The (reasonable) effectiveness of mathematics in empirical science

  • Jairo José da Silva Universidade Estadual Paulista Júlio de Mesquita Filho – Unesp, Brazil
DOI: https://doi.org/10.5281/zenodo.2550834
Keywords: Philosophy of Mathematics, Domains, Formal Structures, Ontology

Abstract

I discuss here the pragmatic problem in the philosophy of mathematics, that is, the applicability of mathematics, particularly in empirical science, in its many variants. My point of depart is that all sciences are formal, descriptions of formal-structural properties instantiated in their domain of interest regardless of their material specificity. It is, then, possible and methodologically justified as far as science is concerned to substitute scientific domains proper by whatever domains —mathematical domains in particular— whose formal structures bear relevant formal similarities with them. I also discuss the consequences to the ontology of mathematics and empirical science of this structuralist approach.

Author Biography

Jairo José da Silva, Universidade Estadual Paulista Júlio de Mesquita Filho – Unesp, Brazil

Jairo José da Silva is a Professor of Mathematics (retired) at the State University of São Paulo and a Researcher at the National Council of Scientific and Technological Development (CNPq) of the Brazilian Ministry of Science and Technology. PhD in Mathematics at the University of California – Berkeley, USA, and a PhD in Philosophy at the Universidade Estadual de Campinas, Brazil. His main interests are the philosophy of formal and empirical sciences, phenomenology and the foundations of mathematics. He is co–author, together with Claire Ortiz Hill, of the book The Road Not Taken – On Husserl’s Philosophy of Logic and Mathematics (London: College Publications, 2013); and author of Mathematics and Its Applications. A Transcendental–Idealist Perspective (Cham, Switzerland: Springer, 2017).

References

Heisenberg, Werner. Discussione sulla fisica moderna. Turin: Enaudi, 1959.

Husserl. Edmund. Die Krisis der europaischen Wissenschaften und die transzendentale Phaenomenologie. Hua VI, Martinus Nijhoof, The Hague, 1954.

Steiner. Mark (1989). “The Application of Mathematics to Natural Science’. Journal of Philosophy 86, 1989.

Steiner. Mark (1995). “The Applicabilities of Mathematics”. Philosophia Mathematica (3) 3.

Steiner. Mark (1998). The Applicability of Mathematics as a Philosophical Problem. Cambridge, MA: Cambridge University Press.

Wigner, Eugene (1960). “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, Communications on Pure and Applied Mathematics. 13: pp. 1–14. https://doi.org/10.1002/cpa.3160130102

Weyl, Hermann (1952). Space – Time – Matter, New York: Dover.
Published
2018-12-31
How to Cite
[1]
da Silva, J.J. 2018. The (reasonable) effectiveness of mathematics in empirical science. Disputatio. 7, 8 (Dec. 2018), a003. DOI:https://doi.org/10.5281/zenodo.2550834.
Issue
Vol. 7 No. 8 (2018)
Section
Articles and Essays

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