A perspective in the philosophy of mathematics is developed from a consideration of the strengths and limitations of both logicism and platonism, with an early focus on Frege’s work. Importantly, although many set-theoretic structures may be developed each of which offers limited isomorphism with the system of natural numbers, no one of them may be identified with it. Furthermore, the timeless, ever present nature of mathematical concepts and results itself offers direct access, in the face of a platonist account which (...) generates a supposed problem of access. Crucially too, pure mathematics has its own distinctive method of confirming or validating results - mathematical proof - which supplies a higher level of confidence and objectivity than that available elsewhere. The dichotomy of invention and discovery is too jejune a framework for analysing creative mathematical activity. The Gödelian platonist perspective is evaluated and queried through scrutiny of the part played by mathematical resources and constraints in relation to human activity. It appears that there can be non-causal mathematical explanations and mathematical constraint on purely natural processes. Valuable implications of Quine’s naturalism are explored, but one must be cautious of his thesis of confirmational holism. The distinction between algebraic and non-algebraic mathematical theories usefully contributes to our understanding of the internally differentiated nature of the subject. (shrink)

James Woodward’s manipulationist counterfactual theory of explanation offers strong tools for an adequate approach to explanation endeavours. One of these tools is the notion of intervention, which serves as a guiding principle for identifying explanations as causal, thus preserving the unidirectionality of explanatory praxis. Nevertheless, in this paper, I argue that in some cases of explanation, this notion has a rather redundant role since it is either impossible to define or it can be replaced by other types of manipulations or (...) both. I shall show these shortcomings of intervention in two particularly detailed analyses of an economic example pertaining to Okun’s law and the pendulum explanation. In analysing the former example, I contend that given the complex causal situation of economic phenomena, the notion of intervention is inept at helping explain them. In the latter example, I show that the notion of intervention is readily replaceable by other types of variation—conceptual or mathematical. Finally, I shall end this article by examining the case of pendulum explanation in light of Woodward’s new approach to explanation direction. In the end, the conclusion is that the variables of the pendulum law are in a symmetrical relationship. (shrink)

Sometimes, scientific models are either intended to or plausibly interpreted as representing nonactual but possible targets. Call this “hypothetical modeling”. This paper raises two epistemological challenges concerning hypothetical modeling. To begin with, I observe that given common philosophical assumptions about the scope of objective possibility, hypothetical models are fallible with respect to what is objectively possible. There is thus a need to distinguish between accurate and inaccurate hypothetical modeling. The first epistemological challenge is that no account of the epistemology of (...) hypothetical models seems to cohere with the most characteristic function of scientific modeling in general, i.e., surrogative representation. The second epistemological challenge is a version of “reliability challenges” familiar from other areas. There is a challenge to explain how hypothetical models could be a reliable guide to what is possible, given that they are not and cannot be compared against their nonactual targets and updated accordingly. I close with some brief remarks on possible solutions to these challenges. (shrink)

Both ecologists and statistical physicists use a variety of highly idealized models to study active matter and self-organizing critical phenomena. In this paper, I show how universality classes play a crucial role in justifying the application of highly idealized ‘minimal’ models to explain and understand the critical behaviors of active matter systems across a wide range of scales and scientific fields. Appealing to universality enables us to see why the same minimal models can be used to explain and understand behaviors (...) across these different systems despite drastic differences in the causes and mechanisms responsible for the behaviors of interest. After analyzing these cases in detail, I argue that accounts that focus on identifying common causes or mechanisms in order to explain patterns are unable to accommodate these cases. In contrast, I argue that the justification for using these minimal models is that they are within the same universality class as real systems whose causes and mechanisms are known to be different. I also use these cases to identify several different kinds of explanatory autonomy that have important implications for how scientists ought to approach the modeling of multiscale phenomena. (shrink)

The problem of explanatory asymmetry remains a serious challenge for non-causal accounts of explanation. This paper proposes a novel solution, and it does so by appealing to the theoretical context in which an explanation is offered. The paper develops the problem of explanatory asymmetry for non-causal dependency accounts of explanation, focusing specifically on Alexander Reutlinger’s Counterfactual Theory of Explanation and recent work by Marc Lange and Lina Jansson. It defends the idea that nomological possibility with respect to a global theory (...) is the right constraint on explanation, and it shows how this breaks the apparent symmetry in counterfactual dependence that is the source of the problem. This solution appeals to theoretical context, and the paper develops and defends the version of contextualism in explanation that is required. (shrink)

We provide two programmatic frameworks for integrating philosophical research on understanding with complementary work in computer science, psychology, and neuroscience. First, philosophical theories of understanding have consequences about how agents should reason if they are to understand that can then be evaluated empirically by their concordance with findings in scientific studies of reasoning. Second, these studies use a multitude of explanations, and a philosophical theory of understanding is well suited to integrating these explanations in illuminating ways.

Recent years have seen growing interest in modifying interventionist accounts of causal explanation in order to characterise noncausal explanation. However, one surprising element of such accounts is that they have typically jettisoned the core feature of interventionism: interventions. Indeed, the prevailing opinion within the philosophy of science literature suggests that interventions exclusively demarcate causal relationships. This position is so prevalent that, until now, no one has even thought to name it. We call it “intervention puritanism” (I-puritanism, for short). In this (...) paper, we mount the first sustained defence of the idea that there are distinctively noncausal explanations which can be characterized in terms of possible interventions; a position we call “intervention liberalism” (I-liberalism, for short). While many have followed James Woodward (2003) in committing to I-puritanism, we trace support for I-liberalism back to the work of Jaegwon Kim (1974). Furthermore, we analyse two recent sources of scepticism regarding I-liberalism: debate surrounding mechanistic constitution; and attempts to provide a monistic account of explanation. We show that neither literature provides compelling reasons for adopting I-puritanism. Finally, we present a novel taxonomy of available positions upon the role of possible interventions in explanation: weak causal imperialism; strong causal imperialism; monist intervention puritanism; pluralist intervention puritanism; monist intervention liberalism; and finally, the specific position defended in this paper, pluralist intervention liberalism. (shrink)

This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the (...) debate on the nature of natural selection intersects the debate on whether mathematical explanations of empirical facts are genuine scientific explanations. I argue that if the explanations provided by population genetics are regarded by the statisticalists as non-causal explanations of that kind, then statisticalism risks being incompatible with a naturalist stance. The statisticalist faces a dilemma: either she maintains statisticalism but has to renounce naturalism; or she maintains naturalism but has to content herself with an account of the explanations provided by population genetics that she deems unsatisfactory. This challenge is relevant to the statisticalists because many of them see themselves as naturalists. (shrink)

Two striking claims are advanced on behalf of the free energy principle in cognitive science and philosophy: that it identifies a condition of the possibility of existence for self-organising systems; and that it has important implications for our understanding of how the brain works, defining a set of process theories—roughly, theories of the structure and functions of neural mechanisms—consistent with the free energy minimising imperative that it derives as a necessary feature of all self-organising systems. I argue that the conjunction (...) of claims and rests on a fallacy of equivocation. The FEP can be interpreted in two ways: as a claim about how it is possible to redescribe the existence of self-organising systems, and as a claim about how such systems maintain their existence. Although the Descriptive FEP plausibly does identify a condition of the possibility of existence for self-organising systems, it has no important implications for our understanding of how the brain works. Although the Explanatory FEP would have such implications if it were true, it does not identify a condition of the possibility of existence for self-organising systems. I consider various ways of responding to this conclusion, and I explore its implications for the role and importance of the FEP in cognitive science and philosophy. (shrink)

Some scientific explanations appear to turn on pure mathematical claims. The enhanced indispensability argument appeals to these ‘mathematical explanations’ in support of mathematical platonism. I argue that the success of this argument rests on the claim that mathematical explanations locate pure mathematical facts on which their physical explananda depend, and that any account of mathematical explanation that supports this claim fails to provide an adequate understanding of mathematical explanation.

Catherine Elgin has recently argued that a nonfactive conception of understanding is required to accommodate the epistemic successes of science that make essential use of idealizations and models. In this paper, I argue that the fact that our best scientific models and theories are pervasively inaccurate representations can be made compatible with a more nuanced form of scientific realism that I call Understanding Realism. According to this view, science aims at (and often achieves) factive scientific understanding of natural phenomena. I (...) contend that this factive scientific understanding is provided by grasping a set of true modal information about the phenomenon of interest. Furthermore, contrary to Elgin’s view, I argue that the facticity of this kind of scientific understanding can be separated from the inaccuracy of the models and theories used to produce it. (shrink)

An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modelled on the deductive-nomological account, is unlikely to satisfy these desiderata. I provide a counterfactual account of DME, the Narrow (...) Ontic Counterfactual Account (NOCA), that can satisfy all three desiderata. NOCA appeals to ontic considerations to account for explanatory asymmetry and ground the relevant counterfactuals. NOCA provides a unification of the causal and the non-causal, the ontic and the modal, by identifying a common core that all explanations share and in virtue of which they are explanatory. (shrink)

Philosophers of psychology debate, among other things, which psychological models, if any, are (or provide) mechanistic explanations. This should seem a little strange given that there is rough consensus on the following two claims: 1) a mechanism is an organized collection of entities and activities that produces, underlies, or maintains a phenomenon, and 2) a mechanistic explanation describes, represents, or provides information about the mechanism producing, underlying, or maintaining the phenomenon to be explained (i.e. the explanandum phenomenon) (Bechtel and Abrahamsen (...) 2005; Craver 2007). If there is a rough consensus on what mechanisms are and that mechanistic explanations describe, represent, or provide information about them, then how is there no consensus on which psychological models are (or provide) mechanistic explanations? Surely the psychological models that are mechanistic explanations are the models that describe, represent, or provide information about mechanisms. That is true, of course; the trouble arises when determining what exactly that involves. Philosophical disagreement over which psychological models are mechanistic explanations is often disagreement about what it means to describe, represent, or provide information about a mechanism, among other things (Hochstein 2016; Levy 2013). In addition, one's position in this debate depends on a host of other seemingly arcane metaphysical issues, such as the nature of mechanisms, computational and functional properties (Piccinini 2016), and realization (Piccinini and Maley 2014), as well as the relation between models, methodologies, and explanations (Craver 2014; Levy 2013; Zednik 2015). Although I inevitably advocate a position, my primary aim in this chapter is to spell out all these relationships and canvas the positions that have been taken (or could be taken) with respect to mechanistic explanation in psychology, using dynamical systems models and cognitive models (or functional analyses) as examples. (shrink)

An important strand in philosophy of science takes scientific explanation to consist in the conveyance of some kind of information. Here I argue that this idea is also implicit in some core arguments of mechanists, some of whom are proponents of an ontic conception of explanation that might be thought inconsistent with it. However, informational accounts seem to conflict with some lay and scientific commonsense judgments and a central goal of the theory of explanation, because information is relative to the (...) background knowledge of agents. Sometimes we make lay judgments about whether a model is an explanation simpliciter, not just an explanation relative to some particular agent. And as philosophers of explanation, we would like a philosophical account to tell us when a model is an explanation simpliciter, not just when a model is an explanation relative to some particular agent. Thus, even if one’s account of explanation is not concerned with explanation qua communicative or speech act, the account’s reliance on the concept of information generates a prima facie conflict between the claims that 1) explanation is the conveyance of information, 2) information is relative to the background knowledge of an agent, and 3) some models are explanations not relative to the background knowledge of any particular agent. I sketch a solution to this puzzle by distinguishing informationally what I call “explanation simpliciter” from what I call “explanation-to,” relativizing the latter to an individual’s background knowledge and the former to what I call “total scientific background knowledge”. (shrink)

The notion of understanding occupies an increasingly prominent place in contemporary epistemology, philosophy of science, and moral theory. A central and ongoing debate about the nature of understanding is how it relates to the truth. In a series of influential contributions, Catherine Elgin has used a variety of familiar motivations for antirealism in philosophy of science to defend a non- factive theory of understanding. Key to her position are: (i) the fact that false theories can contribute to the upwards trajectory (...) of scientific understanding, and (ii) the essential role of inaccurate idealisations in scientific research. Using Elgin’s arguments as a foil, I show that a strictly factive theory of understanding has resources with which to offer a unified response to both the problem of idealisations and the role of false theories in the upwards trajectory of scientific understanding. Hence, strictly factive theories of understanding are viable notwithstanding these forceful criticisms. (shrink)

Most attempts to justify the use of idealized models to explain appeal to the accuracy of the model with respect to difference-making causes. In this article, I argue for an alternative way to just...

The debate over the explanatory nature of cognitive models has been waged mostly between two factions: the mechanists and the dynamical systems theorists. The former hold that cognitive models are explanatory only if they satisfy a set of mapping criteria, particularly the 3M/3m* requirement. The latter have argued, pace the mechanists, that some cognitive models are both dynamical and constitute covering-law explanations. In this paper, I provide a minimal model interpretation of dynamical cognitive models, arguing that this both provides needed (...) clarity to the mechanist versus dynamicist divide in cognitive science and also paves the way towards further insights about scientific explanation generally. (shrink)

According to an increasingly popular view among philosophers of science, both causal and non-causal explanations can be accounted for by a single theory: the counterfactual theory of explanation. A kind of non-causal explanation that has gained much attention recently but that this theory seems unable to account for are grounding explanations. Reutlinger :239-256, 2017) has argued that, despite these appearances to the contrary, such explanations are covered by his version of the counterfactual theory. His idea is supported by recent work (...) on grounding by Schaffer and Wilson who claim there to be a tight connection between grounding and counterfactual dependence. The present paper evaluates the prospects of the idea. We show that there is only a weak sense in which grounding explanations convey information about counterfactual dependencies, and that this fact cannot plausibly be taken to reveal a distinctive feature that grounding explanations share with other kinds of explanations. (shrink)

As the demand for explainable deep learning grows in the evaluation of language technologies, the value of a principled grounding for those explanations grows as well. Here we study the state-of-the-art in explanation for neural models for natural-language processing (NLP) tasks from the viewpoint of philosophy of science. We focus on recent evaluation work that finds brittleness in explanations obtained through attention mechanisms.We harness philosophical accounts of explanation to suggest broader conclusions from these studies. From this analysis, we assert the (...) impossibility of causal explanations from attention layers over text data. We then introduce NLP researchers to contemporary philosophy of science theories that allow robust yet non-causal reasoning in explanation, giving computer scientists a vocabulary for future research. (shrink)

Optimality models are widely used in different parts of biology. Two important questions that have been asked about such models are: are they explanatory and, if so, what type of explanations do they offer? My concern in this paper is with the approach of Rice (2012, 2015) and Irvine (2015), who claim that these models provide non-causal explanations. I argue that there are serious problems with this approach and with the accounts of explanation it is intended to justify. The idea (...) behind this undertaking is to draw attention to an important issue associated with the recent pluralist stance on explanation: the rampant proliferation of theories of explanation. This proliferation supports a pluralist perspective on explanation, and pluralism encourages such a proliferation. But, if we are not careful about how we arrive at and how we justify new accounts of explanation — i.e., if we do not try to avoid the sort of problems discussed in this paper — we may end up trivializing the concept of explanation. (shrink)

Philippe Huneman has recently questioned the widespread application of mechanistic models of scientific explanation based on the existence of structural explanations, i.e. explanations that account for the phenomenon to be explained in virtue of the mathematical properties of the system where the phenomenon obtains, rather than in terms of the mechanisms that causally produce the phenomenon. Structural explanations are very diverse, including cases like explanations in terms of bowtie structures, in terms of the topological properties of the system, or in (...) terms of equilibrium. The role of mathematics in bowtie structured systems and in topologically constrained systems has recently been examined in different papers. However, the specific role that mathematical properties play in equilibrium explanations requires further examination, as different authors defend different interpretations, some of them closer to the new-mechanistic approach than to the structural model advocated by Huneman. In this paper, we cover this gap by investigating the explanatory role that mathematics play in Blaser and Kirschner’s nested equilibrium model of the stability of persistent long-term human-microbe associations. We argue that their model is explanatory because: i) it provides a mathematical structure in the form of a set of differential equations that together satisfy an ESS; ii) that the nested nature of the ESSs makes the explanation of host-microbe persistent associations robust to any perturbation; iii) that this is so because the properties of the ESS directly mirror the properties of the biological system in a non-causal way. The combination of these three theses make equilibrium explanations look more similar to structural explanations than to causal-mechanistic explanation. (shrink)

Equilibrium explanations use an equilibrium to represent and explain a system’s dynamic behavior. They provide a system with the property of global stability: a system will converge towards and remain in equilibrium regardless of its initial conditions and dynamic process. Thus, equilibrium explanations are generally treated as non-causal explanations. There are two claims subsumed under that comprehensive thesis. The first claim is that equilibrium explanations do not identify any causes because a system with global stability resists manipulation. The second claim (...) is that even if equilibrium explanations do identify causes by manipulation, those causes are embedded in a system’s deeper, underlying structural relationships, and those causes are irrelevant to explaining a system’s behavior. Only the system’s structural relationships are relevant. But equilibrium explanations are not monolithic. I compare dynamic systems with multiple, competing equilibria to systems with a globally stable equilibrium. Equilibrium explanations of the former use intervention on a system’s initial conditions and dynamic process to manipulate equilibria, which identifies causes. Furthermore, a system’s initial conditions and dynamic process are relevant to explaining why one equilibrium is selected instead of another. I then apply these lessons to systems with a globally stable equilibrium and discuss when their corresponding equilibrium explanations have a proper role in the parent sciences. (shrink)

Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...) appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts. 1Introduction2Anchoring3The Basic Deductive-Mathematical Account4The Genuineness Problem5Irrelevance6Relevance and Information7Objections and Replies 7.1Against relevance logic7.2Too epistemic7.3Informational containment8Conclusion. (shrink)

Autonomist accounts of cognitive science suggest that cognitive model building and theory construction (can or should) proceed independently of findings in neuroscience. Common functionalist justifications of autonomy rely on there being relatively few constraints between neural structure and cognitive function (e.g., Weiskopf, 2011). In contrast, an integrative mechanistic perspective stresses the mutual constraining of structure and function (e.g., Piccinini & Craver, 2011; Povich, 2015). In this paper, I show how model-based cognitive neuroscience (MBCN) epitomizes the integrative mechanistic perspective and concentrates (...) the most revolutionary elements of the cognitive neuroscience revolution (Boone & Piccinini, 2016). I also show how the prominent subset account of functional realization supports the integrative mechanistic perspective I take on MBCN and use it to clarify the intralevel and interlevel components of integration. (shrink)

The Enhanced Indispensability Argument appeals to the existence of Mathematical Explanations of Physical Phenomena to justify mathematical Platonism, following the principle of Inference to the Best Explanation. In this paper, I examine one example of a MEPP—the explanation of the 13-year and 17-year life cycle of magicicadas—and argue that this case cannot be used defend the EIA. I then generalize my analysis of the cicada case to other MEPPs, and show that these explanations rely on what I will call ‘optimal (...) representations’, which are representations that capture all that is relevant to explain a physical phenomenon at a specified level of description. In the end, because the role of mathematics in MEPPs is ultimately representational, they cannot be used to support mathematical Platonism. I finish the paper by addressing the claim, advanced by many EIA defendants, that quantification over mathematical objects results in explanations that have more theoretical virtues, especially that they are more general and modally stronger than alternative explanations. I will show that the EIA cannot be successfully defended by appealing to these notions. (shrink)

According to a widespread view in metaphysics and philosophy of science, all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper defends this claim (...) and discusses its significance. The second part of the paper considers whether viewing-as explanations occur in the empirical sciences, focusing on the case of so-called fictional models. It’s sometimes suggested that fictional models can be explanatory even though they fail to represent actual worldly dependence relations. Whether or not such models explain, I suggest, depends on whether we think scientific explanations necessarily give information relevant to intervention and control. Finally, I argue that counterfactual approaches to explanation also have trouble accommodating viewing-as cases. (shrink)

Because idealizations frequently advance scientific understanding, many claim that falsehoods play an epistemic role. In this paper, we argue that these positions greatly overstate idealiza...

A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...) treatment of the problem of mathematical explanations of physical phenomena. This problem is of central importance in two different recent philosophical disputes: the dispute about the existence on non-causal scientific explanations and the dispute between realists and antirealists in the philosophy of mathematics. My aim in this paper is twofold. I will first argue that Lange (2013) and Pincock (2015) fail to make a significant contribution to these disputes. They fail to contribute to the dispute in the philosophy of mathematics because, in this context, their approach can be seen as question begging. They also fail to contribute to the dispute in the general philosophy of science because, as I will argue, there are important problems with the cases discussed by Lange and Pincock. I will then argue that the source of the problems with these two papers has to do with the fact that the piecemeal approach used to account for mathematical explanation is problematic. (shrink)

The free-energy principle states that all systems that minimize their free energy resist a tendency to physical disintegration. Originally proposed to account for perception, learning, and action, the free-energy principle has been applied to the evolution, development, morphology, anatomy and function of the brain, and has been called a postulate, an unfalsifiable principle, a natural law, and an imperative. While it might afford a theoretical foundation for understanding the relationship between environment, life, and mind, its epistemic status is unclear. Also (...) unclear is how the free-energy principle relates to prominent theoretical approaches to life science phenomena, such as organicism and mechanism. This paper clarifies both issues, and identifies limits and prospects for the free-energy principle as a first principle in the life sciences. (shrink)

This contribution sheds light on the role of infinite idealization in structural analysis, by exploring how infinite elements and finite element methods are combined in civil engineering models. This combination, I claim, should be read in terms of a ‘complementarity function’ through which the representational ideal of completeness is reached in engineering model-building. Taking a cue from Weisberg’s definition of multiple-model idealization, I highlight how infinite idealizations are primarily meant to contribute to the prediction of structural behavior in Multiphysics approaches.

Recent literature on non-causal explanation raises the question as to whether explanatory monism, the thesis that all explanations submit to the same analysis, is true. The leading monist proposal holds that all explanations support change-relating counterfactuals. We provide several objections to this monist position. 1Introduction2Change-Relating Monism's Three Problems3Dependency and Monism: Unhappy Together4Another Challenge: Counterfactual Incidentalism4.1High-grade necessity4.2Unity in diversity5Conclusion.

This essay develops an inferential account of model explanation, based on Mauricio Suárez’s inferential conception of scientific representation and Alisa Bokulich’s counterfactual account of model explanation. It is suggested that the fact that a scientific model can explain is essentially linked to how a modeler uses an established model to make various inferences about the target system on the basis of results derived from the model. The inference practice is understood as a two-step activity, with the first step involving making (...) counterfactual statements about the model itself and the second step involving making hypothetical statements transferring over claims derived from the model onto the target. To illustrate how this two-step activity proceeds, an agent-based simulation model is discussed. (shrink)

In the spirit of explanatory pluralism, this chapter argues that causal and noncausal explanations of a phenomenon are compatible, each being useful for bringing out different sorts of insights. After reviewing a model-based account of scientific explanation, which can accommodate causal and noncausal explanations alike, an important core conception of noncausal explanation is identified. This noncausal form of model-based explanation is illustrated using the example of how Earth scientists in a subfield known as aeolian geomorphology are explaining the formation of (...) regularlyspaced sand ripples. The chapter concludes that even when it comes to everyday "medium-sized dry goods" such as sand ripples, where there is a complete causal story to be told, one can find examples of noncausal scientific explanations. (shrink)

Traditionally, a scientific model is thought to provide a good scientific explanation to the extent that it satisfies certain scientific goals that are thought to be constitutive of explanation. Problems arise when we realize that individual scientific models cannot simultaneously satisfy all the scientific goals typically associated with explanation. A given model’s ability to satisfy some goals must always come at the expense of satisfying others. This has resulted in philosophical disputes regarding which of these goals are in fact necessary (...) for explanation, and as such which types of models can and cannot provide explanations. Explanatory monists argue that one goal will be explanatory in all contexts, while explanatory pluralists argue that the goal will vary based on pragmatic considerations. In this paper, I argue that such debates are misguided, and that both monists and pluralists are incorrect. Instead of any goal being given explanatory priority over others in a given context, the different goals are all deeply dependent on one another for their explanatory power. Any model that sacrifices some explanatory goals to attain others will always necessarily undermine its own explanatory power in the process. And so when forced to choose between individual scientific models, there can be no explanatory victors. Given that no model can satisfy all the goals typically associated with explanation, no one model in isolation can provide a good scientific explanation. Instead we must appeal to collections of models. Collections of models provide an explanation when they satisfy the web of interconnected goals that justify the explanatory power of one another. (shrink)

This article examines three candidate cases of non-causal explanation in computational neuroscience. I argue that there are instances of efficient coding explanation that are strongly analogous to examples of non-causal explanation in physics and biology, as presented by Batterman, Woodward, and Lange. By integrating Lange’s and Woodward’s accounts, I offer a new way to elucidate the distinction between causal and non-causal explanation, and to address concerns about the explanatory sufficiency of non-mechanistic models in neuroscience. I also use this framework to (...) shed light on the dispute over the interpretation of dynamical models of the brain. _1_ Introduction _1.1_ Efficient coding explanation in computational neuroscience _1.2_ Defining non-causal explanation _2_ Case I: Hybrid Computation _3_ Case II: The Gabor Model Revisited _4_ Case III: A Dynamical Model of Prefrontal Cortex _4.1_ A new explanation of context-dependent computation _4.2_ Causal or non-causal? _5_ Causal and Non-causal: Does the Difference Matter? (shrink)

In this paper, I first argue against various attempts to justify idealizations in scientific models that explain by showing that they are harmless and isolable distortions of irrelevant features. In response, I propose a view in which idealized models are characterized as providing holistically distorted representations of their target system. I then suggest an alternative way that idealized modeling can be justified by appealing to universality.

The epistemic conception of scientific progress equates progress with accumulation of scientific knowledge. I argue that the epistemic conception fails to fully capture scientific progress: theoretical progress, in particular, can transcend scientific knowledge in important ways. Sometimes theoretical progress can be a matter of new theories ‘latching better onto unobservable reality’ in a way that need not be a matter of new knowledge. Recognising this further dimension of theoretical progress is particularly significant for understanding scientific realism, since realism is naturally (...) construed as the claim that science makes theoretical progress. Some prominent realist positions are best understood in terms of commitment to theoretical progress that cannot be equated with accumulation of scientific knowledge. (shrink)

Within the modeling literature, there is often an implicit assumption about the relationship between a given model and a scientific explanation. The goal of this article is to provide a unified framework with which to analyze the myriad relationships between a model and an explanation. Our framework distinguishes two fundamental kinds of relationships. The first is metaphysical, where the model is identified as an explanation or as a partial explanation. The second is epistemological, where the model produces understanding that is (...) related to the explanation of interest. Our analysis reveals that the epistemological relationships are not always dependent on the metaphysical relationships, contrary to what has been assumed by many philosophers of science. Moreover, we identify several importantly different ways that scientific models instantiate these relationships. We argue that our framework provides novel insights concerning the nature of models, explanation, idealization, and understanding. (shrink)

The focus in the literature on scientific explanation has shifted in recent years towards model-based approaches. In recent work, Alisa Bokulich has argued that idealization has a central role to play in explanation. Bokulich claims that certain highly-idealized, structural models can be explanatory, even though they are not considered explanatory by causal, mechanistic, or covering law accounts of explanation. This paper focuses on Bokulich’s account in order to make the more general claim that there are problems with maintaining that a (...) structural criterion can capture the way that highly-idealized models explain. This paper examines Bokulich’s claim that the structural model explanation of quantum wavefunction scarring, featuring semiclassical mechanics, is deeper than the explanation provided by the local quantum model. The challenge for Bokulich is to show that the semiclassical model answers a wider range of w-questions, as this is her method of assessing structural information. I look at two reasonable approaches employing w-questions, and I argue that neither approach is ultimately satisfactory. Because structural similarity has preferences for more fundamental models, I argue that the local quantum model provides explanations that at least as deep as the semiclassical ones. The criterion either wrongly identifies all models as explanatory, or prefers models from fundamental theory. Either way, it cannot capture the way that highly-idealized models explain. (shrink)

Causal accounts of scientific explanation are currently broadly accepted (though not universally so). My first task in this paper is to show that, even for a causal approach to explanation, significant features of explanatory practice are not determined by settling how causal facts bear on the phenomenon to be explained. I then develop a broadly causal approach to explanation that accounts for the additional features that I argue an explanation should have. This approach to explanation makes sense of several aspects (...) of actual explanatory practice, including the widespread use of equilibrium explanations, the formulation of distinct explanations for a single event, and the tight relationship between explanations of events and explanations of causal regularities. (shrink)

Recent years have seen increasing interest in interventionist analyses of metaphysical explanation. One area where interventionism traditionally shines, is in providing an account of explanatory depth; the sense in which explanation comes in degrees. However, the literature on metaphysical explanation has left the notion of depth almost entirely unexplored. In this paper I shall attempt to rectify this oversight by motivating an interventionist analysis of metaphysical explanatory depth (MED), in terms of the range of interventions under which a metaphysically explanatory (...) generalization remains invariant. After elucidating the notion through a toy-example, I demonstrate the important work which MED can perform in characterizing debate within contemporary metaphysics. Focusing upon rival approaches to explaining the identity and distinctness of concrete objects, I argue that the progress achieved in this debate can be characterized in terms of increasing explanatory depth. Having made an initial case for the utility of MED, I then turn this analysis to the metaphysics of explanation itself. By adopting an interventionist framework with respect to MED, I will show that we can assess the depth of competing theories of explanation. This application has two interesting results: first, it suggests that an interventionist analysis of explanation provides deeper explanations of the connection between explanans and explanandum than rival accounts; and second, it suggests that explanations provided by interventionism become deeper still, if one accepts that this methodology ranges over metaphysical, as well as causal, instances. (shrink)

If ontic dependence is the basis of explanation, there cannot be mathematical explanations. Accounting for the explanatory dependency between mathematical properties and empirical phenomena poses i...

Brette argues that coding as a concept is inappropriate for explanations of neurocognitive phenomena. Here, we argue that Brette's conceptual analysis mischaracterizes the structure of causal claims in coding and other forms of analysis-by-decomposition. We argue that analyses of this form are permissible and conceptually coherent and offer essential tools for building and developing models of neurocognitive systems like the brain.

Functional decomposition is an important goal in the life sciences, and is central to mechanistic explanation and explanatory reduction. A growing literature in philosophy of science, however, has challenged decomposition-based notions of explanation. ‘Holists’ posit that complex systems exhibit context-sensitivity, dynamic interaction, and network dependence, and that these properties undermine decomposition. They then infer from the failure of decomposition to the failure of mechanistic explanation and reduction. I argue that complexity, so construed, is only incompatible with one notion of decomposition, (...) which I call ‘atomism’, and not with decomposition writ large. Atomism posits that function ascriptions must be made to parts with minimal reference to the surrounding system. Complexity does indeed falsify atomism, but I contend that there is a weaker, ‘contextualist’ notion of decomposition that is fully compatible with the properties that holists cite. Contextualism suggests that the function of parts can shift with external context, and that interactions with other parts might help determine their context-appropriate functions. This still admits of functional decomposition within a given context. I will give examples based on the notion of oscillatory multiplexing in systems neuroscience. If contextualism is feasible, then holist inferences are faulty—one cannot infer from the presence of complexity to the failure of decomposition, mechanism, and reductionism. (shrink)

Recently, many have argued that there are certain kinds of abstract mathematical explanations that are noncausal. In particular, the irrelevancy approach suggests that abstracting away irrelevant causal details can leave us with a noncausal explanation. In this paper, I argue that the common example of Renormalization Group explanations of universality used to motivate the irrelevancy approach deserves more critical attention. I argue that the reasons given by those who hold up RG as noncausal do not stand up to critical scrutiny. (...) As a result, the irrelevancy approach and the line between casual and noncausal explanation deserves more scrutiny. (shrink)

Candidates for fundamental physical laws rarely, if ever, employ higher than second time derivatives. Easwaran sketches an enticing story that purports to explain away this puzzling fact and thereby provides indirect evidence for a particular set of metaphysical theses used in the explanation. I object to both the scope and coherence of Easwaran's account, before going on to defend an alternative, more metaphysically deflationary explanation: in interacting Lagrangian field theories, it is either impossible or very hard to incorporate higher than (...) second time derivatives without rendering the vacuum state unstable. The so-called Ostrogradski instability represents a powerful constraint on the construction of new field theories and supplies a novel, largely overlooked example of non-causal explanation in physics. (shrink)

Explaining the behaviour of ecosystems is one of the key challenges for the biological sciences. Since 2000, new-mechanicism has been the main model to account for the nature of scientific explanation in biology. The universality of the new-mechanist view in biology has been however put into question due to the existence of explanations that account for some biological phenomena in terms of their mathematical properties (mathematical explanations). Supporters of mathematical explanation have argued that the explanation of the behaviour of ecosystems (...) is usually provided in terms of their mathematical properties, and not in mechanistic terms. They have intensively studied the explanation of the properties of ecosystems that behave following the rules of a non-random network. However, no attention has been devoted to the study of the nature of the explanation in those that form a random network. In this paper, we cover that gap by analysing the explanation of the stability behaviour of the microbiome recently elaborated by Coyte and colleagues, to determine whether it fits with the model of explanation suggested by the new-mechanist or by the defenders of mathematical explanation. Our analysis of this case study supports three theses: (1) that the explanation is not given solely in terms of mechanisms, as the new-mechanists understand the concept; (2) that the mathematical properties that describe the system play an essential explanatory role, but they do not exhaust the explanation; (3) that a non-previously identified appeal to the type of interactions that the entities in the network can exhibit, as well as their abundance, is also necessary for Coyte and colleagues’ account to be fully explanatory. From the combination of these three theses we argue for the necessity of an integrative pluralist view of the nature of behaviour explanation when this is given by appealing to the existence of a random network. (shrink)

In this paper we assess the explanatory role of idealizations in ‘design explanations’, a type of functional explanation used in biology. In design explanations, idealizations highlight which factors make a difference to phenomena to be explained: hypothetical, idealized, organisms are invoked to make salient which traits of extant organisms make a difference to organismal fitness. This result negates the view that idealizations serve only pragmatic benefits, and complements the view that idealizations highlight factors that do not make a difference. This (...) analysis in particular strengthens the perspective that idealizations are means to highlight difference making factors, and identifies a novel, more direct role for idealizations in doing so. It thus offers a novel argument why in some explanatory contexts idealizations are in-eliminable. (shrink)