly the finite aspect, where as "infiniteness" would just be silly. Obviously, the word should be neutral, but describe the polarisation between finite and infinite. Just as "colour" is a totally neutral word not suggesting any particular colour.