Arnon Levy

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?

Carl Craver’s recent book offers an account of the explanatory and theoretical structure of neuroscience. It depicts it as centered around the idea of achieving mechanistic understanding, i.e., obtaining knowledge of how a set of underlying components interacts to produce a given function of the brain. Its core account of mechanistic explanation and relevance is causal-manipulationist in spirit, and offers substantial insight into casual explanation in brain science and the associated notion of levels of explanation. However, the focus on mechanistic explanation leaves some open questions regarding the role of computation and cognition.

This paper derives from a broader project dealing with the notion of causal order. I use this term to signify two kinds of parts-whole dependence: Orderly systems have rich, decomposable, internal structure; specifically, parts play differential roles, and interactions are primarily local. Disorderly systems, in contrast, have a homogeneous internal structure, such that differences among parts and organizational features are less important. Orderliness, I suggest, marks one key difference between individuals and collectives. My focus here will be the connection between order and robustness, i.e. functional resilience in the face of internal or environmental perturbations. I distinguish three varieties of robustness. Ordered robustness is grounded in the system’s specific organizational pattern. In contrast, disorderly robustness stems from the aggregate outcome of many similar parts. In between, we find semi-ordered robustness, wherein a messy ensemble of elements is subjected to a selection or stabilization mechanism. I give brief characterizations of each category, discuss examples and remark on the connection between the order/disorder axis and the notions of individual versus collective.