Conference | Paper

The Scientific Applicability of Mathematics from a Phenomenological Perspective

Jairo José Da Silva

Thursday 6th December 2018

14:20 - 15:20

There is a persistent, but wrong, interpretation of mathematized empirical science, popularized by Galileo, for which nature itself is, at its inner core, mathematical; for otherwise, some reason, how mathematics could be so efficient, when not outright indispensable in disclosing the inner secrets of empirical reality?

 

To dispel the mist clouding the understanding of the true role of mathematics in science one must inquire the inaugural enthronization of mathematical methodology in science. Not as historians, though, but as genetic phenomenologists, and here Husserl, particularly in §9 of his monumental The Crisis of European Sciences and Transcendental Phenomenology, is the perfect guide.
In this work, however, Husserl is not primarily concerned, as I am, with a logical, epistemological and methodological justification of the uses of mathematics in science. Taking Husserl’s analyses as my starting point, I will present my own account of the many roles mathematics play in empirical science, the representative, the instrumental, the predictive and the heuristic, to name them, and how they can be justified.
But I will also ask how my account faces Husserl’s criticism of the “formalist alienation” of science. In fact, as I intend to show, to give free rein to purely symbolic mathematical constructions in science is not only fruitful but methodologically justifiable. Apparently, this conflicts with Husserl’s characterization of the “crisis” of science as consisting essentially in the loss of meaning induced by empty symbolization.
As I read him, however, Husserl does not criticize mathematization per se, no matter how devoid of meaning, but a wrong interpretation of it. I will show how Husserl himself offers ways to cope with mathematization as a methodological strategy by opening to formal logic the realm of formal ontology, where logical relations among empty mathematical structures are investigated that can explain and justify mathematization as a methodological device once mathematical substitutes take the place of perceptual reality as the true objects of immediate scientific concern.