Ontology and Mathematics in Classical Field Theories and Quantum Mechanics

  • Adriano Angelucci Department of Philosophy – Verona University, Italy
  • Vincenzo Fano Department of Philosophy – Urbino University, Italy.
Keywords: quantum mechanics, general relativity, mathematical explanations


A draft of a possible comparison between the use made of mathematics in classical field theories and in quantum mechanics is presented. Hilbert’s space formalism, although not only elegant and powerful but intuitive as well, does not give us a spatio-temporal representation of physical events. The picture of the electromagnetic field as an entity which is real in itself – i.e., as a wave without support – fostered by the emergence of special relativity can be seen as the first step, favored by many physicists and philosophers, of a gradual “escape” from intuition into a purely mathematical representation of the external world. After the introduction, in recent theoretical physics, of fiber bundle formalism the classical notion of field acquires a new spatio-temporal intuitiveness. This intuitiveness is clearly foreshadowed in the Kantian and Meinongian analysis of the notion of magnitude. At the end of the paper we show that, contrary to what happens in quantum mechanics, mathematics plays a truly explicative role in general relativity, without any loss of spatio-temporal intuitiveness.

How to Cite
Angelucci, A., & Fano, V. (2018). Ontology and Mathematics in Classical Field Theories and Quantum Mechanics. HUMANA.MENTE Journal of Philosophical Studies, 4(13), 139-153. Retrieved from https://www.humanamente.eu/index.php/HM/article/view/233