There are two traditions of thinking about idealization offering almost opposite views on their functioning and epistemic status. While one tradition views idealizations as epistemic deficiencies, the other one highlights the epistemic benefits of idealization. Both of these, however, identify idealization with misrepresentation. In this article, we instead approach idealization from the artifactual perspective, comparing it to the distortion-to-reality accounts of idealization, and exemplifying it through the case of the Hodgkin and Huxley model of nerve impulse. From (...) the artifactual perspective, the epistemic benefits and deficiencies introduced by idealization frequently come in a package due to the way idealization draws together different resources in model construction. Accordingly, idealization tends to be holistic in that it is not often easily attributable to just some specific parts of the model. Instead, the idealizing process tightly embeds theoretical concepts and formal tools into the construction of a model. (shrink)

Hodgkin and Huxley’s model of the action potential is an apparent dream case of covering‐law explanation in biology. The model includes laws of physics and chemistry that, coupled with details about antecedent and background conditions, can be used to derive features of the action potential. Hodgkin and Huxley insist that their model is not an explanation. This suggests either that subsuming a phenomenon under physical laws is insufficient to explain it or that (...) class='Hi'>Hodgkin and Huxley were wrong. I defend Hodgkin and Huxley against Weber’s heteronomy thesis and argue that explanations are descriptions of mechanisms. †To contact the author, please write to: Department of Philosophy, Philosophy‐Neuroscience‐Psychology Program, Washington University in St. Louis, One Brookings Drive, Wilson Hall, St. Louis, MO 63130; e‐mail: [email protected]. (shrink)

Natalia Carrillo and Tarja Knuuttila claim that there are two traditions of thinking about idealization offering almost opposite views on their functioning and epistemic status. While one tradition views idealizations as epistemic deficiencies, the other one highlights the epistemic benefits of idealization. Both of them treat idealizations as deliberate misrepresentations, however. They then argue for an artifactual account of idealization, comparing it to the traditional accounts of idealization, and exemplifying it through the Hodgkin and Huxley model of (...) the nerve impulse. From the artifactual perspective, the epistemic benefits and deficiencies introduced by idealization frequently come in a package due to the way idealization draws together different resources in model construction. Accordingly, idealization tends to be holistic in that it is not often easily attributable to some specific parts of the model. They conclude that the artifactual approach offers a unifying view into idealization in that it is able to recover several basic philosophical insights motivating both the deficiency and epistemic benefit accounts, while being simultaneously detached from the idea of distortion by misrepresentation. (shrink)

Using Sneed''s metatheory an attempt is made to reconstruct Hodgkin and Huxley''s theory of excitation of cell membranes. The structure of this theory is uncovered by defining set-theoretical predicates for the partial potential models, potential models, and models of the theory. The function of permeability is said to be the only theoretical function with respect to this theory. The main underlying assumptions of the theory are briefly outlined.

Using Sneed's metatheory an attempt is made to reconstruct Hodgkin and Huxley's theory of excitation of cell membranes. The structure of this theory is uncovered by defining set-theoretical predicates for the partial potential models, potential models, and models of the theory. The function of permeability is said to be the only theoretical function with respect to this theory. The main underlying assumptions of the theory are briefly outlined.

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? (shrink)

Hodgkin and Huxley’s 1952 model of the action potential is an apparent dream case of covering-law explanation. The model appeals to general laws of physics and chemistry (specifically, Ohm’s law and the Nernst equation), and the laws, coupled with details about antecedent and background conditions, entail many of the significant properties of the action potential. However, Hodgkin and Huxley insist that their model falls short of an explanation. This historical fact suggests either that (...) there is more to explaining the action potential than subsuming it under a general laws or that Hodgkin and Huxley were wrong about the explanatory import of their model. In this paper, I defend Hodgkin and Huxley’s view that their model alone does not explain the action potential (contra Weber 2005). I argue further that neuroscientists lacked crucial explanatory details about the action potential until they could describe the molecular and ionic mechanisms by virtue of which their model holds (see Bogen 2005). Mathematical generalizations are important epistemic tools for assessing mechanistic explanations, but they are neither necessary nor sufficient for adequate explanations, even at the lowest levels of organization where biological phenomena are integrated with physics and chemistry. (shrink)

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. For these authors, the Hodgkin-Huxley 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. 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. (shrink)

Alan Hodgkin’s and Andrew Huxley’s mid-20th century work on the ionic currents generating neuron action potentials stands among that century’s great scientific achievements. Unsurprisingly, that case has attracted widespread attention from neuroscientists, historians and philosophers of science. In this paper, I do not propose to add any new insights into the vast historical treatment of Hodgkin’s and Huxley’s scientific discoveries in that much- discussed episode. Instead, I focus on an aspect of it that hasn’t received much (...) attention: Hodgkin’s and Huxley’s own assessments about what their famous “quantitative description” accomplished. The “Hodgkin-Huxley model” is now widely recognized as a foundation of contemporary computational neuroscience. Yet Hodgkin and Huxley expressed serious caveats about their model and what it added to their scientific discoveries, as far back as their (1952d), in which they first presented their model. They were even more critical of its accomplishments in their Nobel Prize addresses a decade later. Most notably, as I argue here, some worries they raised about their quantitative description seem still to be relevant to current work in ongoing computational neuroscience. (shrink)

Different animal groups exhibit a surprisingly diversity of sex determination systems. Moreover, even systems that are superficially similar may utilize different underlying mechanisms. This diversity is illustrated by a comparison of sex determination in three well‐studied model organisms: the fruitfly Drosophila melanogaster, the nematode Caenorhabditis elegans, and the mouse. All three animals exhibit male heterogamety, extensive sexual dimorphism and sex chromosome dosage compensation, yet the molecular and cellular processes involved are now known to be quite unrelated. The similarities must (...) have arisen by convergent evolution. Studies of sex determination demonstrate that evolution can produce a variety of solutions to the same basic problems in development. (shrink)

I claim that the Hodgkin‐Huxley (HH) current equations owe a great deal of their importance to their role in bringing results from experiments on squid giant action preparations to bear on the study of the action potential in other neurons in other in vitro and in vivo environments. I consider ideas from Weber and Craver about the role of Coulomb’s and other fundamental equations in explaining the action potential and in HH’s development of their equations. Also, I offer (...) an embellishment to Schaffner’s emergent unifier conception of the HH model. †To contact the author, please write to: Department of HPS, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected]. (shrink)

Different animal groups exhibit a surprisingly diversity of sex determination systems. Moreover, even systems that are superficially similar may utilize different underlying mechanisms. This diversity is illustrated by a comparison of sex determination in three well‐studied model organisms: the fruitfly Drosophila melanogaster, the nematode Caenorhabditis elegans, and the mouse. All three animals exhibit male heterogamety, extensive sexual dimorphism and sex chromosome dosage compensation, yet the molecular and cellular processes involved are now known to be quite unrelated. The similarities must (...) have arisen by convergent evolution. Studies of sex determination demonstrate that evolution can produce a variety of solutions to the same basic problems in development. (shrink)

Not all models are explanatory. Some models are data summaries. Some models sketch explanations but leave crucial details unspecified or hidden behind filler terms. Some models are used to conjecture a how-possibly explanation without regard to whether it is a how-actually explanation. I use the Hodgkin and Huxley model of the action potential to illustrate these ways that models can be useful without explaining. I then use the subsequent development of the explanation of the action potential to (...) show what is required of an adequate mechanistic model. Mechanistic models are explanatory. (shrink)

New mechanical philosophy posits that explanations in the life sciences involve the decomposition of a system into its entities and their respective activities and organization that are responsible for the explanandum phenomenon. This mechanistic account of explanation has proven problematic in its application to mathematical models, leading the mechanists to suggest different ways of aligning abstract models with the mechanist program. Initially, the discussion centered on whether the Hodgkin-Huxley model is explanatory. Network models provided another complication, as (...) they apply to a wide number of materially diverse systems. In this article, we examine the various attempts to integrate abstract models within the mechanist program, also presenting a further challenge: the Heimburg-Jackson model, which was introduced as an alternative to the Hodgkin-Huxley model. We argue that although the notion of abstraction as the omission of irrelevant mechanistic details appears to give a mechanistic solution for accommodating abstract models, this notion does not suit models whose epistemic strategy is not decompositional. As a result, the mechanist has to choose whether to dilute the mechanistic approach nearly beyond recognition or to claim that many, if not most, abstract theoretical models do not deliver mechanistic explanations, or qualify as explanatory at all. (shrink)

New mechanical philosophy posits that explanations in the life sciences involve the decomposition of a system into its entities and their respective activities and organization that are responsible for the explanandum phenomenon. This mechanistic account of explanation has proven problematic in its application to mathematical models, leading the mechanists to suggest different ways of aligning abstract models with the mechanist program. Initially, the discussion centered on whether the Hodgkin-Huxley model is explanatory. Network models provided another complication, as (...) they apply to a wide number of materially diverse systems. In this article, we examine the various attempts to integrate abstract models within the mechanist program, also presenting a further challenge: the Heimburg-Jackson model, which was introduced as an alternative to the Hodgkin-Huxley model. We argue that although the notion of abstraction as the omission of irrelevant mechanistic details appears to give a mechanistic solution for accommodating abstract models, this notion does not suit models whose epistemic strategy is not decompositional. As a result, the mechanist has to choose whether to dilute the mechanistic approach nearly beyond recognition or to claim that many, if not most, abstract theoretical models do not deliver mechanistic explanations, or qualify as explanatory at all. (shrink)

This article considers claims that biology should seek general theories similar to those found in physics but argues for an alternative framework for biological theories as collections of prototypical interlevel models that can be extrapolated by analogy to different organisms. This position is exemplified in the development of the Hodgkin‐Huxley giant squid model for action potentials, which uses equations in specialized ways. This model is viewed as an “emergent unifier.” Such unifiers, which require various simplifications, involve (...) the types of heuristics discussed in Wimsatt’s writings on reduction, but with a twist. Here, the heuristics are used to generate emergent rather than reductive explanations. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected]. (shrink)

This article examines the role of experimental generalizations and physical laws in neuroscientific explanations, using Hodgkin and Huxley’s electrophysiological model from 1952 as a test case. I show that the fact that the model was partly fitted to experimental data did not affect its explanatory status, nor did the false mechanistic assumptions made by Hodgkin and Huxley. The model satisfies two important criteria of explanatory status: it contains invariant generalizations and it is modular (...) (both in James Woodward’s sense). Further, I argue that there is a sense in which the explanatory heteronomy thesis holds true for this case. †To contact the author, please write to: SNF‐Professorship for Philosophy of Science, University of Basel, Missionsstrasse 21, 4003 Basel, Switzerland; e‐mail: [email protected]. (shrink)

Let us now imagine that some administrative authority, as far superior in power and intelligence to men, as men are to their cattle, is set over the colony, charged to deal with its human elements in such a manner as to assure the victory of the settlement over the antagonistic influences of the state of nature in which it is set down. He would proceed in the same fashion as that in which the gardener dealt with his garden.

Evolution and ethics: prolegomena--Evolution and ethics.--Science and morals.--Capital, the mother of labour.--Social diseases and worse remedies.

Publication of the Vestiges and the rather primitive theory of evolution it expounded thus played a significant role in the careers of Darwin and Wallace. In addition, in spite of his poor opinion of the Vestiges, it presented Huxley with a convenient topic for critical discussion and the opportunity to focus more attention on the subject of evolution. The dynamic interactions among these leading figures of nineteenth-century natural science helped spur the development of more sophisticated models of evolution.Darwin had (...) a proper appreciation of Chambers's contribution to evolutionary thought, although he fully recognized the shortcomings of this work. He understood the importance of allowing fresh ideas about organic change to be ventilated. However, he was primarily concerned with his own theory and viewed all developments in evolutionary biology from this perspective. If he did not give full consideration to Chambers and his book early on, it was due mainly to his feeling that the concepts in the Vestiges were very different from his own; he was therefore reluctant to embrace them as the forerunners of his own theory. As a scholar, he was also troubled by the scientific errors in the book. However, the record demonstrates that he attempted to make amends for any oversight on his part. His generous letter to Chambers's daughter, and his gracious treatment of Chambers during the brief time the latter lived in London, are ample proof of that.The attacks of Huxley, Sedgwick, and other prominent natural historians and geologists at the time, the problems inherent in Chambers's evolutionary theory, and the publication of the Origin, are the major reasons why the Vestiges became a neglected work. Nevertheless, Chambers's contribution will always stand out because, together with those of other late eighteenth- and early nineteenth-century predecessors of Darwin, it laid the foundations of modern evolutionary thought and, more importantly, helped prepare the scientific community for the more fully developed ideas of Darwin and Wallace. (shrink)

Hume: Hume's life. Hume's philosophy.--Helps to the study of Berkeley: Bishop Berkeley on the metaphysics of sensation (1871). On sensation and the unity of structure of sensiferous organs (1879).

Much research effort has been directed in different physiological contexts towards describing realistic behaviors with differential equations. One observes obviously that more state-variables give the model more accuracy. Unfortunately, the computational cost involved is higher. A new algorithm is presented for simulating a model described by a system of differential equations in which efficiency may not be altered by its size. In order to do this, the method is based on a polynomial description of the state-variables' evolution and (...) on a computation distributed control. Evaluations and results performed with classical models like Fitzhugh Nagumo or Hodgkin Huxley, allow validation of the method and exhibits its potential to decrease the computational costs. (shrink)

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos (...) theory, topology, mathematical physics, and the solution of Fermat's Last Theorem.Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos (...) theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)

The concept of evolution is of fundamental importance to any general scheme of thought: and one of the ways in which its importance is greatest is in defining the place of mind within any such scheme. If bodies and their contained brains have evolved, why not the accompanying minds? Indeed, to-day the question can only be properly put the other way round: how can the minds not have evolved? Mental evolution can only have failed to occur if we deny to (...) mind the principle of continuity, which is one of our axioms on the physical side: only, that is to say, if the world ceases to be rational. (shrink)

Known as 'Darwin's Bulldog', the biologist Thomas Henry Huxley was a tireless supporter of the evolutionary theories of his friend Charles Darwin. Huxley also made his own significant scientific contributions, and he was influential in the development of science education despite having had only two years of formal schooling. He established his scientific reputation through experiments on aquatic life carried out during a voyage to Australia while working as an assistant surgeon in the Royal Navy; ultimately he became (...) President of the Royal Society. Throughout his life Huxley struggled with issues of faith, and he coined the term 'agnostic' to describe his beliefs. This nine-volume collection of Huxley's essays, which he edited and published in 1893–4, demonstrates the wide range of his intellectual interests. Volume 1 begins with a brief autobiography, and examines the development and progress of scientific practice and knowledge. (shrink)

The Perennial Philosophy is defined by its author as "The metaphysic that recognizes a divine Reality substantial to the world of things and lives and minds." With great wit and stunning intellect, Aldous Huxley examines the spiritual beliefs of various religious traditions and explains them in terms that are personally meaningful.