The (reasonable) effectiveness of mathematics in empirical science

Jairo José da Silva
Universidade Estadual Paulista Júlio de Mesquita Filho – Unesp, Brazil | dasilvajairo1@gmail.com

Received: 27-April-2018 | Accepted: 30-November-2018 | Published: 31-December-2018
Disputatio [Dec. 2018], Vol. 7, No. 8, a003 | DOI: 10.5281/zenodo.2550834
Article | [EN] | Full Text | Statistics | Copyright Notice [es] | Vol. 7 No. 8

How to cite this article:
da Silva, Jairo José (2018). «The (reasonable) effectiveness of mathematics in empirical science». Disputatio. Philosophical Research Bulletin 7, no. 8: a003.


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.
Keywords |
 Philosophy of Mathematics · Domains · Formal Structures · Ontology.

La efectividad (razonable) de la matemática en las ciencias empíricas

Resumen | Discuto en este artículo el problema pragmático en la filosofía de la matemática, es decir, la aplicabilidad de la matemática, en particular en las ciencias empíricas, en sus múltiples variantes. Mi punto de partida es que todas las ciencias son descripciones formales [o bien: “formales, es decir, descripciones”] de propiedades formales/estructurales [o: “estructurares formales”], ejemplificadas en su dominio de interés, sin que importara su especificidad material. Entonces es posible y metodológicamente justificado, desde el punto de vista de la ciencia, sustituir los dominios científicos, propiamente, por cualquier dominio que sea —en particular dominios matemáticos— cuya estructura formal muestre similitudes formales con ellos. También exploro las consecuencias de este planteamiento estructuralista para la ontología de la matemática y de las ciencias empíricas.
Palabras Clave | Filosofía de la matemática · Dominios · Estructuras formales · Ontología.


References

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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.


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