The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century ed. by Geoffrey Gorham et al. (review)

The broadly-stated aim of this rich collection is to reevaluate and reconceptualize the mathematization thesis, which the editors take to signify “above all the transformation of scientific concepts and methods, especially those concerning the nature of matter, space, and time, through the introduction of mathematical (or geometrical) techniques and ideas” (1). As a historiographical thesis, it is the thesis that “the scientific revolution, and by implication modern science as a whole, is guided by the project of mathematization” (8).

In the introduction to the volume, the editors acknowledge the virtues of the historiographical thesis, which explain its persistence. For example, it highlights a constitutive feature of modern scientific practice, that is, its aim to provide “mathematically precise and rigorous explanations of natural phenomena”; it offers a “framework for following the transformation of a discipline into a properly scientific one”; it “unifies disparate figures and groups into a single movement”; and it “makes sense of how the unification of phenomena [e.g. celestial and terrestrial movements] was achieved” (14). It should not come as a surprise that a set of virtues such as these comes at a cost.

As one might expect from such a broad unifying thesis, the story of the development of modern science is considerably more complicated than the thesis suggests. Careful and detailed historical work over the last thirty years, in particular from a contextualist approach to history, have put pressure on the mathematization thesis to the point where “there seems to be no place” for it in current history of science (15). The specific goals of this volume are to rethink (i) what mathematization does or should consist in; (ii) how it squares with recent scholarship; and (iii) its overall value as a historical framework for the emergence of science in the seventeenth century (15). The volume provides evidence that there is still a place for this thesis, even if not as the narrative of the scientific revolution.

Roger Ariew’s contribution, “The Mathematization of Nature in Descartes and the First Cartesians,” represents the most skeptical position with respect to the mathematization thesis and argues that a contextualist approach to history reveals that it has no value as a historical framework for the study of seventeenth-century science. After arguing against the “prominent” views of Burtt, Dijksterhuis, and Koyré, Ariew offers an excellent exemplar of the contextualist approach by surveying how Descartes was received by followers such as Du Roure, Rohault, Le Grand, and Régis. The noble aim of the survey is to capture “what these thinkers found so appealing about Descartes (and what the anti-Cartesians found so dangerous)” (128). Ariew uncovers a range of different views about the relations between mathematics and natural philosophy, their demarcation, their respective methods, their relative certainty and persuasiveness, but notably not the view expressed by the mathematization thesis. This is a helpful corrective to the extreme versions of the thesis canvassed in this paper.

Several other contributions work to recover a defensible version of the mathematization thesis. For example, in her paper on Francis Bacon, Dana Jalobeanu suggests an expanded notion of mathematization (in accordance with aim (i) above) in order to include a figure who was previously viewed as an exception to the thesis. Bacon’s role in the traditional narrative is exemplified by the Kuhnian distinction between “proper” mathematical sciences and Baconian sciences. Jalobeanu reconstructs a Baconian version of mathematical-physics by considering more carefully what Bacon and his contemporaries meant by ‘physics’ and ‘mathematics,’ together with his notion of “reductive experiment.” In her paper “The Geometrical Method as a New Standard of Truth, Based on the Mathematization of Nature,” Ursula Goldenbaum takes the mathematization framework as useful not just for conceptualizing seventeenth-century science, but for philosophy itself. She argues that the opposition...