It's not my definition of sharpness--"sharp" just means "cuts well". To use it colloquially to mean something more specific will only cause confusion, and is unnecessary, since there are more accurate terms for the qualities of a knife that are often refered to as "sharpness". One that comes to mind is "a polished edge". A tissue-paper slice test does not test the cutting efficiency of a tool--only shows how well the bevels are matched and polished--and I've seen more than one knife that will push-cut paper and still cuts food like crap.
An example of a knife that is thick and cuts well would be a Shigefusa--thick, and cuts with primo efficiency, because Iizuka san has nailed the profile, distal taper, balance point and face grind. A thick knife that cuts like crap would be a Farberware--thick in the back, poorly ground, and not matter how you sharpen it, it will always cut like crap. Compare that Farberware to a Tojiro DP, which has a simple grind and bad balance, and the Tojiro will out perform the Farberware even when dull--simply because it is thinner.
There are factors to a knife other than cutting power, but when it comes to that, the CCK 1303 is a bang-for-the-buck MONSTER.