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)

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)

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.

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 philosophical literature on scientific explanation in neuroscience has been dominated by the idea of mechanisms. The mechanist philosophers often claim that neuroscience is in the business of finding mechanisms. This view has been challenged in numerous ways by showing that there are other successful and widespread explanatory strategies in neuroscience. However, the empirical evidence for all these claims was hitherto lacking. Empirical evidence about the pervasiveness and uses of various explanatory strategies in neuroscience is particularly needed because examples and (...) case studies that are used to illustrate philosophical claims so far tend to be hand-picked. The risk of confirmation bias is therefore considerable: when looking for white swans, all one finds is that swans are white. The more systematic quantitative and qualitative bibliometric study of a large body of relevant literature that we present in this paper can put such claims into perspective. Using bibliometric tools, we identify the typical linguistic patterns used in the alleged mechanistic, dynamical, and topological explanations in the literature, their preponderance and how they change over time. Our findings show abundant use of mechanistic language, but also the presence of a significant neuroscience literature using topological and dynamical explanatory language, which grows over time and increasingly differentiates from each other and from mechanistic explanations. (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 ofbeing 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)

Extra-mathematical explanations explain natural phenomena primarily by appeal to mathematical facts. Philosophers disagree about whether there are extra-mathematical explanations, the correct account of them if they exist, and their implications (e.g., for the philosophy of scientific explanation and for the metaphysics of mathematics) (Baker 2005, 2009; Bangu 2008; Colyvan 1998; Craver and Povich 2017; Lange 2013, 2016, 2018; Mancosu 2008; Povich 2019, 2020; Steiner 1978). In this discussion note, I present three desiderata for any account of extra-mathematical explanation and argue (...) that Baron’s (2020) U-Counterfactual Theory fails to meet each of them. I conclude with some reasons for pessimism that a successful account will be forthcoming. (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)

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)

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)

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)

Opinionated state of the art paper on scientific explanation. Analysis and discussion of the most relevant models and theories in the contemporary literature, namely, the deductive-nomological model, the models of inductive-statistical and statistical relevance, the pragmatic theory of why questions, the unifying theory of standard arguments, and the causal/non-causal counterfactual theory.

Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.

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.

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)

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)

Recent rival attempts in the philosophy of science to put forward a general theory of the properties that all (and only) natural kinds across the sciences possess may have proven to be futile. Instead, I develop a general methodological framework for how to philosophically study kinds. Any kind has to be investigated and articulated together with the human aims that motivate referring to this kind, where different kinds in the same scientific domain can answer to different concrete aims. My core (...) contention is that non-epistemic aims, including environmental, ethical, and political aims, matter as well. This is defended and illustrated based on several examples of kinds, with particular attention to the role of social-political aims: species, race, gender, as well as personality disorders and oppositional defiant disorder as psychiatric kinds. Such non-epistemic aims and values need not always be those personally favoured by scientists, but may have to reflect values that matter to relevant societal stakeholders. Despite the general agenda to study ‘kinds,’ I argue that philosophers should stop using the term ‘natural kinds,’ as this label obscures the relevance of humans interests and the way in which many kinds are based on contingent social processes subject to human responsibility. (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)

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, (...) requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz. (shrink)

In the last couple of years a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the question what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e. explanations that don’t cite causes in the explanans) sometimes take a form of the question what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue of what (...) they are explanatory. These questions raise further issues about counterfactuals, modality and explanatory asymmetries, i.e. do mathematical and non-causal explanations support counterfactuals, and how to understand explanatory asymmetries in non-causal explanations. Even though these are very common issues in the philosophy of physics and mathematics, they can be found in different guises in the philosophy of biology, where there is the statistical interpretation of the Modern Synthesis theory of evolution, according to which the post-Darwinian theory of natural selection explains evolutionary change by citing statistical properties of populations and not the causes of changes. These questions also arise in philosophy of ecology or neuroscience in regard to the nature of topological explanations. The question here is whether in network models in biology, ecology, neuroscience and computer science the mathematical or more precisely topological properties can be explanatory of physical phenomena, or they are just different ways to represent causal structures. The aim of the special issue is to unify all these debates around several overlapping questions. (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)

We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to key (...) intuitions traded in the debate, regarding mathematics’ procurement of explanatory generality, and adjudicates unambiguously in favour of the nominalist, at least as far as explanatory generality is concerned. (shrink)

In this paper I defend an intermediate position between the ‘bare mathematical results’ view and the ‘transmission’ view of mathematical explanations of physical phenomena (MEPPs). I argue that, in MEPPs, it is not enough to deduce the explanandum from the generalizations cited in the explanans. Rather, we must add information regarding why those generalizations obtain. However, I also argue that it is not necessary to provide explanatory proofs of the mathematical theorems that represent those generalizations. I illustrate this with the (...) bridges of Königsberg case. -/- . (shrink)

This paper examines some recent attempts that use counterfactuals to understand the asymmetry of non-causal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit non-causal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of non-causal explanation. This paper argues that several recent (...) accounts Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 117–140, 2018; Jansson and Saatsi in Br J Philos Sci, forthcoming; Jansson in J Philos 112:7–599, 2015; Saatsi and Pexton in Philos Sci 80: 613–624, 2013; French and Saatsi, in: Reutlinger and Saatsi Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 185–205, 2018) fail to meet this challenge. The paper then sketches a more positive proposal for dealing with explanatory asymmetry in non-causal explanations. (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)

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)

One can find in the literature two sets of views concerning the relationship between understanding and explanation: that one understands only if 1) one has knowledge of causes and 2) that knowledge is provided by an explanation. Taken together, these tenets characterize what I call the narrow knowledge account of understanding. While the first tenet has recently come under severe attack, the second has been more resistant to change. I argue that we have good reasons to reject it on the (...) basis of theoretical models that provide how-possibly explanations. These models, while they do not explain in the strict sense, afford understanding. In response, I propose an alternative epistemology of understanding, broad KAU, that takes cases of theoretical modelling into account. (shrink)

There is an old meta-philosophical worry: very roughly, metaphysical theories have no observational consequences and so the study of metaphysics has no value. The worry has been around in some form since the rise of logical positivism in the early twentieth century but has seen a bit of a renaissance recently. In this paper, I provide an apology for metaphysics in the face of this kind of concern. The core of the argument is this: pure mathematics detaches from science in (...) much the same manner as metaphysics and yet it is valuable nonetheless. The source of value enjoyed by pure mathematics extends to metaphysics as well. Accordingly, if one denies that metaphysics has value, then one is forced to deny that pure mathematics has value. The argument places an added burden on the sceptic of metaphysics. If one truly believes that metaphysics is worthless (as some philosophers do), then one must give up on pure mathematics as well. (shrink)

In the last couple of years a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences sometimes take a form of the question what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue of what they are explanatory. These questions raise further issues about (...) counterfactuals, modality, and explanatory asymmetries: i.e., do mathematical and non-causal explanations support... (shrink)