Mechanism and determinism

With recursion theory being a relatively young discipline, the notion of “physical determinism” in classical physics lets unspecified the exact recursion theoretic status of the physical entities. In this chapter, such a specification is attempted, re-interpreting the classical meaning recursion-theoretically. It is not unreasonable to assume that a recursive evolution seems to be “at the heart” of the classical notion of “determinism.” Usually, these evolution functions are defined on continua, such as ℝⁿ. In particular, the initial values and the solutions are defined in ℝⁿ. Yet, by theorem 1.7, p. 12, “almost all” elements of the continuum are uncomputable. In particular, the assumption of an exact (i.e., effectively computable) description of the initial value(s) becomes ridiculed…