Most everyone is half right regarding blades cutting. There are two parts to cutting pinching or cleaving and sawing. In simple terms the latter is what Brendan is describing and the former is what the others are talking about.
To the OP JP knives should be REALLY sharp but everyone sees REALLY as a different thing. Although I don't fool with knives anymore I always got a few nicks setting blades and never thought of them as being anything but "razor sharp" when I installed them. I never tested them by cutting paper but I will point out cutting paper is far from a universal constant since there is a technique to it and the "better" you are the duller the blade one can get to cut paper, even if we assume all "printer" paper is the same. Since there is no easy way for the average woodworker to quantify sharpness you just have to do your best to subjectively or objectively rate the results and longevity of the edge.
Now if someone wants to build a sharpness jig it seems possible and rather easy, you would need a consistent substance that could be consistently dimensioned and could cut by the blade in question relatively easily then a way to bring the blade in contact with, and guide it through, the material along with a force gauge for the imperical measurement...