This chapter provides a systematic overview of topological explanations in the philosophy of science literature. It does so by presenting an account of topological explanation that I (Kostić and Khalifa 2021; Kostić 2020a; 2020b; 2018) have developed in other publications and then comparing this account to other accounts of topological explanation. Finally, this appraisal is opinionated because it highlights some problems in alternative accounts of topological explanations, and also it outlines responses to some of the main criticisms raised by the (...) so-called new mechanists. (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)

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

After Wesley Salmon’s causal-mechanical stance on explanation in the 1980s, the ontic-epistemic debate of scientific explanations appeared to be resolved in the philosophy of science. However, since the twenty-first century, this debate has been rekindled among philosophers who focus on mechanistic explanations. Nevertheless, its issues have evolved, necessitating scrutiny of the new trends in this debate and a comparison with the original controversy between Carl Hempel and Salmon. The primary objective of this paper is to elucidate three categorical dimensions in (...) the ontic-epistemic debates, spanning from the original to the recent controversies. Subsequently, it will explore why the conception of explanation is linked to representations, what conditions are necessary for linguistic expressions to be explanatory, and what roles norms play in explanation. Consequently, contrary to the common stereotype, it will be argued that mechanistic explanations are more likely to be epistemic rather than ontic. (shrink)

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

Completeness is an important but misunderstood norm of explanation. It has recently been argued that mechanistic accounts of scientific explanation are committed to the thesis that models are complete only if they describe everything about a mechanism and, as a corollary, that incomplete models are always improved by adding more details. If so, mechanistic accounts are at odds with the obvious and important role of abstraction in scientific modelling. We respond to this characterization of the mechanist’s views about abstraction and (...) articulate norms of completeness for mechanistic explanations that have no such unwanted implications. _1_ Introduction _2_ A Balancing Act: When Do Details Matter? _3_ The Norms of Causal Explanation _4_ The Norms of Constitutive Explanation _5_ Salmon-Completeness _6_ From More Details to More Relevant Details _7_ Non-explanatory Virtues of Abstraction _8_ From Explanatory Models to Explanatory Knowledge _9_ Mechanistic Completeness Reconsidered _10_ Conclusion. (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)

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)

The concept of explanation is central to scientific practice. However, scientists explain phenomena in very different ways. That is, there are many different kinds of explanation; e.g. causal, mechanistic, statistical, or equilibrium explanations. In light of the myriad kinds of explanation identified in the literature, most philosophers of science have adopted some kind of explanatory pluralism. While pluralism about explanation seems plausible, it faces a dilemma Explanation beyond causation, Oxford University Press, Oxford, pp 39–56, 2018). Either there is nothing that (...) unifies all instances of scientific explanation that makes them count as explanations, or there is some set of unifying features, which seems incompatible with explanatory pluralism. Different philosophers have adopted different horns of this dilemma. Some argue that no unified account of explanation is possible. Others suggest that there is a set of necessary features that can unify all explanations under a single account Explanation beyond causation, Oxford University Press, Oxford, pp 74–95, 2018; Strevens in Depth: an account of scientific explanation, Harvard University Press, Cambridge, 2008). In this paper, we argue that none of the features identified by existing accounts of explanation are necessary for all explanations. However, we argue that a unified account can still be provided that accommodates pluralism. This can be accomplished, we argue, by reconceiving of scientific explanation as a cluster concept: there are multiple subsets of features that are sufficient for providing an explanation, but no single feature is necessary for all explanations. Reconceiving of explanation as a cluster concept not only accounts for the diversity of kinds of explanations, but also accounts for the widespread disagreement in the explanation literature and enables explanatory pluralism to avoid Pincock’s dilemma. (shrink)

In “What Makes a Scientific Explanation Distinctively Mathematical?” (2013b), Lange uses several compelling examples to argue that certain explanations for natural phenomena appeal primarily to mathematical, rather than natural, facts. In such explanations, the core explanatory facts are modally stronger than facts about causation, regularity, and other natural relations. We show that Lange's account of distinctively mathematical explanation is flawed in that it fails to account for the implicit directionality in each of his examples. This inadequacy is remediable in each (...) case by appeal to ontic facts that account for why the explanation is acceptable in one direction and unacceptable in the other direction. The mathematics involved in these examples cannot play this crucial normative role. While Lange's examples fail to demonstrate the existence of distinctively mathematical explanations, they help to emphasize that many superficially natural scientific explanations rely for their explanatory force on relations of stronger-than-natural necessity. These are not opposing kinds of scientific explanations; they are different aspects of scientific explanation. (shrink)

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

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)

We provide three innovations to recent debates about whether topological or “network” explanations are a species of mechanistic explanation. First, we more precisely characterize the requirement that all topological explanations are mechanistic explanations and show scientific practice to belie such a requirement. Second, we provide an account that unifies mechanistic and non-mechanistic topological explanations, thereby enriching both the mechanist and autonomist programs by highlighting when and where topological explanations are mechanistic. Third, we defend this view against some powerful mechanist objections. (...) We conclude from this that topological explanations are autonomous from their mechanistic counterparts. (shrink)

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

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