Positivism in Newtonian Mechanics: The Ousia or a Historical Liability?

Abstract: 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.