An argument for an indeterministic interpretation of classical physics (i.e., Newton's mechanics and Maxwell's electrodynamics) was put forth by Gisin and Del Santo in  (see also    and  ). They maintained that although classical physics has traditionally been construed as deterministic (i.e., the physical laws determine a unique definite future (and past) state of a physical system once its current state is fixed, as famously revealed in the scenario of "Laplace's Demon"), it is not necessarily the case. There are metaphysical assumptions behind the traditional deterministic interpretation, and it is possible to give an alternative indeterministic interpretation by revising those assumptions, they contended. In particular, the usual practice that real numbers are used to represent physical quantities was held to be problematic, because this would lead to the unacceptable consequence of "infinite information density" (as related to the infinite string of digits following the decimal point of a real number) in the relevant physical space, according to them.The paper does not agree with these conclusions, but I do.
I have argued here that classical mechanics is not really deterministic. Calculations always have error bars, just like any other part of science. Laplace's Demon is just a big straw man, like Schroedinger's cat.
Almost all real numbers have infinite information content, and such things are not observable.