Reasoning with Mechanism Diagrams (Presented at the Society for Philosophy of Science in Practice, Toronto, June 2013)
William Bechtel
Department of Philosophy, Center for Chronobiology, and Interdisciplinary Programs in Cognitive Science and Science Studies
University of California, San Diego
When scientists advance a new model of a mechanism, they often represent the proposed mechanism in a diagram. They take advantage of two dimensions of space and features such as color to represent the identified parts of a mechanism and how they are thought to relate, spatially or functionally, to each other. Often arrows are used to indicate causal interactions whereby the execution of an operation by one part affects another part, although other conversions are occasionally invoked. Diagrams of this sort sometimes appear in research articles, typically as the last figure, and more often in reviews and discussion papers and talks. They are also common in graphical abstracts, a relatively new representational format introduced by some journals. They clearly constitute a major communicative device. But, as I will argue in this paper, they are often tools for reasoning by scientists, not just readers but also the authors themselves. They are not just representations of the proffered explanation, but vehicles that serve to guide further investigation. I will focus on two such ways in which diagrams of mechanisms serve this role: by identifying features of the account not yet worked out and by serving as a foundation for computational modeling.
One clue to the role of mechanism diagrams in reasoning is that a surprising number contain questions marks. I will present examples that illustrated somewhat different uses. Sometimes they simply indicate that the evidence for a given part or operation represented in the diagram is more problematic than for other parts or operations. In other diagrams question marks signal gaps in the understanding of the operations, prompting inquiry into what are possible intermediates that could connect two known operations that are thought to connect to each other. In yet other diagrams alternative components and pathways are marked with question marks to indicate that they are regarded as the possibilities for which evidence is required in order to decide between them. A further indication that these mechanism diagrams are meant to support reasoning is that they sometimes include representations of the phenomenon to be explained.
A second way diagrams foster reasoning and thinking about mechanisms is by providing the basis for computational modeling in terms of systems of differential equations. Such modeling requires transforming a representation of the parts and operations in the mechanism into identifying variables and parameters that then are incorporated into equations. This is often worked out on diagrams of the parts and operations. Although some computational models attempt to incorporate all parts and operations, many are based on selective or partial models that are employed to try to relate different components of the mechanism to different features of the phenomenon and diagrams often serve to identify the components to be included or excluded in the computational model. Finally, I will examine diagrams develop to depict the behavior of the model, showing how it links up to the phenomenon to be explained.