A Defense of Scientific Platonism without Metaphysical\ud Presuppositions

From the Platonistic standpoint, mathematical edifices form an immaterial, unchanging, and eternal world that exists independently of human thought. By extension, “scientific Platonism” says that directly mathematizable physical phenomena – in other terms, the research field of physics – are governed by entities belonging to this objectively existing mathematical world.\ud Platonism is a metaphysical theory. But since metaphysical theories, by definition, are neither provable nor refutable, anti-Platonistic approaches cannot be less metaphysical than Platonism itself. In other words, anti-Platonism is not “more scientific” than Platonism. All we can do is to compare Platonism and its negations under epistemological criteria such as simplicity, economy of hypotheses, or consistency with regard to their respective consequences.\ud In this paper I intend to show that anti-Platonism claiming in a first approximation (i) that mathematical edifices consist of meaningless signs assembled according to arbitrary rules, and (ii) that the adequacy of mathematical entities and phenomena covered by physics results from idealization of these phenomena, is based as much as Platonism on metaphysical presuppositions. Thereafter, without directly taking position, I try to launch a debate focusing on the following questions: \ud (i) To maintain its coherence, is anti-Platonism not constrained to adopt extremely complex assumptions, difficult to defend, and not always consistent with current realities or practices of scientific knowledge? \ud (ii) Instead of supporting anti-Platonism whatever the cost, in particular by the formulation of implausible hypotheses, would it not be more adequate to accept the idea of a mathematical world existing objectively and governing certain aspects of the material world, just as we note the existence of the material world which could also not exist?\u