  The positivistic assumptions of determinism and objectivism in the realm of
Newtonian mechanics are questioned in this paper. While objectivism is only
challenged through proposing the mildest form of subjectivism, determinism is
structurally disputed by proposing that the physical reality, at least in the
examples discussed, is, in essence, probabilistic and unpredictable. It is
discussed that the physical reality and experimenter's identification of it
could basically have inconsistent characteristics, and the study of the
physical reality can therefore be conducted in ontic and epistemic levels,
leading to two distinct identifications. Four scientific topics, showing two
different types of indeterminacy, are introduced and briefly reviewed: chaotic
systems, turbulence, fluid transport in porous media, and hydromechanics of
fractures. It is proposed that determinism is only meaningful in epistemic
level, the first two examples are ontically indeterministic, the last two
examples are epistemically indeterministic, and more examples of
indeterministic phenomena could, most likely, be found in the nature.
Indeterminacy of the physical reality, it is discussed, has always been
considered in engineering design processes and such effects have normally been
covered through safety factors and feedback loops. By reviewing Hadamard's
well-posedness criteria, Poincae's complete deterministic approach, and
Leibniz's principles of sufficient reason and identity of indiscernibles, it is
claimed that positivism stands on Leibniz's metaphysical assumptions, which are
not necessarily in full agreement with the physical reality. A few suggestions
for a path beyond positivism in Newtonian mechanics are finally provided.
