Yeah, it is sorta specific, but remember, it is Beethoven. I was always told that, especially in his piano music, he means EXACTLY what he writes, I've been told that I play too much to "my liking" of his piano sonatas, just be more strict with my playing, so I suppose he would want to have specific pedal markings. Big asterisks would be pedal off, and pedale or ped would be pedal on. Goodluck in this sonata DinosaurTales, Its one of my favourites, technically very demanding work!
I wonder if anybody has examined facsimiles of Beethoven's autographs to see how he indicated pedal-markings?