If the universe cannot contain infinite amount of information then it follows that there are infinite knowledge we cannot know - simply because we cannot store it anywhere (in brains or computers or anywhere).
For example: exact prime factorization of all natural numbers, etc...
Of course this is true only if you accept induction. So you can still back off by declaring yourself finitist* ;)
Assuming a big bang is the source of all matter. Our observable universe may only be a spec in something much larger with out violating any of our "laws" of physics.