Physically speaking, we don’t know that the universe isn’t fundamentally discrete. But the more pertinent question is whether what the brain does couldn’t be approximated well enough with a finite state space. I’d argue that books, music, speech, video, and the like demonstrate that it could, since those don’t seem qualitatively much different from how other, analog inputs stimulate our intellect. Or otherwise you’d have to explain why an uncountable state space would be needed to deal with discrete finite inputs.