Understanding Theories in Practice: Representational and Computational Aspects

In this paper, I construe scientific understanding not only as understanding the phenomena by means of some theoretical material (theory, law or model), but more fundamentally as understanding the theoretical material itself that is supposed to explain the phenomena. De Regt and Dieks (2005) emphasise the contextual aspects of the intelligibility of theories, showing that it depends on their ―virtues‖, on the historical standards of intelligibility, and on the particular ―skills‖of their users. My paper aims at continuing this proposal, first by giving a more precise definition of one's understanding of a theory and then by emphasising the importance, for this issue, of the particular formats in which a theory is expressed and hence grasped by its users. To defend this, I take the example of the versions of classical mechanics and the various formats of representation of its main principles and models. What does ―understanding a theory‖ mean? At first sight, we could say that it amounts to having a clear view of the logical relations between its core principles and theorems. This kind of understanding, though global, is quite abstract: one can understand the logical structure of a theory without being able to connect it to the phenomena. Moreover, this definition depends on how one construes the structure of theories: it will vary according to whether one defines theories as logical sets of statements with interpretative rules (following the ―syntactic conception‖ of theories) or as families of models (―semantic conception‖). I thus suggest that there is another sense of ―understanding a theory‖ that itself has two aspects. To understand a theory, one has to understand both what the theory says or means and how it works; in other words, one has to understand it as representing the phenomena (representational aspect) and to be able to manipulate it and make it fit the phenomena (computational aspect). I claim that these are essentially contextual and practical matters, and that the particular format in which the theoretical content is displayed is crucial to them. Following Humphreys' proposal (2004), I claim that one never accesses to a theory as a whole. Be it a set of statements or a class of models, in practice, it is always displayed in some particular equations, statements, images, graphs, diagrams. Humphreys' proposal of the notion of ―template‖ to complement the classical ―units of analysis‖ of science, like theories and models, may be a good candidate to study the relationship between the representational and computational aspects of understanding: a template is a ―concrete piece of syntax‖ (most of the time an equation, but I suggest that Humphreys' claim could be extended to other formats) that has both a representational and computational function. With the example of classical mechanics, I show how these two functions are interrelated and, as Humphreys suggests, are sometimes in tension with each other. Adressing these issues by focusing on the particular formats that are dealt with in practice may enlight this problematic relationship