Mathematizing Physics or Physicalizing Mixed Mathematics?, 1–2 October 2018

Afis MathemathicsOrganizers: Grigore Vida, Ovidiu Babeș

Invited speaker: John Schuster (University of Sydney)

Participants: Robert Arnăutu (independent, Cluj), Ovidiu Babeș (IRH-ICUB), Mihnea Dobre (IRH-ICUB), Dana Jalobeanu (IRH-ICUB), Grigore Vida (IRH-ICUB)

The workshop is organized under the framework of the national research grant (code: PN-III-P4-ID-PCE-2016-0228), “The emergence of mathematical physics in the context of experimental philosophy.”

The history of the emergence of modern science is still very much about how natural philosophy became mathematical. But the classical narrative about the “mathematization of nature” (at least in the Koyré version) has become somewhat obsolete, with its claims about a replacement of the Aristotelian view with the Platonic one, which recognized a mathematical structure of reality. Instead, historians prefer now to speak about “forms of mathematization” and to focus on practices, understood in such a broad way that they can cover both experimental procedures and aspects of theory formation. According to this approach, various forms of mathematical practices came to play an important role in natural philosophy prior to, and sometimes independent of philosophical reflections on the status of mathematics, or the relation between mathematics and natural philosophy.

Another tread that was followed was the reconstruction of the categories used by the actors to describe what they were doing – a safe historical method which has already furnished important results. “Physico-mathematics”, a key-term for Beeckman, Descartes, and Mersenne, has received lately the needed attention, but work still remains to be done. Besides “physico-mathematics”, however, there was another form of “blending” mathematics with physics, sometimes called by its practitioners “mathematical physics”, which has remained very much understudied until today. It emerged out of an experimental context and can be contrasted with the “physico-mathematical” approach: while the latter starts with usually strong metaphysical presuppositions, mixing axioms of mathematics with axioms or principles of natural philosophy, “mathematical physics” is a much more bottom-up procedure, in which mathematical objects are constructed trough measurement and quantification. It shows that Thomas Kuhn’s division between the mathematical and experimental traditions is too rigid, since the two could, in fact, nurture each other.

John Schuster has proposed an important view, according to which it is more appropriate to speak about a “physicalization” of the mixed mathematical sciences instead of a mathematization of physics. This workshop will provide an opportunity to critically discuss his thesis and put it against the case studies (Descartes, Mersenne, Rohault, Roberval) that the members of our team will present.

The programme is available here.