Duhem and Cassirer on the Symbolic Form of Physical Reality

Francesca Biagioli

New Europe College – Institute for Advanced Study, Bucharest, Romania

The French physicist, philosopher, and historian of science Pierre Duhem maintained that the mathematical development of scientific theories, which is required for inferring theoretical consequences to be put to the test, presupposes that empirical facts have been transformed and put into a symbolic form. Therefore, he defined physical laws as symbolic relations whose application to the concrete reality requires that a whole group of theories be known and accepted. I will consider the reasons given by Duhem for his conception of laws in a series of papers he published in the 1890s in the Revue des Questions Scientifiques, in his study on the evolution of mechanics (1903), and in his work on the aim and structure of physical theory (1906). Duhem’s reasons are found in his analysis of measurement and, in particular, in his insights into the use of numerical symbols for physical qualities. He defended the view that physics, owing to the symbolic nature of its concepts, can be a science of quality, which corresponded to the nineteenth-century project of a generalized thermodynamics called “energetics.” Furthermore, I will discuss some of the consequences of Duhem’s definition of physical law for his philosophy of science. Firstly, this definition is strictly related to Duhem holism and plays an important role in his argument against the possibility of a crucial experiment. Secondly, the symbolic character of physical laws suggests a conception of scientific theories as reflected images of real matters of fact: the aim of such a theory is not so much to provide us with causal explanations as to represent the set of experimental laws governing a field of appearances. This view enabled Duhem to sharply distinguish physics from metaphysics, and to adopt intellectual liberalism regarding the use of models. At the same time, he argued for the logical unity of physical theory as an ideal to be pursued. Regarding the second point, I will raise the following objection: Duhem seems to reintroduce metaphysical assumptions to justify his identification of the logical organization of knowledge with the allegedly natural character of the classification of physical laws. I will refer to Ernst Cassirer in order to defend a Duhemian conception of the relationship between facts and laws, regardless of Duhem’s commitment to a copy theory of knowledge. Cassirer’s understanding of the notion of “symbolic form” is strictly related to his reception of Duhem’s works. At the same time, Cassirer emphasized that the use of symbols is not limited to designating something, but also plays an active role in the determination of physical reality. His analysis of the concept of symbol enabled him to readapt the notions of explanation and understanding of natural phenomena to the context of nineteenth- and early twentieth-century natural sciences, after the crisis of mechanism: scientific explanations depend not so much on immutable rational principles as on the univocal coordination between the elements of a theory, including symbolized facts, laws, and relativized principles.