Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting Potential Controversies: Causation and the Hodgkin and Huxley Equations Abstract The import of Hodgkin and Huxley’s classic model of the action potential has been hotly debated in recent years, with particular controversy surrounding claims by prominent proponents of mechanistic explanation (Bogen, 2008; Craver, 2008). For these authors, the Hodgkin-Huxley (HH) model is an excellent predictive tool but ultimately lacks causal/explanatory import. What is more, they claim that this is how Hodgkin and Huxley themselves saw the model. In the following, I argue that these claims rest on a problematic reading of the work. Hodgkin and Huxley’s model is both causal and, in an important sense, explanatory. Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting 1. Introduction The Hodgkin and Huxley model of the action potential is in many ways the last thing one would expect to be the subject of controversy. It is a mainstay of neuroscience education and stands among the most celebrated achievements in its various histories and retrospectives. One need not look far to see comments like Armstrong and Hille’s that “the period from 1939 to 1952 was a heroic time in the study of membrane biophysics” (1998, 371)1 or Francisco Bezanilla’s that “the beauty and simplicity of voltage-dependent conductances in the Hodgkin and Huxley (HH) equations goes way beyond explaining the generation and propagation of the action potential” (2008, 457). In recent years, however, the model and its significance have received considerable scrutiny. According to an interpretation defended by well-known proponents of mechanistic explanation (Bogen, 2008; Craver, 2007; 2008), the model cannot, when taken in historical context, be understood as a genuine causal explanation. What Hodgkin and Huxley provided, they argue, was a phenomenal model able to “describe the electrical behavior of giant squid axon preparations in a mathematically convenient form” (Bogen, 2008, 1036) but silent about how it is produced. The HH model, they allege, occupies a space not unlike Ptolemaic astronomy (Craver, 2008, 1026). At the outset, it is important to know the basic model. At its core lies the so-called total current equation: (1) I = CMdV/dt + Gkn 4(V - Vk) + GNam 3h(V - VNa) + Gl(V - Vl) On the left side, we have “total” current, on the right lies the capacitive current and three ionic currents corresponding to potassium, sodium, and leak channels, respectively. The three channel terms have both “G’s,” representing their maximum conductances, and driving forces, in which each ionic equilibrium voltage is subtracted from the present voltage (the greater the difference, the stronger the force). The middle two terms likewise feature 1 The reason given, unsurprisingly, is that “During this period, Hodgkin and Huxley explained the propagated action potential” (371). Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting conductance terms, n, m, and h, which were chosen for a mixture of theoretical reasons, simplicity, and goodness of fit. The equation’s implications will be explored in greater detail below, but for now it suffices to say that it provides highly accurate predictions about the form of the action potential. The predictive success is not what is at issue, however. What matters is whether the model offers a causal explanation. For the above-cited authors, it does not. This is because, they argue, causal explanations must make contact with the entities and activities underlying the phenomenon. They need to tell us what sodium and potassium channels do to produce action potentials. The HH model, they allege, is agnostic about such things. Indeed, it would be decades before the relevant physical mechanisms would be even dimly understood. In support of this interpretation, the authors rely on two important claims. The first is that Hodgkin and Huxley do not offer a causal interpretation of the model in their paper. Indeed, they “insist” otherwise (Craver, 2008, 1022). Particularly supportive is a passage toward the end of the 1952 paper where the model is proposed. Their predictive success, Hodgkin and Huxley claim, “must not be taken as evidence that our equations are anything more than an empirical description of the time-course of the changes in permeability to sodium and potassium. An equally satisfactory description of the voltage clamp data could no doubt have been achieved with equations of very different form…the success of the equations is no evidence in favour of the mechanism of permeability change that we tentatively had in mind when formulating them” (1952c, 541). Roughly put, if Hodgkin and Huxley did not think of the model in causal terms, we should not either. The second major point concerns the role curve fitting played in the fixation of the conductance terms, n, m, and h. The functional relationship between these terms and the axon membrane potential was, they note, selected by Hodgkin and Huxley according to how well the function fit antecedently gathered data. The problem is that the results of such “curve fitting” measures carry no force. They may provide a good “data summary” (Craver, 1030), but strictly speaking, the equations will be “neither true nor false, neither explanatory nor descriptive” (Bogen, 2008, 1034). Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting Overall, they present a persuasive picture. After reading the mechanists’ papers, it is hard to think of the model as aiming for a causal explanation. Nevertheless, I argue, it does. In the following I hope to show why. First, I present textual evidence that Hodgkin, Huxley, and their contemporaries interpreted the model (including the controversial conductance terms) causally. Evidence to the contrary, such as the quote above, can be defused without too much trouble. Next, I argue that worries about “curve fitting” are exaggerated. The method by which they arrived at their conductance terms was theoretically motivated and came with important causal implications. Finally, I consider whether the model “explains” the action potential. I argue that Hodgkin and Huxley explained the action potential as they conceived of it but perhaps not on other potential ways of framing the phenomenon. 2. Interpreting HH Causally I begin with the most general arguments against a causal reading. Though both mechanists make the claim, I shall focus on Craver’s argument, as he spends the more time on the issue. The non-causal reading is supported by at least two historical claims, one negative and the other positive. On the negative side, he argues that there is insufficient evidence in the quantitative paper and subsequent work to indicate that the authors saw the model as anything more than a mere formalism. We can choose to interpret it causally, but Hodgkin and Huxley give us no reason to (truthfully, they actively oppose it). In the positive part, he makes the additional claim that the state of knowledge at the time renders a causal/explanatory interpretation anachronistic. Our reading, Craver alleges, is tinted by factors “difficult for those who know much more than Hodgkin and Huxley did about the mechanism of the action potential to forget” (1028). If we were to strip away this implicit background knowledge, it would become clear that the authors didn’t have enough knowledge to meaningfully interpret the model (and the conductance terms in particular) causally. Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting Both claims draw on a conceptual distinction between mathematical structure of the kind seen in the HH model (that conductance is a function of voltage, say) and causal relations (that voltage causes conductance change). The two are easily equivocated, but they involve very different commitments. In and of itself, Craver argues, the mathematical model doesn’t separate causal relations mere correlations. More powerfully still, its deductive consequences will be the same “whatever one’s interpretation of the causal structure” (1030). We can manipulate the model however we like. He is not arguing the “absurd” position that causal explanations cannot be given in mathematical language, but if the math is meant to embody causal claims, this must be made clear: “the equations must be supplemented by a causal interpretation: one might, for example, agree by convention that the effect variable is represented on the left, and the cause variables are represented on the right, or one might add ‘these are not mere mathematical relationships among variables but descriptions of causal relationships in which this variable is a cause and this other is an effect’” (2008, 1027). From here, the argument moves to the historical contention that Hodgkin and Huxley provide no such interpretation. This premise may be supported by the supposed absence of an interpretation in their writing, quotes where Hodgkin and Huxley seem to rebuff causal readings, and the aforementioned claim that details needed to provide a proper causal interpretation weren’t available at the time. To be clear, there is no denial that the authors had some relevant causal knowledge of the system, it’s that they did not have enough and that what they did have they generally did not “include explicitly in the model” (1027). First, let’s assess the claim that they don’t give the model a causal reading. It’s true that they don’t state “these are not mere mathematical relationships,” but this is far from damning. Such statements don’t occur in most scientific papers. More commonly, context specifies whether a mathematical dependency (or an arrow in a picture, or the phrase “depends on” in a sentence) is causal. Hodgkin and Huxley’s case is no different. When one examines the experiments discussed and the way they talk about the model, there is more than enough material to unambiguously indicate a causal reading. To start with, they use a lot of causal terms (a fact noted by Weber, 2008), even when discussing the conductance terms Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting (challenging Weber’s (2008, 1000) conductance-excluding view (see below)). One finds passages like: “an effect of this kind is to be expected on our formulation, since the entry of Na+ which causes the rising phase, and the loss of K+ which causes the falling phase, are consequent on increases in the conductance of the membrane to currents carried by these ions” (1952c, 529, emphasis mine). Likewise, in his Nobel speech, Huxley describes the calculations much as one would discuss concrete experimental preparations, writing that “we…calculated the responses of our mathematical representations of the nerve membrane to the equivalent of an electrical stimulus” and “calculating the effect of a stimulus [to the model]…one would see the forces of accommodation-inactivation of the sodium channel, and the delayed rise of potassium permeability-creeping up and reducing the excitatory effect of the rapid rise of sodium permeability” (1972, 61; again, it seems like conductance is included, as the “forces of…inactivation” likely refers to the h conductance term). None of these quotes suggests the authors saw the model or “formulation” as causally uncommitted. The major hurdle to the causal reading is, of course, the lengthy quote claiming that predictive success “must not be taken as evidence that our equations are anything more than an empirical description” (541). It’s easy to see this as offering a phenomenal interpretation of the model, even if the quotes above speak against this view. If one considers the full quote and its context, however, another interpretation emerges: they are merely expressing a transient underdetermination claim. They faced a modelling choice between first-order and higher-order kinetics for conductance (see below). The available evidence did not favor either, though they did imply different kinds of systems (Hodgkin and Huxley, 1952c, 512). Knowing this, the “must not be taken as evidence” probably refers to the fact that the likelihood of their model given the evidence was no greater than the likelihood of the alternative higher-order model. This gains support from the fact that the immediately following sentence refers to an “equally satisfactory alternative.” If so, the causal reading of the equations would be insulated. No one is defending the thesis that causal claims cannot be underdetermined at the time of their introduction. Moreover, if they are discussing comparative evidence, it would actually presuppose a causal view. The hallmark of a Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting phenomenal model is that it is not intended to make claims about the world. It’s not the kind of thing one gathers evidence for or against. What about the claim that Hodgkin and Huxley didn’t have enough information for a legitimate causal interpretation? One of the main contentions, recall, is that explanatory readings inadvertently import background knowledge unavailable before the 70s or 80s. Weber in particular is taken to task for the “historically inaccurate” suggestion that they “had any knowledge of voltage-gated channels” (Craver, 2008, 1031). Even if the previous paragraph is correct in its argument, this claim could still pose a problem. A model can be presumed to capture causal regularities without its creators actually knowing enough to make sense of its workings. That is, one could grant that they read the model causally and still think that they only had sufficient background to meaningfully interpret half of it. To assess the issue more clearly, we first need a sense of what a causal interpretation demands. Obviously, if the only thing sufficient to provide an interpretation is molecular detail, then Hodgkin and Huxley did not have enough information. It’s doubtful that the mechanists are making such a demand, though. Although molecular details may be emphasized (Craver, 2008, 1029), other writings suggest a less firmly reductionist stance. Craver (2007), for example, states that nothing on his view implies “a privileged level at which all causes act or at which all relevant causes are located” (2007, 104), noting that causal variables could be as broad as socio-economic status. In any event, the fact is that we still don’t know all the central molecular details. When it comes to sodium channels, for example, the term “conformational change” plays a role not unlike “inactivation” once did. Hodgkin and Huxley couldn’t have explained the action potential because we haven’t. Rather than molecular detail, then, I’ll follow Craver (2007) in adopting a broadly interventionist stance on causation (Pearl, 2000; Woodward, 2003). The model will have a causal interpretation if its features map onto (potentially “ideal”) interventions on the system. To avoid anachronisms, I’ll require that these interventions be recognized by the authors or their near-contemporaries. It isn’t enough that we can interpret parts of the model as transmembrane integral proteins if nobody near the time would have. Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting The issue, then, is whether the equations embody interventions recognized by Hodgkin, Huxley, and their peers. I claim they do. The model contains a particular set of mathematical dependencies (Craver, 2008). Total current (I) is a function of four sub-currents. These are then functions of still further variables and so on until we arrive at a set of exogenous variables that are left as-is. The relationships are a bit easier to see if, following conventions from the causal modelling literature, they are represented as a directed graph (fig.1). Figure 1. A graphical representation of functional relationships in the HH equations. Arrows reflect causal and constitutive relations between variables. V represents voltage, I’s represent the total and component currents, and E’s represent equilibrium voltages. Primed variables reflect the rate of change of the conductance terms m, n, and h. Terms not shown, such as the alphas and betas for sodium and potassium, are treated as parameters. Following Iwasaki and Simon (1994) and Voortman, Dash, and Druzdzel (2012), integration over time is represented with dashed lines. Consistent with their experimental practice, voltage is treated as an exogenous, experimenter-controlled variable. In simulating the action potential and related phenomena, V is no longer regarded as exogenous and is instead determined by integrating ionic currents (Hodgkin and Huxley’s discussion of simulation procedures covers 522-40 in the paper). Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting Are the mathematical dependencies in the system something Hodgkin and Huxley could’ve given sufficient interpretation? I claim that they are. There is obviously quite a lot here, and there is neither space nor reason to discuss every dependency. We can, however, cover some of the more salient features. Each of the following relates to some experiment, physical basis, or otherwise cause- or intervention-implying language (parentheses contain 1952c page numbers unless otherwise stated): a) Independence of potassium, sodium, and leak equilibrium potentials (the “Es”) (505) b) Independence of potassium, leak, and sodium permeability, contingent on voltage (V) (503) c) Dependence of both sodium and potassium channel conductance on the “effect of the electric field on the distribution or orientation of molecules” that allow/prevent ionic passage (501, 507, 512) d) A distinct inactivating agent for the sodium (h) but not potassium channels (503, 512) e) Myriad facts about how modulating temperature and ionic concentrations will impact neuron (525-6; Huxley, 1972, 64-7) Many of these had been tested by Hodgkin and Huxley themselves. Point (a), for example, implies that one may change the various ions’ equilibrium potentials individually, selectively altering the ionic currents associated with each (Hodgkin and Huxley, 1952a), while (b) implies the dissociability of the channels (suggested in Hodgkin and Huxley, 1952b) and shown by later blockage experiments. Not every part had a prior experiment, of course. This is certainly true of the much-maligned conductance terms. Yet it’s worth noting that even in this uncertain element of the model we find discussions in concrete terms. Potential interventions are obvious. The presence of an inactivating agent for sodium channels implies the dissociability of sodium inactivation from sodium conductance, for example. This ideal intervention became a real one when Armstrong, Bezanilla, and Rojas (1973) (who explicitly Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting discuss the HH model) found they could selectively eliminate sodium inactivation using intercellular enzymes. Finally, though (a)-(e) are all dependencies that panned out, there is one important instance where the model got it wrong. Sodium is inactivated by a distinct “particle,” but it is not voltage-dependent as implied. This might seem detrimental to my case, but the fact is that this was/is regarded as a shortcoming in the model (Aldrich, 2001). Thus, on this issue, Armstrong et al. indicate that their results implied an inactivation mechanism “not entirely consistent with the Hodgkin and Huxley equations” (1973, 388). If the equations can get interventions wrong, however, it clearly cannot be the case that they make no commitments (Craver, 2008, 1026) or are “neither true nor false” (Bogen, 2008, 1034). 3. What about curve fitting? Despite the arguments listed above, there’s likely some residual uneasiness about the methods used to determine the conductance terms. The precise form each took and the values of the alpha and beta functions associated with them were determined largely as a matter of convenience and agreement with experimentally derived curves. Bogen, for instance, labels the n, m, and h terms “uninterpreted weighting constants” (1042). Even Weber (2008), who I have otherwise found much reason to agree with, grants that “the conductance model was purely a result of curve fitting to which Hodgkin and Huxley tried to give a physical rationale later” (1001), arguing that the explanatory work is done by the rest of the model. Such negative assessments are unwarranted, I argue, not only because Hodgkin and Huxley thought of the conductances in causal terms (see above) but because their methods have been unfairly criticized. In particular, previous commenters have not distinguished between two relevantly different modeling practices. The first, which I’ll simply call curve fitting, involves fitting a stock function to some data set. The prototypical case is something like linear regression, where the parameters have no theoretical basis and involve no causal commitments. A relevantly different process, sometimes called model fitting, is carried out to Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting estimate the value of parameters2 in an antecedently hypothesized system. The fundamental causal model (what connects to what) stays the same, one simply pins down the precise amounts, rates, etc. involved. Hodgkin and Huxley’s practice is better seen as the latter. The path Hodgkin and Huxley took ran roughly as follows. First, each conductance term was taken, for theoretical reasons, to be a dimensionless variable sensitive to voltage and time (rather than, say, current; 501, 507). From here, they had to choose whether the variables would obey higher-order differential equations or first-order equations. The evidence didn’t favor either, but first-order kinetics were simpler. Each conductance term was modeled in terms of shifting “particles” obeying the equation: (2) dx dt = αx(1 − x) − βxx where x stands for n, m, or h depending on the context and alpha and beta stand for the rates (i.e., frequencies) at which particles transition between allowing and preventing ions to pass through the membrane. The rates at which these particles transitioned were taken to be voltage-dependent, and functions mapping voltage to each were selected based on fit. Despite earlier (Weber, 2008) claims that Hodgkin and Huxley developed their physical model of the channel as an afterthought, there is evidence to suggest that the decision to model the system as they did was theoretically motivated. Circumstantially, it’s a bit easier to see a pre-existing “gating” picture leading to equation (2) than it is to see (2) emerging first and leading to the theory later on. Moreover, if Weber is correct in thinking that Hodgkin and Huxley’s comment that “the success of the equations is no evidence in favour of the mechanism of permeability change that we tentatively had in mind when formulating them” (541, italics mine) refers to the conductance terms, then it would imply that the interpretation came first. Finally, we have Huxley’s (2002) retrospective assertion that their final voltage- 2 See also Pearl (2000) on the distinction between “causal” and “statistical” parameters, the latter being embedded in a causal model and the former making “no assumption whatsoever regarding the existence or nonexistence of unobserved variables” (38). Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting clamp results were interpreted “on the assumption that the ions crossed through channels that were opened or closed by alterations in the membrane potential” (557). This strongly suggests that the channel idea occurred to them on the heels of the experiments and was developed simultaneously with or prior to the formal 1952 model. If we grant this theoretical background, though, it’s hard to see the process as particularly suspect. The causal picture is in place. The only thing left over are a few parameters, each playing a clear role in the system. The power to which the terms are raised, for instance, are taken by Hodgkin and Huxley to reflect the number of “particles.” Values were estimated and, while not perfect, weren’t bad (sodium channels, m, have 4 rather than 3 subunits). One could double down on this shortcoming, but it would be splitting hairs, especially given the estimates were as close as they were. If I claim that an object thrown at x miles per hour (or more, Hodgkin and Huxley, 1952c, 509) broke a window, my account isn’t devastated if it happens that the object was actually going y > x miles per hour. The alpha and beta terms seem more complex on the surface, but the same basic point holds. They are rate constants given theoretically-motivated dimensions and functional roles by Hodgkin and Huxley. At base, they amount to a claim about the probability that (or “frequency” with which) a “particle” switches between states. One might claim that estimating the probabilities isn’t enough, that the reason why the probabilities take the values they do must be given, but this would clearly prove too much. It would amount to disputing probabilistic causality, as the rate constants simply represent the claim that modulating voltage will increase or decrease the frequency of a given kind of particle state-transition. What’s more, we still don’t build these terms “from the bottom up,” as the objection would demand; rather, there is a mix of macroscopic modelling techniques, with Hodgkin and Huxley’s remaining popular (Carbonell-Pascual et al., 2016). If the inability to unpack these fundamental probabilities undermines Hodgkin and Huxley, it undermines us too. Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting 4. Concluding Remarks on Explanation The previous two sections argue that a causal reading of the HH model, conductance terms included, is most consistent with its authors’ scientific practice and published statements. This still leaves open the issue of explanation, though. It may be argued that, while causal, the model is still only a mechanism sketch, an explanation that leaves critical features unexplored (Craver, 2008, 1027). In response to this, I may point to the interventions enumerated above or to still others left unmentioned. I could cite earlier authors who have argued forcefully that the features left out of the model do not matter for the relevant explanatory purposes (Levy, 2014; Weber, 2008). Ultimately, though, there is a sense in which the sketch claim is correct. In his Nobel speech, Huxley plainly states that he and Hodgkin took the model as “a first approximation…for the actual mechanism of the permeability changes on the molecular scale” (1972, 69). This is not something that I think is sufficiently captured in either Weber or Levy’s discussions. Weber pins all non-explanatory talk on the conductance terms, but the quote above is directed at the “these equations” generally, rather than the conductance terms specifically. Levy grants that the model is not a sufficient molecular-level explanation but contends that it is “implausible” to regard the HH model as aiming toward such explanatory goals (482) and that, even if they started with this aim, their interests had shifted by the writing of the quantitative paper (487, fn. 9). Here again, though, Huxley does seem to think of the model as addressing, in a tentative way, some molecular concerns. I take it, then, that we ought not to deny that the authors sought a molecular explanation and successfully produced a “sketch” of one. Nevertheless, it cannot fairly be claimed that “if Hodgkin and Huxley are right, one needs to know [complex mechanistic details] to explain the action potential” (Craver, 2008, 1025) or that explanatory claims stem from illusions about the state of molecular neuroscience at the time (1030). When Hodgkin and Huxley speak of having a “sufficient explanation” of the relevant phenomena or when Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting contemporaries like Bezanilla claim that the model “goes way beyond explaining” the action potential, we cannot simply sweep it under the rug. What I would like to suggest in the brief space remaining is that Hodgkin and Huxley did explain the action potential as they understood it (1952c, 500, 541), but not as it might be interpreted by all parties involved. In other words, we are dealing with different explananda. The action potential could be understood in a “thin” way that refers only to the voltage spike familiar to physiologists going back to the 19th century. So understood, the action potential would be tied to a specific set of results, including things like anode breaks, voltage “overshoot,” and refractory periods (to list the phenomena cited by Hodgkin and Huxley, 1952c; Huxley, 1972; Huxley, 2002). The action potential of an author like Craver (2008), by contrast, may be better described as a complex thing-in-the-world (Cf. Craver, 2014)—the kind of object molecular processes could be said to “make up” (1025). It involves a “thick” or open-ended notion more akin to Huxley’s “actual mechanism…on the molecular scale” (1972, 69). One is an object of classical electrophysiology, the other of biochemistry. In wondering whether Hodgkin and Huxley “explained the action potential,” then, one could be asking at least two different questions. If the goal is to account for voltage and current dynamics and to chart how they behave under interventions like the shifting of ionic concentrations or the elimination of specific channels, then the model appears sufficient. A few elements proved inaccurate (e.g. the voltage-dependence of sodium inactivation), but the model captures sufficiently many causal relations and experimental phenomena to be called an “explanation,” at least as the term is usually understood. However, if the aim is to characterize the biochemical mechanisms at play—to know about the structure, composition, or operation of ion channels (Cf. Bogen, 2008, 1043)—then Hodgkin and Huxley’s charged “particles” provide only the roughest of approximations. The causal picture from the previous sections may provide leads for investigating these matters, such as the existence of distinct agents of sodium inactivation, but they are highly general. The term “sketch” does not seem inappropriate. Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting Thus, depending on one’s interest, it may still be possible to side with Craver and Bogen in believing that the model does not “explain the action potential.” One’s reasons for doing so will need to differ from theirs, however. It cannot rightly be claimed that Hodgkin and Huxley make no causal commitments. As we have seen, the model is rich with implications, and many of them were followed up on by Hodgkin, Huxley, and their peers. Nor is it reasonable to criticize the model because of the role “curve fitting” played in its development. Doing so would catch perfectly legitimate causal modelling procedures in the cross-fire. Finally, it would not be fair to claim that the popular history of the model is anachronistic or that Hodgkin and Huxley themselves claimed not to have explained the “action potential.” This would mean interpreting the term quite differently than the authors or subsequent researchers in the same tradition. Bezanilla, Armstrong, and Hille, who did so much to discover the form and composition of ion channels, are not simply confused about how much Hodgkin and Huxley knew about these mechanisms. In the end, one parts little from the received view. The model provides a causal account of neuronal voltage dynamics and a very limited guide to molecular mechanisms. In other words, Hodgkin and Huxley explained the action potential to the extent that is generally recognized, but no more. Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting References Aldrich, Richard. 2001. “Fifty Years of Inactivation.” Nature 411 (6838): 643–4. Armstrong, Clay, Francisco Bezanilla, and Eduardo Rojas. 1973. “Destruction of Sodium Conductance Inactivation in Squid Axons Perfused with Pronase.” The Journal of General Physiology 62 (4): 375–91. Armstrong, Clay, and Bertil Hille. 1998. “Voltage-Gated Ion Channels and Electrical Excitability.” Neuron 20 (3): 371–80. Bezanilla, Francisco. 2008. “Ion Channels: From Conductance to Structure.” Neuron 60 (3): 456–68. Bogen, Jim. 2008. “The Hodgkin-Huxley Equations and the Concrete Model: Comments on Craver, Schaffner, and Weber.” Philosophy of Science 75 (5): 1034–46. Carbonell-Pascual, Beatriz, Eduardo Godoy, Ana Ferrer, Lucia Romero, and Jose M. Ferrero. 2016. “Comparison between Hodgkin–Huxley and Markov Formulations of Cardiac Ion Channels.” Journal of Theoretical Biology 399: 92–102. Craver, Carl. 2007. Explaining the Brain. Oxford: Oxford University Press. ———. 2008. “Physical Law and Mechanistic Explanation in the Hodgkin and Huxley Model of the Action Potential.” Philosophy of Science 75 (5): 1022–33. ———. 2014. “The Ontic Account of Scientific Explanation.” In Explanation in the Special Sciences, edited by Marie I. Kaiser, Oliver R. Scholz, Daniel Plenge, and Andreas Hüttemann, 27–52. Synthese Library, vol. 367. Dordrecht: Springer Netherlands. Hodgkin, Allan L., and Andrew F. Huxley. 1952a. “Currents Carried by Sodium and Potassium Ions through the Membrane of the Giant Axon of Loligo.” The Journal of Physiology 116 (4): 449–72. Hodgkin, Allan L., and Andrew F. Huxley. 1952b. “The Components of Membrane Conductance in the Giant Axon of Loligo.” The Journal of Physiology116 (4): 473-99. Copyright Philosophy of Science 2017 Preprint (not copyedited or formatted) Please use DOI when citing or quoting Hodgkin, Allan L., and Andrew F. Huxley. 1952c. “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve.” The Journal of Physiology 117 (4): 500–44. Huxley, Andrew F. 1972. “Excitation and Conduction in Nerve: Quantitative Analysis.” In Nobel Lectures, Physiology or Medicine 1963-1970. 52-69. New York: Elsevier. Huxley, Andrew F. 2002. “From Overshoot to Voltage Clamp.” Trends in Neurosciences 25 (11): 553–8. Iwasaki, Yumi, and Herbert A. Simon. 1994. “Causality and Model Abstraction.” Artificial Intelligence 67 (1): 143–94. Levy, Arnon. 2014. “What Was Hodgkin and Huxley’s Achievement?” The British Journal for the Philosophy of Science 65: 469–92. Voortman, Mark, Denver Dash, and Marek J. Druzdzel. 2012. “Learning Why Things Change: The Difference-Based Causality Learner.” arXiv Preprint arXiv:1203.3525. Weber, Marcel. 2008. “Causes without Mechanisms: Experimental Regularities, Physical Laws, and Neuroscientific Explanation.” Philosophy of Science 75 (5): 995–1007. Woodward, James. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press.