Arnon Levy

Modeling is an important scientific practice, yet it raises significant philosophical puzzles. Models are typically idealized, and they are often explored via imaginative engagement and at a certain “distance” from empirical reality. These features raise questions such as what models are and how they relate to the world. Recent years have seen a growing discussion of these issues, including a number of views that treat modeling in terms of indirect representation and analysis. Indirect views treat the model as a bona fide object, specified by the modeler and used to represent and reason about some portion of the concrete empirical world. On some indirect views, model systems are abstract entities, such as mathematical structures, while on other views they are concrete hypothetical things. Here I assess these views and offer a novel account of models. I argue that regarding models as abstracta results in some significant tensions with the practice of modeling, especially in areas where non-mathematical models are common. Furthermore, viewing models as concrete hypotheticals raises difficult questions about model-world relations. The view I argue for treats models as direct, albeit simplified, representations of targets in the world. I close by suggesting a treatment of model-world relations that draws on a recent work by Stephen Yablo concerning the notion of partial truth

Proponents of mechanistic explanation all acknowledge the importance of organization. But they have also tended to emphasize specificity with respect to parts and operations in mechanisms. We argue that in understanding one important mode of organization—patterns of causal connectivity—a successful explanatory strategy abstracts from the specifics of the mechanism and invokes tools such as those of graph theory to explain how mechanisms with a particular mode of connectivity will behave. We discuss the connection between organization, abstraction, and mechanistic explanation and illustrate our claims by looking at an example from recent research on so-called network motifs.

The Hodgkin–Huxley (HH) model of the action potential is a theoretical pillar of modern neurobiology. In a number of recent publications, Carl Craver ([2006], [2007], [2008]) has argued that the model is explanatorily deficient because it does not reveal enough about underlying molecular mechanisms. I offer an alternative picture of the HH model, according to which it deliberately abstracts from molecular specifics. By doing so, the model explains whole-cell behaviour as the product of a mass of underlying low-level events. The issue goes beyond cellular neurobiology, for the strategy of abstraction exhibited in the HH case is found in a range of biological contexts. I discuss why it has been largely neglected by advocates of the mechanist approach to explanation. 1 Introduction2 A Primer on the HH Model2.1 The basic qualitative picture2.2 The quantitative model3 Interlude: What Did Hodgkin and Huxley Think?4 Craver’s View4.1 Mechanistic explanation4.2 Sketches4.3 Craver's view: The HH model as a mechanism sketch5 An Alternative View of the HH Model5.1 Another look at the equations5.2 The discrete-gating picture5.3 The road paved by Hodgkin and Huxley5.4 Summary and comparison to Craver6 Conclusion: The HH Model and Mechanistic Explanation6.1 Sketches and abstractions6.2 Why has aggregative abstraction been overlooked?