Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defenses, objections, and replies into a convincing defense of the core of his theory, which is that we can analyze causation by appeal to the notion of manipulation.

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defences, objections, and replies into a convincing defence of the core of his theory, which is that we can analyse causation by appeal to the notion of manipulation.

This paper explores the question of whether all or most explanations in biology are, or ideally should be, ‘mechanistic’. I begin by providing an account of mechanistic explanation, making use of the interventionist ideas about causation I have developed elsewhere. This account emphasizes the way in which mechanistic explanations, at least in the biological sciences, integrate difference‐making and spatio‐temporal information, and exhibit what I call fine‐tunedness of organization. I also emphasize the role played by modularity conditions in mechanistic explanation. I (...) will then argue, in agreement with John Dupré, that, given this account, it is plausible that many biological systems require explanations that are relatively non‐mechanical or depart from expectations one associates with the behaviour of machines. (shrink)

This essay advocates a “functional” approach to causation and causal reasoning: these are to be understood in terms of the goals and purposes of causal thinking. This approach is distinguished from accounts based on metaphysical considerations or on reconstruction of “intuitions.”.

Philosophers of science increasingly recognize the importance of idealization: the intentional introduction of distortion into scientific theories. Yet this recognition has not yielded consensus about the nature of idealization. e literature of the past thirty years contains disparate characterizations and justifications, but little evidence of convergence towards a common position.

Mechanistic explanation has an impressive track record of advancing our understanding of complex, hierarchically organized physical systems, particularly biological and neural systems. But not every complex system can be understood mechanistically. Psychological capacities are often understood by providing cognitive models of the systems that underlie them. I argue that these models, while superficially similar to mechanistic models, in fact have a substantially more complex relation to the real underlying system. They are typically constructed using a range of techniques for abstracting (...) the functional properties of the system, which may not coincide with its mechanistic organization. I describe these techniques and show that despite being non-mechanistic, these cognitive models can satisfy the normative constraints on good explanations. (shrink)

Cognitive science has always included multiple methodologies and theoretical commitments. The philosophy of cognitive science should embrace, or at least acknowledge, this diversity. Bechtel’s (2009a) proposed philosophy of cognitive science, however, applies only to representationalist and mechanist cognitive science, ignoring the substantial minority of dynamically oriented cognitive scientists. As an example of nonrepresentational, dynamical cognitive science, we describe strong anticipation as a model for circadian systems (Stepp & Turvey, 2009). We then propose a philosophy of science appropriate to nonrepresentational, dynamical (...) cognitive science. (shrink)

Several articles have recently appeared arguing that there really are no viable alternatives to mechanistic explanation in the biological sciences (Kaplan and Bechtel; Kaplan and Craver). We argue that mechanistic explanation is defined by localization and decomposition. We argue further that systems neuroscience contains explanations that violate both localization and decomposition. We conclude that the mechanistic model of explanation needs to either stretch to now include explanations wherein localization or decomposition fail or acknowledge that there are counterexamples to mechanistic explanation (...) in the biological sciences. (shrink)

An increasing number of philosophers have promoted the idea that mechanism provides a fruitful framework for thinking about the explanatory contributions of computational approaches in cognitive neuroscience. For instance, Piccinini and Bahar :453–488, 2013) have recently argued that neural computation constitutes a sui generis category of physical computation which can play a genuine explanatory role in the context of investigating neural and cognitive processes. The core of their proposal is to conceive of computational explanations in cognitive neuroscience as a subspecies (...) of mechanistic explanations. This paper identifies several challenges facing their mechanistic account and sketches an alternative way of thinking about the epistemic roles of computational approaches used in the study of brain and cognition. Drawing on examples from both low-level and systems-level computational neuroscience, I argue that at least some computational explanations of neural and cognitive processes are partially independent from mechanistic constraints. (shrink)

The Enhanced Indispensability Argument (Baker [ 2009 ]) exemplifies the new wave of the indispensability argument for mathematical Platonism. The new wave capitalizes on mathematics' role in scientific explanations. I will criticize some analyses of mathematics' explanatory function. In turn, I will emphasize the representational role of mathematics, and argue that the debate would significantly benefit from acknowledging this alternative viewpoint to mathematics' contribution to scientific explanations and knowledge.

We reassess Woodward’s counterfactual account of explanation in relation to regularity explananda. Woodward presents an account of causal explanation. We argue, by using an explanation of Kleiber’s law to illustrate, that the account can also cover some noncausal explanations. This leads to a tension between the two key aspects of Woodward’s account: the counterfactual aspect and the causal aspect. We explore this tension and make a case for jettisoning the causal aspect as constitutive of explanatory power in connection with regularity (...) explananda. (shrink)

Kaplan and Craver claim that all explanations in neuroscience appeal to mechanisms. They extend this view to the use of mathematical models in neuroscience and propose a constraint such models must meet in order to be explanatory. I analyze a mathematical model used to provide explanations in dynamical systems neuroscience and indicate how this explanation cannot be accommodated by the mechanist framework. I argue that this explanation is well characterized by Batterman’s account of minimal model explanations and that it demonstrates (...) how relationships between explanatory models in neuroscience and the systems they represent is more complex than has been appreciated. (shrink)

Recently philosophers of science have begun to pay more attention to the use of highly idealized mathematical models in scientific theorizing. An important example of this kind of highly idealized modeling is the widespread use of optimality models within evolutionary biology. One way to understand the explanations provided by these models is as a censored causal explanation: an explanation that omits certain causal factors in order to focus on a modular subset of the causal processes that led to the explanandum. (...) In this paper, I first argue that the censored causal model approach fails to establish a permanent explanatory role for optimality models in biology and mischaracterizes the explanatory virtues of biological optimality modeling. In addition, I argue that many biological optimality explanations cannot be characterized as censored causal explanations. In response, I propose an alternative approach that analyzes optimality models’ reliance on synchronically representing a system’s constraints and tradeoffs as well as their employment of various kinds of idealization in order to provide equilibrium explanations. (shrink)

A prominent approach to scientific explanation and modeling claims that for a model to provide an explanation it must accurately represent at least some of the actual causes in the event's causal history. In this paper, I argue that many optimality explanations present a serious challenge to this causal approach. I contend that many optimality models provide highly idealized equilibrium explanations that do not accurately represent the causes of their target system. Furthermore, in many contexts, it is in virtue of (...) their independence of causes that optimality models are able to provide a better explanation than competing causal models. Consequently, our account of explanation and modeling must expand beyond the causal approach. (shrink)

We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism—neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous (...) signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non-neural notions of computation ought to be replaced or reinterpreted in terms of neural computation. (shrink)

We sketch a framework for building a unified science of cognition. This unification is achieved by showing how functional analyses of cognitive capacities can be integrated with the multilevel mechanistic explanations of neural systems. The core idea is that functional analyses are sketches of mechanisms , in which some structural aspects of a mechanistic explanation are omitted. Once the missing aspects are filled in, a functional analysis turns into a full-blown mechanistic explanation. By this process, functional analyses are seamlessly integrated (...) with multilevel mechanistic explanations. (shrink)

Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of more complicated logical means for nets containing circles; and that for any logical expression satisfying certain conditions, one can find a net behaving in the fashion it describes. It is shown that many particular choices among possible neurophysiological assumptions (...) are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under the other and gives the same results, although perhaps not in the same time. Various applications of the calculus are discussed. (shrink)

The concept of mechanism is analyzed in terms of entities and activities, organized such that they are productive of regular changes. Examples show how mechanisms work in neurobiology and molecular biology. Thinking in terms of mechanisms provides a new framework for addressing many traditional philosophical issues: causality, laws, explanation, reduction, and scientific change.

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)

Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...) the facts doing the explaining are modally stronger than ordinary causal laws or are understood in the why question’s context to be constitutive of the physical arrangement at issue. A distinctively mathematical explanation works by showing the explanandum to be more necessary than ordinary causal laws could render it. Distinctively mathematical explanations thus supply a kind of understanding that causal explanations cannot. 1 Introduction2 Some Distinctively Mathematical Scientific Explanations3 Are Distinctively Mathematical Explanations Set Apart by their Failure to Cite Causes? 4 Distinctively Mathematical Explanations do not Exploit Causal Powers5 How these Distinctively Mathematical Explanations Work6 Conclusion. (shrink)

We argue that dynamical and mathematical models in systems and cognitive neuro- science explain (rather than redescribe) a phenomenon only if there is a plausible mapping between elements in the model and elements in the mechanism for the phe- nomenon. We demonstrate how this model-to-mechanism-mapping constraint, when satisfied, endows a model with explanatory force with respect to the phenomenon to be explained. Several paradigmatic models including the Haken-Kelso-Bunz model of bimanual coordination and the difference-of-Gaussians model of visual receptive fields are (...) explored. (shrink)

The central aim of this paper is to shed light on the nature of explanation in computational neuroscience. I argue that computational models in this domain possess explanatory force to the extent that they describe the mechanisms responsible for producing a given phenomenon—paralleling how other mechanistic models explain. Conceiving computational explanation as a species of mechanistic explanation affords an important distinction between computational models that play genuine explanatory roles and those that merely provide accurate descriptions or predictions of phenomena. It (...) also serves to clarify the pattern of model refinement and elaboration undertaken by computational neuroscientists. (shrink)

Abstract While agreeing that dynamical models play a major role in cognitive science, we reject Stepp, Chemero, and Turvey's contention that they constitute an alternative to mechanistic explanations. We review several problems dynamical models face as putative explanations when they are not grounded in mechanisms. Further, we argue that the opposition of dynamical models and mechanisms is a false one and that those dynamical models that characterize the operations of mechanisms overcome these problems. By briefly considering examples involving the generation (...) of action potentials and circadian rhythms, we show how decomposing a mechanism and modeling its dynamics are complementary endeavors. (shrink)

This paper is aimed at identifying how a model’s explanatory power is constructed and identified, particularly in the practice of template-based modeling (Humphreys, Philos Sci 69:1–11, 2002; Extending ourselves: computational science, empiricism, and scientific method, 2004), and what kinds of explanations models constructed in this way can provide. In particular, this paper offers an account of non-causal structural explanation that forms an alternative to causal–mechanical accounts of model explanation that are currently popular in philosophy of biology and cognitive science. Clearly, (...) defences of non-causal explanation are far from new (e.g. Batterman, Br J Philos Sci 53:21–38, 2002a; The devil in the details: asymptotic reasoning in explanation, reduction, and emergence, 2002b; Pincock, Noûs 41:253–275, 2007; Mathematics and scientific representation 2012; Rice, Noûs. doi:10.1111/nous.12042, 2013; Biol Philos 27:685–703, 2012), so the targets here are focused on a particular type of robust phenomenon and how strong invariance to interventions can block a range of causal explanations. By focusing on a common form of model construction, the paper also ties functional or computational style explanations found in cognitive science and biology more firmly with explanatory practices across model-based science in general. (shrink)

This paper argues that besides mechanistic explanations, there is a kind of explanation that relies upon “topological” properties of systems in order to derive the explanandum as a consequence, and which does not consider mechanisms or causal processes. I first investigate topological explanations in the case of ecological research on the stability of ecosystems. Then I contrast them with mechanistic explanations, thereby distinguishing the kind of realization they involve from the realization relations entailed by mechanistic explanations, and explain how both (...) kinds of explanations may be articulated in practice. The second section, expanding on the case of ecological stability, considers the phenomenon of robustness at all levels of the biological hierarchy in order to show that topological explanations are indeed pervasive there. Reasons are suggested for this, in which “neutral network” explanations are singled out as a form of topological explanation that spans across many levels. Finally, I appeal to the distinction of explanatory regimes to cast light on a controversy in philosophy of biology, the issue of contingence in evolution, which is shown to essentially involve issues about realization. (shrink)

Network analysis is increasingly used to discover and represent the organization of complex systems. Focusing on examples from neuroscience in particular, I argue that whether network models explain, how they explain, and how much they explain cannot be answered for network models generally but must be answered by specifying an explanandum, by addressing how the model is applied to the system, and by specifying which kinds of relations count as explanatory.

In a recent paper, Kaplan (Synthese 183:339–373, 2011) takes up the task of extending Craver’s (Explaining the brain, 2007) mechanistic account of explanation in neuroscience to the new territory of computational neuroscience. He presents the model to mechanism mapping (3M) criterion as a condition for a model’s explanatory adequacy. This mechanistic approach is intended to replace earlier accounts which posited a level of computational analysis conceived as distinct and autonomous from underlying mechanistic details. In this paper I discuss work in (...) computational neuroscience that creates difficulties for the mechanist project. Carandini and Heeger (Nat Rev Neurosci 13:51–62, 2012) propose that many neural response properties can be understood in terms of canonical neural computations. These are “standard computational modules that apply the same fundamental operations in a variety of contexts.” Importantly, these computations can have numerous biophysical realisations, and so straightforward examination of the mechanisms underlying these computations carries little explanatory weight. Through a comparison between this modelling approach and minimal models in other branches of science, I argue that computational neuroscience frequently employs a distinct explanatory style, namely, efficient coding explanation. Such explanations cannot be assimilated into the mechanistic framework but do bear interesting similarities with evolutionary and optimality explanations elsewhere in biology. (shrink)

We provide a taxonomy of the two most important debates in the philosophy of the cognitive and neural sciences. The first debate is over methodological individualism: is the object of the cognitive and neural sciences the brain, the whole animal, or the animal--environment system? The second is over explanatory style: should explanation in cognitive and neural science be reductionist-mechanistic, inter-level mechanistic, or dynamical? After setting out the debates, we discuss the ways in which they are interconnected. Finally, we make some (...) recommendations that we hope will help philosophers interested in the cognitive and neural sciences to avoid dead ends. (shrink)

Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another justification (...) derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds. (shrink)

Scientific models invariably involve some degree of idealization, abstraction, or nationalization of their target system. Nonetheless, I argue that there are circumstances under which such false models can offer genuine scientific explanations. After reviewing three different proposals in the literature for how models can explain, I shall introduce a more general account of what I call model explanations, which specify the conditions under which models can be counted as explanatory. I shall illustrate this new framework by applying it to the (...) case of Bohr's model of the atom, and conclude by drawing some distinctions between phenomenological models, explanatory models, and fictional models. (shrink)

In semiclassical mechanics one finds explanations of quantum phenomena that appeal to classical structures. These explanations are prima facie problematic insofar as the classical structures they appeal to do not exist. Here I defend the view that fictional structures can be genuinely explanatory by introducing a model-based account of scientific explanation. Applying this framework to the semiclassical phenomenon of wavefunction scarring, I argue that not only can the fictional classical trajectories explain certain aspects of this quantum phenomenon, but also that (...) an explanation that does not make reference to these classical structures is, in a certain sense, deficient. (shrink)

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would (...) have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

This article argues that the basic account of mechanism and mechanistic explanation, involving sequential execution of qualitatively characterized operations, is itself insufficient to explain biological phenomena such as the capacity of living organisms to maintain themselves as systems distinct from their environment. This capacity depends on cyclic organization, including positive and negative feedback loops, which can generate complex dynamics. Understanding cyclically organized mechanisms with complex dynamics requires coordinating research directed at decomposing mechanisms into parts and operations with research using computational (...) models to recompose mechanisms and determine their dynamic behavior. This coordinated endeavor yields dynamic mechanistic explanations. (shrink)

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.

This article discusses minimal model explanations, which we argue are distinct from various causal, mechanical, difference-making, and so on, strategies prominent in the philosophical literature. We contend that what accounts for the explanatory power of these models is not that they have certain features in common with real systems. Rather, the models are explanatory because of a story about why a class of systems will all display the same large-scale behavior because the details that distinguish them are irrelevant. This story (...) explains patterns across extremely diverse systems and shows how minimal models can be used to understand real systems. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...) are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, but the other of which yields explanations that are distinctively mathematical in terms of nomological strength. In the first, one first picks out a system or class of systems, finds that the equations hold in a causal -explanatory way; in the second, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non- causal explanations can complement one another. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non-causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka–Volterra equations. There are (...) at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, and another that yields explanations that are distinctively mathematical in terms of nomological strength. In the first case, one first picks out a system or class of systems, and finds that the equations hold in a causal–explanatory way. In the second case, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non-causal explanations can complement one another. _1_. Introduction _2._ Delineating the Boundaries of Causal Explanation _2.1._ Why construe causal explanation narrowly? The land of explanation versus grain-focusing _2.2._ Reasons to narrow the scope of causal explanation _3._ Broadening the Scope of Mathematical Explanation _4._ Lotka–Volterra: Same Model, Different Explanation Types _4.1._ General biocide in the Lotka–Volterra model _4.2._ Two ways a model can hold, yielding causal versus mathematical explanations _5._ Four Complementary Relationships between Mathematical and Causal Explanation _5.1._ Slight reformulations of explananda _5.2._ Causal distortion of idealized mathematical models _5.3._ Partial explanations requiring supplementation _5.4._ Explanatory dimensionality _6._ Conclusion. (shrink)

Carl F. Craver investigates what we are doing when we use neuroscience to explain what's going on in the brain. When does an explanation succeed and when does it fail? Craver offers explicit standards for successful explanation of the workings of the brain, on the basis of a systematic view about what neuroscientific explanations are.

Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.

We review the pros and cons of analog and digital computation. We propose that computation that is most efficient in its use of resources is neither analog computation nor digital computation but, rather, a mixture of the two forms. For maximum efficiency, the information and information-processing resources of the hybrid form must be distributed over many wires, with an optimal signal-to-noise ratio per wire. Our results suggest that it is likely that the brain computes in a hybrid fashion and that (...) an underappreciated and important reason for the efficiency of the human brain, which consumes only 12 W, is the hybrid and distributed nature of its architecture. (shrink)

Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.

Debate about adaptationism in biology continues, in part because within “the” problem of assessing adaptationism, three distinct problems are mixed together. The three problems concern the assessment of three distinct adaptationist positions, each of which asserts the central importance of adaptation and natural selection to the study of evolution, but conceives this importance in a different way. As there are three kinds of adaptationism, there are three distinct "anti-adaptationist" positions as well. Or putting it more formally, there are three different (...) dimensions here, and strongly adaptationist views, strongly anti-adaptationist views, and moderate views are possible for each dimension. (shrink)

Recently, Piccinini and Craver have stated three theses concerning the relations between functional analysis and mechanistic explanation in cognitive sciences: No Distinctness: functional analysis and mechanistic explanation are explanations of the same kind; Integration: functional analysis is a kind of mechanistic explanation; and Subordination: functional analyses are unsatisfactory sketches of mechanisms. In this paper, I argue, first, that functional analysis and mechanistic explanations are sub-kinds of explanation by scientific (idealized) models. From that point of view, we must take into account (...) the tradeoff between the representational/explanatory goals of generality and precision that govern the practice of model-building. In some modeling scenarios, it is rational to maximize explanatory generality at the expense of mechanistic precision. This tradeoff allows me to put forward a problem for the mechanist position. If mechanistic modeling endorses generality as a valuable goal, then Subordination should be rejected. If mechanists reject generality as a goal, then Integration is false. I suggest that mechanists should accept that functional analysis can offer acceptable explanations of cognitive phenomena. (shrink)