This chapter examines the relationship between laws and mechanisms as approaches to characterising generalizations and explanations in science. I give an overview of recent historical discussions where laws failed to satisfy stringent logical criteria, opening the way for mechanisms to be investigated as a way to explain regularities in nature. This followed by a critical discussion of contemporary debates about the role of laws versus mechanisms in describing versus explaining regularities. I conclude by offering new arguments for two roles for (...) laws that mechanisms cannot subsume, one epistemically optimistic and one pessimistic, both broadly Humean. Do note that this piece is not primarily Hume exegesis; it is more of a riff in the key of Hume. (shrink)

In this paper I present and critically discuss the main strategies that Bohr used and could have used to fend off the charge that his interpretation does not provide a clear-cut distinction between the classical and the quantum domain. In particular, in the first part of the paper I reassess the main arguments used by Bohr to advocate the indispensability of a classical framework to refer to quantum phenomena. In this respect, by using a distinction coming from an apparently unrelated (...) philosophical corner, we could say that Bohr is not a revisionist philosopher of physics but rather a descriptivist one in the sense of Strawson. I will then go on discussing the nature of the holistic link between classical measurement apparatuses and observed system that he also advocated. The oft-repeated conclusion that Bohr’s interpretation of the quantum formalism is untenable can only be established by giving his arguments as much force as possible, which is what I will try to do in the following by remaining as faithful as possible to his published work. (shrink)

The goal of this paper is to develop a counterfactual theory of explanation. The CTE provides a monist framework for causal and non-causal explanations, according to which both causal and non-causal explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I argue that the CTE is applicable to two paradigmatic examples of non-causal explanations: Euler’s explanation and renormalization group explanations of universality.

A number of philosophers have recently suggested that some abstract, plausibly non-causal and/or mathematical, explanations explain in a way that is radically dif- ferent from the way causal explanation explain. Namely, while causal explanations explain by providing information about causal dependence, allegedly some abstract explanations explain in a way tied to the independence of the explanandum from the microdetails, or causal laws, for example. We oppose this recent trend to regard abstractions as explanatory in some sui generis way, and argue (...) that a prominent ac- count of causal explanation can be naturally extended to capture explanations that radically abstract away from microphysical and causal-nomological details. To this end, we distinguish di erent senses in which an explanation can be more or less abstract, and analyse the connection between explanations’ abstractness and their explanatory power. According to our analysis abstract explanations have much in common with counterfactual causal explanations. (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)

This paper examines explanations that turn on non-local geometrical facts about the space of possible configurations a system can occupy. I argue that it makes sense to contrast such explanations from "geometry of motion" with causal explanations. I also explore how my analysis of these explanations cuts across the distinction between kinematics and dynamics.

The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles—some ‘thick’ and ontologically committing, others ‘thin’ (...) and ontologically peripheral—and examine this distinction in relation to some notable ‘ontic’ accounts of explanation. I also discuss the issue in the broader context of other ‘explanationist’ realist arguments. (shrink)

This paper argues that in at least some cases, one proof of a given theorem is deeper than another by virtue of supplying a deeper explanation of the theorem — that is, a deeper account of why the theorem holds. There are cases of scientific depth that also involve a common abstract structure explaining a similarity between two otherwise unrelated phenomena, making their similarity no coincidence and purchasing depth by answering why questions that separate, dissimilar explanations of the two phenomena (...) cannot correctly answer. The connections between explanation, depth, unification, power, and coincidence in mathematics and science are compared. (shrink)

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

Sober [2011] argues that some causal statements are a priori true and that a priori causal truths are central to explanations in the theory of natural selection. Lange and Rosenberg [2011] criticize Sober's argument. They concede that there are a priori causal truths, but maintain that those truths are only ‘minimally causal’. They also argue that explanations that are built around a priori causal truths are not causal explanations, properly speaking. Here we criticize both of Lange and Rosenberg's claims.

It is widely believed that mathematics carries a substantial part of the explanatory burden in science. However, mathematics can also play important heuristic roles of a different kind, being a source of new ideas and approaches, allowing us to build toy models, enhancing expressive power and providing fruitful conceptualizations. In this paper, we focus on the application of dynamical systems theory (DST) within the extended cognition (EC) field of cognitive science, considering this case study to be a good illustration of (...) a general phenomenon. In the paper, we justify both a negative and a positive claim. The negative claim is that dynamical systems theory hardly plays any explanatory role in EC research. We justify our claim by analyzing several accounts of the explanatory role of mathematics and stressing the way mathematical arguments are used in explanations. Our positive claim is that even though, for now, DST has no explanatory power in many of the EC approaches, it still plays an important heuristic role there. In particular, using mathematical notions improves the expressive power of the language and gives a sense of understanding of the phenomena under investigation. The case study of EC allows us to identify and analyze this important role of mathematics, which seems to be neglected in contemporary discussions. (shrink)

The ontic conception of explanation is predicated on the proposition that “explanation is a relation between real objects in the world” and hence, according to this approach, scientific explanation cannot take place absent such a premise. Despite the fact that critics have emphasized several drawbacks of the ontic conception, as for example its inability to address the so-called “abstract explanations”, the debate is not settled and the ontic view can claim to capture cases of explanation that are non-abstract, such as (...) causal relations between events. However, by eliminating the distinction between abstract and non-abstract explanations, it follows that ontic and epistemic proposals can no longer contend to capture different cases of explanation and either all are captured by the ontic view or all are captured by the epistemic view. On closer inspection, it turns out that the ontic view deals with events that fall outside the scientists’ scope of observation and that it does not accommodate common instances of explanation such as explanations from false propositions and hence it cannot establish itself as the dominant philosophical stance with respect to explanation. On the contrary, the epistemic conception does account for almost all episodes of explanation and can be described as a relation between representations, whereby the explanans transmit information to the explanandum and that this information can come, dependent on context, in the form of any of the available theories of explanation (law-like, unificatory, causal and non-causal). The range of application of the ontic view thus is severely restricted to trivial cases of explanation that come through direct observation of the events involved in an explanation and explanation is to be mostly conceived epistemically. (shrink)

There is a major debate as to whether there are non-causal mathematical explanations of physical facts that show how the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws. We focus on Marc Lange’s account of distinctively mathematical explanations to argue that purported mathematical explanations are essentially causal explanations in disguise and are no different from ordinary applications of mathematics. This is because these explanations work not by appealing to what the (...) world must be like as a matter of mathematical necessity but by appealing to various contingent causal facts. (shrink)

In this article I examine several related views expressed by Robin Hendry concerning molecular structure, emergence and chemical bonding. There is a long-standing problem in the philosophy of chemistry arising from the fact that molecular structure cannot be strictly derived from quantum mechanics. Two or more compounds which share a molecular formula, but which differ with respect to their structures, have identical Hamiltonian operators within the quantum mechanical formalism. As a consequence, the properties of all such isomers yield precisely the (...) same calculated quantities such as their energies, dipole moments etc. The only means through which the difference between the isomers can be recovered is to build their structures into the quantum mechanical calculations, something that is carried out by the application of the Born-Oppenheimer approximation. Consequently, it has been argued by many authors that molecular structure is written in ‘by hand’ rather than derived. Robin Hendry is one such author, but he goes a great deal further by proposing that this situation implies the existence of emergence and downward causation. In the current article I argue that there are alternative explanations which render emergence and downward causation redundant. Such an alternative lies in the notion of quantum decoherence and the appeal to work in the foundations of physics, which posits that the various isomers exist as a superposition until their wavefunctions are collapsed either by observation or by interacting with their environment. Hendry also alludes to a debate among chemists as to whether chemical bonds are real or not, in the sense of directional connections between two or more nuclei in any given molecule. I reject this view and propose that the structural and energetic views of chemical bonding, that have been discussed by some philosophers of chemistry including Hendry, do not refer to any essential ontological differences. I agree that chemists view bonding in a more realistic fashion and may consider bonds to be in some senses real, while physicists may consider bonding in more abstract energetic terms. However, I do not believe that such differences in scientific practice and attitudes should be considered to offer a window as to the ontological status of bonding or whether bonding is real. Finally, I discuss the kinetic energy school of chemical bonding which would seem to challenge any notion of bonds as directional entities, since bonding is no longer regarded as being primarily due to the build-up of electron density between nuclei. (shrink)

The philosophical debate around the impact of machine learning in science is often framed in terms of a choice between AI and classical methods as mutually exclusive alternatives involving difficult epistemological trade-offs. A common worry regarding machine learning methods specifically is that they lead to opaque models that make predictions but do not lead to explanation or understanding. Focusing on the field of molecular biology, I argue that in practice machine learning is often used with explanatory aims. More specifically, I (...) argue that machine learning can be tightly integrated with other, more traditional, research methods and in a clear sense can contribute to insight into the causal processes underlying phenomena of interest to biologists. One could even say that machine learning is not the end of theory in important areas of biology, as has been argued, but rather a new beginning. I support these claims with a detailed discussion of a case study involving gene regulation by microRNAs. (shrink)

Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic structures and the explanatory relation between them as an ontic relation (e.g., Pincock 2015, Povich 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it (...) is ontic, the conventionalist account seems to avoid a convincing objection to other ontic accounts (Kuorikoski 2021). (shrink)

Whatever you think of Bertrand Russell’s famous claim that the ‘law of causality’ is (at least as of 1912) redundant in the ‘advanced sciences’, it is nonethele.

One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should not be thought of as describing, in any substantive sense, (...) an abstract realm of eternal mathematical objects, as traditional platonists have thought. In Rules to Infinity, this view, which I call mathematical normativism, is updated with contemporary philosophical tools, and it is argued that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the platonistic idea that there exist abstract mathematical objects that explain such truths. Furthermore, Rules to Infinity defends a particular account of the distinction between scientific explanations that are in some sense distinctively mathematical – those that explain natural phenomena in some uniquely mathematical way – and those that are only standardly mathematical, and it lays out desiderata for any account of this distinction. Normativism is compared with other prominent views in the philosophy of mathematics such as neo-Fregeanism, fictionalism, conventionalism, and structuralism. Rules to Infinity serves as an entry point into debates at the forefront of philosophy of science and mathematics, and it defends novel positions in these debates. (shrink)

Most psychological research aims to uncover generalizations about the mind that hold across subjects. Philosophical discussions of scientific explanation have focused on such generalizations, but in doing so, have often overlooked an important phenomenon: variation. Variation is ubiquitous in psychology and many other domains, and an important target of explanation in its own right. Here I characterize explananda that concern individual differences and formulate an account of what it takes to explain them. I argue that the notion of actual difference (...) making, the only causal concept in the literature that explicitly addresses variation, cannot be used to ground such an account. Instead, I propose a view on which explaining individual differences involves identifying causes that could be intervened on to reduce the variability in the population. This account provides criteria of success for explaining variation and deepens our understanding of causal explanation. (shrink)

The reduction of grounding to causation, or each to a more general relation of which they are species, has sometimes been justified by the impressive inferential capacity of structural equation modelling, causal Bayes nets, and interventionist causal modelling. Many criticisms of this assimilation focus on how causation is inadequate for grounding. Here, I examine the other direction: how treating grounding in the image of causation makes the resulting view worse for causation. The distinctive features of causal modelling that make this (...) connection appealing are distorted beyond use by forcing them to fit onto grounding. The very inferential strength that makes causation attractive is only possible because of a narrow construal of what counts as a causal relation; as soon as that broadens, the inferential capacity markedly diminishes. Making causation suitable for application to grounding spoils what was appealing about causation for this task in the first place. However, grounding need not appeal to causation: causal modelling does not have exclusive claim to structural equation modeling or other formal techniques of modelling structure. I offer a case in favour of a different kind of metaphysical frugality, which tend towards narrow, more restrictive construals of relations like causation or grounding, because then each relation behaves more homogenously. This more homogenous behavior delivers stronger inferential power per relation even though there may be more relations to which one is committed. (shrink)

The bridges of Königsberg case has been widely cited in recent philosophical discussions on scientific explanation as a potential example of a structural explanation of a physical phenomenon. However, when discussing this case, different authors have focused on two different versions, depending on what they take the explanandum to be. In one version, the explanandum is the _failure_ of a given individual in performing an Eulerian walk over the bridge system. In the other version, the explanandum is the _impossibility_ of (...) performing an Eulerian walk over the bridges. The goal of this paper is to show that only the latter version amounts to a real case of a structural explanation. I will also suggest how to fix the first version, and show how my remarks apply to other purported cases of structural explanations. (shrink)

Arguments for an extended evolutionary synthesis often center on the concept of “reciprocal causation.” Proponents argue that reciprocal causation is superior to standard models of evolutionary causation for at least two reasons. First, it leads to better scientific models with more predictive power. Second, it more accurately represents the causal structure of the biological world. Simply put, proponents of an extended evolutionary synthesis argue that reciprocal causation is empirically and explanatorily apt relative to competing causal frameworks. In this paper, I (...) present quantitative survey data from faculty members in biology departments at universities across the United States to evaluate this claim. The survey data indicate that a majority of the participants do not agree (i.e., most either disagree or neither agree nor disagree) that the concept of reciprocal causation confers a larger advantage on research practices. However, a majority of the participants agree that the causal framework of the extended evolutionary synthesis more accurately represents the structure of the biological world. These results demonstrate that the explanatory merits of a conceptual framework and its practical utility can come apart in interesting and informative ways. (shrink)

Accounts of scientific explanation disagree about what’s required for a cause, law, or other fact to be a reason why an event occurs. In short, they disagree about the conditions for explanatory relevance. Nonetheless, most accounts presuppose that claims about explanatory relevance play a descriptive role in tracking reality. By rejecting the need for this descriptivist assumption, I develop an expressivist account of explanatory relevance and explanation: to judge that an answer is explanatory is to express an attitude of _being (...) for being satisfied by that answer_. I show how expressivism vindicates ordinary scientific discourse about explanation, including claims about the objectivity and mind-independence of explanations. By avoiding commitment to ontic relevance relations, I rehabilitate an irrealist conception of explanation. (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

A central goal of the scientific endeavor is to explain phenomena. Scientists often attempt to explain a phenomenon by way of representing it in some manner—such as with mathematical equations, models, or theory—which allows for an explanation of the phenomenon under investigation. However, in developing scientific representations, scientists typically deploy simplifications and idealizations. As a result, scientific representations provide only partial, and often distorted, accounts of the phenomenon in question. Philosophers of science have analyzed the nature and function of how (...) scientists construct representations, deploy idealizations, and provide explanations. As such, our aim in this special issue is to bring these three pillars of research into closer contact with the contributions to it focusing on three main themes. -/- The first set of papers, Alan Baker (2021) and Marc Lange (2021), address mathematical explanations in science. Baker (2021), a proponent of mathematical Platonism, examines its capacity to evade the critique that the so-called Enhanced Indispensability Argument is circular. Lange (2021) examines distinctively mathematical explanations, arguing that neither Platonism nor representationalism are successful paths, and instead argues in favor of Aristotelian realism. A second theme emerging from the papers in this special issue is the impact that various conceptualizations of idealization have on our abilities to offer scientific explanations, to pro- duce an analysis of what explanations are or should be, and to understand scientific representation. Peter Tan (2021) suggests amending inferentialist accounts of scientific representation to account for inconsistent idealizations. Michael Strevens (2021) advocates a view wherein the introduction of idealizations into a model is legitimate so long as it pertains to non-difference-making factors, arguing for a logical reading of the notion of difference-making. Natalia Carrillo and Tarja Knuuttila (2022) offer an alternative account to the idealization-as-distortion view, emphasizing instead the holistic nature of idealization. -/- Finally, contributions by Carrillo and Knuuttila (2022), Terzian (2021), Valente (2021), and Rodriguez (2021) illustrate how issues regarding idealization, representation, and explanation are applied to specific contexts and across various sciences. Carrillo and Knuuttila (2022) examine conceptions of idealization in the context of models of the nerve impulse. Giulia Terzian (2021) extends the discussion of idealizations to the context of generative linguistics. Giovanni Valente (2021) examines how idealizations and evaluations of accurate representation impact capacities to explain phenomena in the context of statistical thermodynamics. Quentin Rodriguez (2021) examines the role of idealizations and analogies in various strategies to explain critical phenomena. -/- In what follows, we offer a brief overview of important philosophical issues connected to representation, idealization, and explanation in science. We then provide short summaries of the eight papers in this special issue. (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)

In this paper I present a case study of mathematical explanation in science that is new to the philosophical literature, and that arises in the context of estimating the energetic costs of running in bipedal animals. I refer to this as the Bipedal Gait Costs explanation. I argue that it is important for examples of applied mathematics to be driven not just by philosophical and mathematical concerns but also by scientific concerns. After a detailed presentation of the BGC case study, (...) I discuss ways in which it is different from standard examples of MES. One distinctive aspect of BGC is that substantive mathematics occurs at two different levels. I argue for a distinction to be drawn between the mathematical modeling that occurs at one level, which is non-explanatory, and the mathematical theorem which is applied to results gleaned from these models, which is explanatory. I conclude by drawing some connections with broader indispensability-based arguments for platonism in the philosophy of mathematics. (shrink)

Recently, there have been several attempts to generalize the counterfactual theory of causal explanations to mathematical explanations. The central idea of these attempts is to use conditionals whose antecedents express a mathematical impossibility. Such countermathematical conditionals are plugged into the explanatory scheme of the counterfactual theory and—so is the hope—capture mathematical explanations. Here, I dash the hope that countermathematical explanations simply parallel counterfactual explanations. In particular, I show that explanations based on countermathematicals are susceptible to three problems counterfactual explanations do (...) not face. These problems seriously challenge the prospects for a counterfactual theory of explanation that is meant to cover mathematical explanations. (shrink)

Non-causal accounts of action explanation have long been criticized for lacking a positive thesis, relying primarily on negative arguments to undercut the standard Causal Theory of Action The Stanford Encyclopedia of Philosophy, 2016). Additionally, it is commonly thought that non-causal accounts fail to provide an answer to Donald Davidson’s challenge for theories of reasons explanations of actions. According to Davidson’s challenge, a plausible non-causal account of reasons explanations must provide a way of connecting an agent’s reasons, not only to what (...) she ought to do, but to what she actually does. That is, such explanations must be truth-apt, not mere rationalizations. My aim in this paper is to show how a non-causal account of action can provide explanations that are truth-apt and genuinely explanatory. To make this argument, I take as a given an account of the practical syllogism discussed by Michael Thompson and Eric Wiland, according to which the practical syllogism is truly practical rather than propositional in nature. Next, I present my primary positive thesis: reasons for actions have explanatory power in virtue of being parts of a structure—the practical syllogism—that contains the action being explained. I then argue that structural action explanations can meet Davidson’s challenge and that they genuinely explain actions. Finally, I conclude by addressing some objections to my argument. (shrink)

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...) should accept that physical systems have mathematical properties, and why a property based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot. (shrink)

Proponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the ‘directionality’ of explanation, i.e., the requirement that if X explains Y , then not-Y does not explain not-X . Using topological explanations as an illustration, we argue that non-ontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which neuroscientists rely on multiplexes (...) involving both functional and anatomical connectivity in their topological explanations vividly illustrate why ontic considerations are frequently (if not always) irrelevant to explanatory directionality. Therefore, directionality poses no problem to non-ontic conceptions of explanation. (shrink)

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is to (...) show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...) that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

The dominant view today on evolutionary progress is that it has been thoroughly debunked. Even value-neutral progress concepts are seen to lack important theoretical underpinnings: natural selection provides no rationale for progress, and natural selection need not even be invoked to explain large-scale evolutionary trends. In this paper I challenge this view by analysing how natural selection acts in heterogeneous environments. This not only undermines key debunking arguments, but also provides a selectionist rationale for a pattern of “evolutionary unfolding”, where (...) life radiates across an increased range of exploitation of environmental heterogeneity. (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)

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...

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)

Is it possible to know anything about life we have not yet encountered? We know of only one example of life: our own. Given this, many scientists are inclined to doubt that any principles of Earth’s biology will generalize to other worlds in which life might exist. Let’s call this the “N = 1 problem.” By comparison, we expect the principles of geometry, mechanics, and chemistry would generalize. Interestingly, each of these has predictable consequences when applied to biology. The surface-to-volume (...) property of geometry, for example, limits the size of unassisted cells in a given medium. This effect is real, precise, universal, and predictive. Furthermore, there are basic problems all life must solve if it is to persist, such as resistance to radiation, faithful inheritance, and energy regulation. If these universal problems have a limited set of possible solutions, some common outcomes must consistently emerge. In this chapter, I discuss the N = 1 problem, its implications, and my response (Mariscal 2014). I hold that our current knowledge of biology can justify believing certain generalizations as holding for life anywhere. Life on Earth may be our only example of life, but this is only a reason to be cautious in our approach to life in the universe, not a reason to give up altogether. In my account, a candidate biological generalization is assessed by the assumptions it makes. A claim is accepted only if its justification includes principles of evolution, but no contingent facts of life on Earth. (shrink)

Mathematics is often taken to play one of two roles in the empirical sciences: either it represents empirical phenomena or it explains these phenomena by imposing constraints on them. This article identifies a third and distinct role that has not been fully appreciated in the literature on applicability of mathematics and may be pervasive in scientific practice. I call this the “bridging” role of mathematics, according to which mathematics acts as a connecting scheme in our explanatory reasoning about why and (...) how two different descriptions of an empirical phenomenon relate to each other. I discuss two bridging roles appearing in biological and physical explanations. (shrink)

This thesis starts with three challenges to the structuralist accounts of applied mathematics. Structuralism views applied mathematics as a matter of building mapping functions between mathematical and target-ended structures. The first challenge concerns how it is possible for a non-mathematical target to be represented mathematically when the mapping functions per se are mathematical objects. The second challenge arises out of inconsistent early calculus, which suggests that mathematical representation does not require rigorous mathematical structures. The third challenge comes from renormalisation group (...) (RG) explanations of universality. It is argued that the structural mapping between the world and a highly abstract minimal model adds little value to our understanding of how RG obtains its explanatory force. I will address the first and second challenges from the similarity perspective. The similarity account captures representations as similarity relations, providing a more flexible and broader conception of representation than structuralism. It is the specification of the respect and degree of similarity that forges mathematics into a context of representation and directs it to represent a specific system in reality. Structuralism is treatable as a tool for explicating similarity rela-tions set-theoretically. The similarity account, combined with other approaches (e.g., Nguyen and Frigg’s extensional abstraction account and van Fraassen’s pragmatic equivalence), can dissolve the first challenge. Additionally, I will make a structuralist response to the second challenge, and suggestions regarding the role of infinitesimals from the similarity perspective. In light of the similarity account, I will propose the “hotchpotch picture” as a method-ological reflection of our study of representation and explanation. Its central insight is to dissect a representation or an explanation into several aspects and use different theories (that are usually thought of competing) to appropriate each of them. Based on the hotchpotch picture, RG explanations can be dissected to the “indexing” and “inferential” conceptions of explanation, which are captured or characterised by structural mappings. Therefore, structuralism accommodates RG explanations, and the third challenge is resolved. (shrink)

Science frequently gives us multiple, compatible ways of solving the same problem or formulating the same theory. These compatible formulations change our understanding of the world, despite providing the same explanations. According to what I call "conceptualism," reformulations change our understanding by clarifying the epistemic structure of theories. I illustrate conceptualism by analyzing a typical example of symmetry-based reformulation in chemical physics. This case study poses a problem for "explanationism," the rival thesis that differences in understanding require ontic explanatory differences. (...) To defend conceptualism, I consider how prominent accounts of explanation might accommodate this case study. I argue that either they do not succeed, or they generate a skeptical challenge. (shrink)

When a train operator tells us that our train will be late ‘because of delays’, their attempt at explanation fails because there is insufficient distance between the explanans and the explanandum. In this paper, I motivate and defend an account of ‘explanatory distance’, based on the idea that explanations give information about dependence. I show that this account offers useful resources for addressing problem cases, including recent debates about grounding explanation, and the historical case of Molière’s dormitive virtue.

Many philosophers argue that explanatoriness plays no special role in confirmation – that “inference to the best explanation” (IBE) incorrectly demands giving hypotheses extra credit for their potential explanatory qualities beyond the credit they already deserve for their predictive successes. This paper argues against one common strategy for responding to this thought – that is, for trying to fit IBE within a Bayesian framework. That strategy argues that a hypothesis’ explanatory quality (its “loveliness”) contributes either to its prior probability or (...) to its likelihood. This paper argues that this strategy fails because it must give different treatments to two hypotheses that are unlovely for the very same reason. The strategy therefore loses the insight into scientific reasoning that its reconstruction in terms of IBE is supposed to provide. The paper then provides a Bayesian account of the confirmatory role of explanatoriness that represents explanatory quality as having an impact in the same place for two hypotheses that are unlovely for the very same reason. This approach works by “putting explanation back into IBE” – that is, by invoking hypotheses that refer explicitly to scientific explanation and by invoking the agent's background opinions regarding the kind of explanation that the evidence is liable to have. On this approach, there is no list of “explanatory virtues” the possession of which always helps to make an explanation better. Rather, for different facts, there are different characteristics that our background knowledge of other explanations gives us some reason to expect the given fact's explanation to possess. (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)

At the beginning of the 20th century, Gestalt psychologists put forward the concept of psychoneural isomorphism, which was meant to replace Fechner’s obscure notion of psychophysical parallelism and provide a heuristics that may facilitate the search for the neural correlates of the mind. However, the concept has generated much confusion in the debate, and today its role is still unclear. In this contribution, I will attempt a little conceptual spadework in clarifying the concept of psychoneural isomorphism, focusing exclusively on conscious (...) visual perceptual experience and its neural correlates. Firstly, I will outline the history of our concept, and its alleged metaphysical and epistemic roles. Then, I will clarify the nature of isomorphism and rule out its metaphysical role. Finally, I will review some epistemic roles of our concept, zooming in on the work of Jean Petitot, and suggest that it does not play a relevant heuristic role. I conclude suggesting that psychoneural isomorphism might be an indicator of robustness for certain mathematical descriptions of perceptual content. (shrink)

In the last two decades, philosophy of neuroscience has predominantly focused on explanation. Indeed, it has been argued that mechanistic models are the standards of explanatory success in neuroscience over, among other things, topological models. However, explanatory power is only one virtue of a scientific model. Another is its predictive power. Unfortunately, the notion of prediction has received comparatively little attention in the philosophy of neuroscience, in part because predictions seem disconnected from interventions. In contrast, we argue that topological predictions (...) can and do guide interventions in science, both inside and outside of neuroscience. Topological models allow researchers to predict many phenomena, including diseases, treatment outcomes, aging, and cognition, among others. Moreover, we argue that these predictions also offer strategies for useful interventions. Topology-based predictions play this role regardless of whether they do or can receive a mechanistic interpretation. We conclude by making a case for philosophers to focus on prediction in neuroscience in addition to explanation alone. (shrink)

Lange argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations, the core explanatory facts are either modally stronger than facts about ordinary causal law or understood to be constitutive of the physical task or arrangement at issue. Craver and Povich argue that Lange’s account of DME fails to exclude certain “reversals”. Lange has replied that his account can avoid these directionality charges. Specifically, Lange argues that in legitimate DMEs, (...) but not in their “reversals,” the empirical fact appealed to in the explanation is “understood to be constitutive of the physical task or arrangement at issue” in the explanandum. I argue that Lange’s reply is unsatisfactory because it leaves the crucial notion of being “understood to be constitutive of the physical task or arrangement” obscure in ways that fail to block “reversals” except by an apparent ad hoc stipulation or by abandoning the reliance on understanding and instead accepting a strong realism about essence. (shrink)

Scientists appeal to models when explaining phenomena. Such explanations are often dubbed model explanations or model-based explanations. But what are the precise conditions for ME? Are ME special explanations? In our paper, we first rebut two definitions of ME and specify a more promising one. Based on this analysis, we single out a related conception that is concerned with explanations that are induced from working with a model. We call them ‘model-induced explanations’. Second, we study three paradigmatic cases of alleged (...) ME. We argue that all of them are MIE, upon closer examination. Third, we argue that this undermines the building consensus that model explanations are special explanations that, e.g., challenge the factivity of explanation. Instead, it suggests that what is special about models in science is the epistemology behind how models induce explanations. (shrink)