I have a Physics question for you: is time continuous? I mean, is any given extent of time always further divisible into extents of time?
I'm sorry, I really don't know. In fact, I don't think I even know what the majority opinion is among physicists (if there is one).
At the face of it, it seems like if spacetime is discrete, then up until now, the unit of discreteness is small enough to allow us to do calculus (which assumes continuity) with impunity, even at the smallest of scales our experiments go to. So, as far as experimental evidence goes, there's no reason to believe in discreteness. But I guess your question is whether there are any theoretical arguments which suggest discreteness... to which I really don't have an answer. If I understand some interesting argument in the future, I'll get back to you.