Platonismo y realismo en matemáticas y física: un estudio ontológico y epistemológico

Abstract

This study examines, from an ontological and epistemological perspective, the fertile tension between mathematical Platonism —according to which mathematical objects and structures exist independently of the human mind— and scientific realism, which conceives physical theories as descriptions of entities and processes that exist objectively. Adopting a qualitative theoretical-analytical approach, the paper develops four central axes: (i) the genealogy of Platonism, from Plato to its contemporary reformulations in authors such as Gödel and Penrose; (ii) the status of realism in physics in light of the conceptual transformations introduced by relativity and quantum mechanics; (iii) the so-called mathematical–physical «bridge», evidenced by the unreasonable effectiveness of mathematics (Wigner) and radicalized in the Mathematical Universe Hypothesis (Tegmark); and (iv) a critical examination of alternative positions —nominalism, formalism, constructivism, and instrumentalism— together with their main contemporary objections.

From a methodological standpoint, the study combines historical-conceptual analysis, critical review of classical and contemporary sources, and a theoretical–practical articulation through paradigmatic cases (Dirac, Maxwell, and the wave function). In addition, a hermeneutic-critical analysis of contrasting philosophical positions is developed, leading to a conceptual triangulation —ontological, epistemological, and methodological— that allows tensions to be understood not as obstacles but as heuristic resources. The author’s own contributions (Ruiz Castillo, 2024, 2025) show how computational complexity, dynamical systems, and the Collatz conjecture enter into dialogue with the Ontosemiotic Approach, illuminating the co-constitution of the mathematical and the physical.

The central result argues that Platonism and realism, far from being mutually exclusive, are complementary: mathematics does not merely function as an instrument for physics but also contributes to structuring the ontological intelligibility of the world. The debate remains open regarding the dichotomy between discovery and invention; however, an intermediate position is proposed, according to which the construction of formal languages encounters structural constraints that point to an independent reality, thereby configuring mathematical–scientific practice as an activity that is simultaneously rational, critical, and contemplative.