It would only have that sense if you added. It's like when saying did you know strawberries aren't berries, but bananas are?, i didn't know if. Earth is the only planet we know of where life exists.
Sabrina Carpenter’s Dating History From Joshua Bassett to Barry Keoghan
Recently one of my friends told me that there is distinct difference between 'know of something' and 'know about something' expressions. This sentence is from the commentary of planet earth. In my understanding, ' as we know it ' usually follows a noun phrase and means like the building as we know it = the version/condition of.
Why it is know of in.
Because you've just told them! Why do you think that he doesn't know him from his schooldays means that he does know him?