Scientific understanding, this paper argues, can be analyzed entirely in terms of a mental act of “grasping” and a notion of explanation. To understand why a phenomenon occurs is to grasp a correct explanation of the phenomenon. To understand a scientific theory is to be able to construct, or at least to grasp, a range of potential explanations in which that theory accounts for other phenomena. There is no route to scientific understanding, then, that does not go by way of (...) scientific explanation. (shrink)

Epistemology has for a long time focused on the concept of knowledge and tried to answer questions such as whether knowledge is possible and how much of it there is. Often missing from this inquiry, however, is a discussion on the value of knowledge. In The Value of Knowledge and the Pursuit of Understanding Jonathan Kvanvig argues that epistemology properly conceived cannot ignore the question of the value of knowledge. He also questions one of the most fundamental assumptions in epistemology, (...) namely that knowledge is always more valuable than the value of its subparts. Taking Platos' Meno as a starting point of his discussion, Kvanvig tackles the different arguments about the value of knowledge and comes to the conclusion that knowledge is less valuable than generally assumed. Clearly written and well argued, this 2003 book will appeal to students and professionals in epistemology. (shrink)

This article analyzes the epistemic value of understanding and offers an account of the role of understanding in science. First, I discuss the objectivist view of the relation between explanation and understanding, defended by Carl Hempel and J. D. Trout. I challenge this view by arguing that pragmatic aspects of explanation are crucial for achieving the epistemic aims of science. Subsequently, I present an analysis of these pragmatic aspects in terms of ‘intelligibility’ and a contextual account of scientific understanding based (...) on this notion. †To contact the author, please write to: Faculty of Philosophy, VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands; e‐mail: [email protected]. (shrink)

Not all models are explanatory. Some models are data summaries. Some models sketch explanations but leave crucial details unspecified or hidden behind filler terms. Some models are used to conjecture a how-possibly explanation without regard to whether it is a how-actually explanation. I use the Hodgkin and Huxley model of the action potential to illustrate these ways that models can be useful without explaining. I then use the subsequent development of the explanation of the action potential to show what is (...) required of an adequate mechanistic model. Mechanistic models are explanatory. (shrink)

Simulations using idealized numerical models can often generate behaviors or patterns that are visually very similar to the natural phenomenon being investigated and to be explained. The question arises, when should these model simulations be taken to provide an explanation for why the natural phenomena exhibit the patterns that they do? An important distinction for answering this question is that between ‘how-possibly’ explanations and ‘how-actually’ explanations. Despite the importance of this distinction there has been surprisingly little agreement over how exactly (...) this distinction should bedrawn. I shall argue that inadequate attention has been paid to the different contexts in which an explanation can be given and the different levels of abstraction at which the explanandum phenomenon can be framed. By tracing how scientists are using model simulations to explain a striking periodic banding of vegetation known as tiger bush, I will show how our understanding of the distinction between how-possibly and how-actually model explanations needs to be revised. (shrink)

I defend the claim that understanding is the goal of explanation against various persistent criticisms, especially the criticism that understanding is not truth-connected in the appropriate way, and hence is a merely psychological state. Part of the reason why understanding has been dismissed as the goal of explanation, I suggest, is because the psychological dimension of the goal of explanation has itself been almost entirely neglected. In turn, the psychological dimension of understanding—the Aha! experience, the sense that a certain explanation (...) “feels right”, and so on—has been conspicuously overemphasized. I try to correct for both of these exaggerations. Just as the goal of explanation includes a richer psychological—including phenomenological—dimension than is generally acknowledged, so too understanding has a stronger truth connection than is generally acknowledged.Keywords: Understanding; Explanation; Philosophy of science; Epistemology. (shrink)

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

Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an account sketched by (...) Mark Steiner), according to which a genuine MES incorporates an explanatory proof of the mathematical result being used. The central case study involves an explanation for why bees build the cells of their honeycombs in the shape of hexagons. I make a distinction between two kinds of MES, mathematics-driven explanation in science and science-driven mathematical explanation, and argue that it is the second category which is both scientifically and philosophical more central. I conclude that the explanatory relation involved in MES is genuinely scientific and hence that the phenomenon of MES poses a challenge to general accounts of scientific explanation. (shrink)

Understanding is a central aim of science and highly important in present-day society. But what precisely is scientific understanding and how can it be achieved? This book answers these questions, through philosophical analysis and historical case studies, and presents a philosophical theory of scientific understanding that highlights its contextual nature.

This is an introduction to the volume "Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations", edited by A. Reutlinger and J. Saatsi (OUP, forthcoming in 2017). -/- Explanations are very important to us in many contexts: in science, mathematics, philosophy, and also in everyday and juridical contexts. But what is an explanation? In the philosophical study of explanation, there is long-standing, influential tradition that links explanation intimately to causation: we often explain by providing accurate information about the causes of the (...) phenomenon to be explained. Such causal accounts have been the received view of the nature of explanation, particularly in philosophy of science, since the 1980s. However, philosophers have recently begun to break with this causal tradition by shifting their focus to kinds of explanation that do not turn on causal information. The increasing recognition of the importance of such non-causal explanations in the sciences and elsewhere raises pressing questions for philosophers of explanation. What is the nature of non-causal explanations - and which theory best captures it? How do non-causal explanations relate to causal ones? How are non-causal explanations in the sciences related to those in mathematics and metaphysics? This volume of new essays explores answers to these and other questions at the heart of contemporary philosophy of explanation. The essays address these questions from a variety of perspectives, including general accounts of non-causal and causal explanations, as well as a wide range of detailed case studies of non-causal explanations from the sciences, mathematics and metaphysics. (shrink)

From antiquity to the end of the twentieth century, philosophical discussions of understanding remained undeveloped, guided by a 'received view' that takes understanding to be nothing more than knowledge of an explanation. More recently, however, this received view has been criticized, and bold new philosophical proposals about understanding have emerged in its place. In this book, Kareem Khalifa argues that the received view should be revised but not abandoned. In doing so, he clarifies and answers the most central questions in (...) this burgeoning field of philosophical research: what kinds of cognitive abilities are involved in understanding? What is the relationship between the understanding that explanations provide and the understanding that experts have of broader subject matters? Can there be understanding without explanation? How can one understand something on the basis of falsehoods? Is understanding a species of knowledge? What is the value of understanding? (shrink)

Explanations are very important to us in many contexts: in science, mathematics, philosophy, and also in everyday and juridical contexts. But what is an explanation? In the philosophical study of explanation, there is long-standing, influential tradition that links explanation intimately to causation: we often explain by providing accurate information about the causes of the phenomenon to be explained. Such causal accounts have been the received view of the nature of explanation, particularly in philosophy of science, since the 1980s. However, philosophers (...) have recently begun to break with this causal tradition by shifting their focus to kinds of explanation that do not turn on causal information. The increasing recognition of the importance of such non-causal explanations in the sciences and elsewhere raises pressing questions for philosophers of explanation. What is the nature of non-causal explanations – and which theory best captures it? How do non-causal explanations relate to causal ones? How are non-causal explanations in the sciences related to those in mathematics and metaphysics? This volume of new essays explores answers to these and other questions at the heart of contemporary philosophy of explanation. The essays address these questions from a variety of perspectives, including general accounts of non-causal and causal explanations, as well as a wide range of detailed case studies of non-causal explanations from the sciences, mathematics and metaphysics. (shrink)

This paper discusses the epistemic import of highly abstract and simplified theoretical models using Thomas Schelling’s checkerboard model as an example. We argue that the epistemic contribution of theoretical models can be better understood in the context of a cluster of models relevant to the explanatory task at hand. The central claim of the paper is that theoretical models make better sense in the context of a menu of possible explanations. In order to justify this claim, we introduce a distinction (...) between causal scenarios and causal mechanism schemes. These conceptual tools help us to articulate the basis for modelers’ intuitive confidence that their models make an important epistemic contribution. By focusing on the role of the menu of possible explanations in the evaluation of explanatory hypotheses, it is possible to understand how a causal mechanism scheme can improve our explanatory understanding even in cases where it does not describe the actual cause of a particular phenomenon. (shrink)

Comparisons of rival explanations or theories often involve vague appeals to explanatory power. In this paper, we dissect this metaphor by distinguishing between different dimensions of the goodness of an explanation: non-sensitivity, cognitive salience, precision, factual accuracy and degree of integration. These dimensions are partially independent and often come into conflict. Our main contribution is to go beyond simple stipulation or description by explicating why these factors are taken to be explanatory virtues. We accomplish this by using the contrastive-counterfactual approach (...) to explanation and the view of understanding as an inferential ability. By combining these perspectives, we show how the explanatory power of an explanation in a given dimension can be assessed by showing the range of answers it provides to what-if-things-had-been-different questions and the theoretical and pragmatic importance of these questions. Our account also explains intuitions linking explanation to unification or to exhibition of a mechanism. (shrink)

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

How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical how-possibly explanation (...) which establishes claims of mathematical dependence. The account developed reveals how mathematical knowledge can inform claims about the world, allow ‘what-if-things-had-been-different’ inferences, and thus improve our understanding. (shrink)

One puzzle concerning highly idealized models is whether they explain. Some suggest they provide so-called ‘how-possibly explanations’. However, this raises an important question about the nature of how-possibly explanations, namely what distinguishes them from ‘normal’, or how-actually, explanations? I provide an account of how-possibly explanations that clarifies their nature in the context of solving the puzzle of model-based explanation. I argue that the modal notions of actuality and possibility provide the relevant dividing lines between how-possibly and how-actually explanations. Whereas how-possibly (...) explanations establish claims of possible explanations, how-actually explanations establish claims of actual ones. Models, in turn, simply provide evidence for these claims. (shrink)

The present paper argues that there is a structural difference between classical cases involving knowledge-undermining environmental luck, and cases where a subject acquires understanding in the presence of environmental luck. This difference appears to bear on arguments against the reductionist thesis that understanding is a special form of knowledge.

Philosophers agree that scientific explanations aim to produce understanding, and that good ones succeed in this aim. But few seriously consider what understanding is, or what the cues are when we have it. If it is a psychological state or process, describing its specific nature is the job of psychological theorizing. This article examines the role of understanding in scientific explanation. It warns that the seductive, phenomenological sense of understanding is often, but mistakenly, viewed as a cue of genuine understanding. (...) The article closes with a discussion of several new paths of research that tie the psychology of scientific explanation to cognate notions of learning, testimony, and understanding. (shrink)

This paper asks how, in science in general and in economics in particular, theoretical models aid the understanding of real-world phenomena. Using specific models in economics and biology as test cases, it considers three alternative answers: that models are tools for isolating the ‘capacities’ of causal factors in the real world; that modelling is ‘conceptual exploration’ which ultimately contributes to the development of genuinely explanatory theories; and that models are credible counterfactual worlds from which inductive inferences can be made. The (...) paper argues that the ‘credible worlds’ account captures significant aspects of scientific practice, even if many modellers see their work as conceptual exploration. (shrink)

Philosophers have proposed many alleged examples of non-causal explanations of particular events. I discuss several well-known examples and argue that they fail to be non-causal. 1 Questions2 Preliminaries3 Explanations That Cite Causally Inert Entities4 Explanations That Merely Cite Laws I5 Stellar Collapse6 Explanations That Merely Cite Laws II7 A Final Example8 Conclusion.

Philosophers have proposed many alleged examples of non-causal explana- tions of particular events. I discuss several well-known examples and argue that they fail to be non-causal.

This article introduces and defends a probabilistic measure of the explanatory power that a particular explanans has over its explanandum. To this end, we propose several intuitive, formal conditions of adequacy for an account of explanatory power. Then, we show that these conditions are uniquely satisfied by one particular probabilistic function. We proceed to strengthen the case for this measure of explanatory power by proving several theorems, all of which show that this measure neatly corresponds to our explanatory intuitions. Finally, (...) we briefly describe some promising future projects inspired by our account. (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.

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.

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.

Can one still have understanding in situations that involve the kind of epistemic luck that undermines knowledge? Kvanvig (The value of knowledge and the pursuit of understanding, 2003; in: Haddock A, Miller A, Pritchard D (eds) Epistemic value, 2009a; in: Haddock A, Miller A, Pritchard D (eds) Epistemic value, 2009b) says yes, Prichard (Grazer Philos Stud 77:325–339, 2008; in: O’Hear A (ed) Epistemology, 2009; in: Pritchard D, Millar A, Haddock A (eds) The nature and value of knowledge: three investigations, 2010) (...) say sometimes, DePaul and Grimm (Philos Phenomenol Res 74:498–514, 2007) and Grimm (Br J Philos Sci 57:515–535, 2006; in: Bernecker S, Pritchard D (eds) The Routledge companion to epistemology, 2011), Kvanvig’s critics, say no. The cases put forth by Kvanvig’s critics share a common feature, which seems to drive the intuition that understanding can’t be lucky: the fact that the information that makes up the individual’s understanding comes exclusively from a bad source. I formulate a case that lacks this feature, drawing on the fact that understanding produced from scientific inquiry is often produced by collaboration. I argue that my case provides good evidence that understanding is not a species of knowledge. (shrink)

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

Highly idealized models, such as the Hawk-Dove game, are pervasive in biological theorizing. We argue that the process and motivation that leads to the introduction of various idealizations into these models is not adequately captured by Michael Weisberg’s taxonomy of three kinds of idealization. Consequently, a fourth kind of idealization is required, which we call hypothetical pattern idealization. This kind of idealization is used to construct models that aim to be explanatory but do not aim to be explanations.

This paper analyzes two ways idealized biological models produce factive scientific understanding. I then argue that models can provide factive scientific understanding of a phenomenon without providing an accurate representation of the features of their real-world target system. My analysis of these cases also suggests that the debate over scientific realism needs to investigate the factive scientific understanding produced by scientists’ use of idealized models rather than the accuracy of scientific models themselves.

Toy models are highly idealized and extremely simple models. Although they are omnipresent across scientific disciplines, toy models are a surprisingly under-appreciated subject in the philosophy of science. The main philosophical puzzle regarding toy models concerns what the epistemic goal of toy modelling is. One promising proposal for answering this question is the claim that the epistemic goal of toy models is to provide individual scientists with understanding. The aim of this article is to precisely articulate and to defend this (...) claim. In particular, we will distinguish between autonomous and embedded toy models, and then argue that important examples of autonomous toy models are sometimes best interpreted to provide how-possibly understanding, while embedded toy models yield how-actually understanding, if certain conditions are satisfied. _1_ Introduction _2_ Embedded and Autonomous Toy Models _2.1_ Embedded toy models _2.2_ Autonomous toy models _2.3_ Qualification _3_ A Theory of Understanding for Toy Models _3.1_ Preliminaries and requirements _3.2_ The refined simple view _4_ Two Kinds of Understanding with Toy Models _4.1_ Embedded toy models and how-actually understanding _4.2_ Against a how-actually interpretation of all autonomous toy models _4.3_ The how-possibly interpretation of some autonomous toy models _5_ Conclusion. (shrink)

Toy models are highly idealized and extremely simple models. Although they are omnipresent across scientific disciplines, toy models are a surprisingly under-appreciated subject in the philosophy of science. The main philosophical puzzle regarding toy models is that it is an unsettled question what the epistemic goal of toy modeling is. One promising proposal for answering this question is the claim that the epistemic goal of toy models is to provide individual scientists with understanding. The aim of this paper is to (...) precisely articulate and to defend this claim. In particular, we will distinguish between autonomous and embedded toy models, and, then, argue that important examples of autonomous toy models are sometimes best interpreted to provide how-possibly understanding, while embedded toy models yield how-actually understanding, if certain conditions are satisfied. (shrink)

Renormalization group (RG) methods are an established strategy to explain how it is possible that microscopically different systems exhibit virtually the same macro behavior when undergoing phase-transitions. I argue – in agreement with Robert Batterman – that RG explanations are non-causal explanations. However, Batterman misidentifies the reason why RG explanations are non-causal: it is not the case that an explanation is non- causal if it ignores causal details. I propose an alternative argument, according to which RG explanations are non-causal explanations (...) because their explanatory power is due to the application mathematical operations, which do not serve the purpose of representing causal relations. (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.

In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation (CTE) captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I (...) support this claim by illustrating that CTE is applicable to Euler’s explanation (an example of a non-causal scientific explanation) and Loewer’s explanation (an example of a non-causal metaphysical explanation). (shrink)

In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I support (...) this claim by illustrating that CTE is applicable to Euler’s explanation and Loewer’s explanation. (shrink)

Biologists in many different fields of research give how-possibly explanations of the phenomena they study. Although such explanations lack empirical support, and might be regarded by some as unscientific, they play an important heuristic role in biology by helping biologists develop theories and concepts and suggesting new areas of research. How-possibly explanations serve as a useful framework for conducting research in the absence of adequate empiri cal data, and they can even become how-actually explanations if they gain enough empirical support.

Achieving understanding of nature is one of the aims of science. In this paper we offer an analysis of the nature of scientific understanding that accords with actual scientific practice and accommodates the historical diversity of conceptions of understanding. Its core idea is a general criterion for the intelligibility of scientific theories that is essentially contextual: which theories conform to this criterion depends on contextual factors, and can change in the course of time. Our analysis provides a general account of (...) how understanding is provided by scientific explanations of diverse types. In this way, it reconciles conflicting views of explanatory understanding, such as the causal-mechanical and the unificationist conceptions. (shrink)

Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do (...) science. This account successfully reconciles theoretical indispensability and metaphysical dispensability and has important consequences for both advocates and critics of indispensability arguments for platonism about mathematics. (shrink)

This article focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau’s laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations.explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear how to unify (...) abstract and causal explanations as instances of a single sort of thing. I conclude by examining the implications of the claim that explanations require objective dependence relations. If this claim is accepted, then there are several kinds of objective dependence relations. 1 Introduction2 A Case3 Abstract and Causal Explanations4 Recent Work on Mathematical Explanation5 Explanation and Dependence6 Conclusion. (shrink)

This paper examines a series of Schelling-like models of residential segregation, in which agents prefer to be in the minority. We demon- strate that as long as agents care about the characteristics of their wider community, they tend to end up in a segregated state. We then investigate the process that causes this, and conclude that the result hinges on the similarity of informational states amongst agents of the same type. This is quite di erent from Schelling-like behavior, and sug- (...) gests (in his terms) that segregation is an instance of macro behavior which can arise from a wide variety of micro motives. (shrink)

It is plausible to think that the epistemic benefit of having an explanation is understanding. My focus in this article is on the extent to which explanatory understanding, perhaps unlike knowledge, is compatible with certain forms of luck—the extent to which one can understand why something is the case when one is lucky to truly believe an explanatorily relevant proposition. I argue, contra Stephen Grimm ([2006]) and Duncan Pritchard ([2008], [2009]), that understanding quite generally is compatible with luckily believing a (...) true, explanatorily relevant proposition. My strategy is to argue that various intuitions that seem to rule against lucky understanding can be explained away, and thus do not compel us to reject the thesis that, in general, understanding tolerates luck. In arriving at this conclusion, I address some salient issues regarding the testimony of others, and also draw out the consequences of my discussions for the status of understanding as a cognitive achievement. (shrink)

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

This paper provides an inferentialist account of model-based understanding by combining a counterfactual account of explanation and an inferentialist account of representation with a view of modeling as extended cognition. This account makes it understandable how the manipulation of surrogate systems like models can provide genuinely new empirical understanding about the world. Similarly, the account provides an answer to the question how models, that always incorporate assumptions that are literally untrue of the model target, can still provide factive explanations. Finally, (...) the paper shows how the contrastive counterfactual theory of explanation can provide tools for assessing the explanatory power of models. (shrink)