Yes, classical mechanics suggests infinity, eg. the Newtonian method and infinitesimals, which is just as problematic as a Turing Machine's infinite tape or Max

Yes, classical mechanics suggests infinity, eg. the Newtonian method and infinitesimals, which is just as problematic as a Turing Machine's infinite tape or Maxwell's Demon. Really classical, platonic geometry requiring atoms with hard bounds is also inconceivable. The uncertainty principle and stuff like Noether's theorem should nicely limit how to ask the right questions. Now I'm not sure if Noether's is a proof by contradiction that would answer the question directly, I rather doubt it. It's a valid question for the sake of didactics at least, how much can be simplified and explained in classical terms without catastrophic loss of precision. Conversely, the slit-experiments for example are a probably the most prominent display of quantum effects in the experiential domain.