There is increasing attention to the centrality of idealization in science. One common view is that models and other idealized representations are important to science, but that they fall short in one or more ways. On this view, there must be an intermediary step between idealized representation and the traditional aims of science, including truth, explanation, and prediction. Here I develop an alternative interpretation of the relationship between idealized representation and the aims of science. In my view, continuing, widespread idealization (...) calls into question the idea that science aims for truth. I argue that understanding must replace truth as the ultimate epistemic aim of science. Additionally, science has a wide variety aims, epistemic and non-epistemic, and these aims motivate different kinds of scientific products. Finally, I show how these diverse aims---all rather distant from truth---result in the expanded influence of social values on science. (shrink)

Many accounts of scientific modelling assume that models can be decomposed into the contributions made by their accurate and inaccurate parts. These accounts then argue that the inaccurate parts of the model can be justified by distorting only what is irrelevant. In this paper, I argue that this decompositional strategy requires three assumptions that are not typically met by our best scientific models. In response, I propose an alternative view in which idealized models are characterized as holistically distorted representations that (...) are justified by allowing for the application of various modelling techniques. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealisedexplanation gamein which players collaborate to find the best explanation(s) for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal patterns of (...) variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a (conditionally) optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Explainable AI (xAI) methods are important for establishing trust in using black-box models. However, recent criticism has mounted against current xAI methods that they disagree, are necessarily false, and can be manipulated, which has started to undermine the deployment of black-box models. Rudin (2019) goes so far as to say that we should stop using black-box models altogether in high-stakes cases because xAI explanations ‘must be wrong’. However, strict fidelity to the truth is historically not a desideratum in science. Idealizations (...) – the intentional distortions introduced to scientific theories and models – are commonplace in the natural sciences and are seen as a successful scientific tool. Thus, it is not falsehood qua falsehood that is the issue. In this paper, I outline the need for xAI research to engage in idealization evaluation. Drawing on the use of idealizations in the natural sciences and philosophy of science, I introduce a novel framework for evaluating whether xAI methods engage in successful idealizations or deceptive explanations (SIDEs). SIDEs evaluates whether the limitations of xAI methods, and the distortions that they introduce, can be part of a successful idealization or are indeed deceptive distortions as critics suggest. I discuss the role that existing research can play in idealization evaluation and where innovation is necessary. Through a qualitative analysis we find that leading feature importance methods and counterfactual explanations are subject to idealization failure and suggest remedies for ameliorating idealization failure. (shrink)

I argue that moral principles, construed as moral generalizations, can be genuinely explanatory. Specifically, I present and respond to a challenge according to which moral generalizations are explanatorily redundant. In response, I present and defend an explanatory dimension of moral generalizations that is based on the idea of unification. I do so in the context of motivating a realist-friendly moral explanatory pluralism (i.e., the view that there can be many, equally legitimate, explanations of moral facts). Finally, I appeal to the (...) same theoretical resources to tackle an objection from explanatory circularity. (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)

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)

Much recent work on explanation in the interventionist tradition emphasizes the explanatory value of stable causal generalizations—i.e., causal generalizations that remain true in a wide range of background circumstances. We argue that two separate explanatory virtues are lumped together under the heading of `stability’. We call these two virtues breadth and guidance respectively. In our view, these two virtues are importantly distinct, but this fact is neglected or at least under-appreciated in the literature on stability. We argue that an adequate (...) theory of explanatory goodness should recognize breadth and guidance as distinct virtues, as breadth and guidance track different ideals of explanation, satisfy different cognitive and pragmatic ends, and play different theoretical roles in helping us understand the explanatory value of mechanisms. Thus keeping track of the distinction between these two forms of stability yields a more accurate and perspicuous picture of the role that stability considerations play in explanation. (shrink)

Social scientists have offered a number of explanations for why Americans commonly deny that human-caused climate change is real. In this paper, I argue that these explanations neglect an important group of climate change deniers: those who say they are on the side of science while also rejecting what they know most climate scientists accept. I then develop a “nature of science” hypothesis that does account for this group of deniers. According to this hypothesis, people have serious misconceptions about what (...) scientific inquiry ought to look like. Their misconceptions interact with partisan biases to produce denial of human-caused climate change. After I develop this hypothesis, I propose ways of confirming that it is true. Then I consider its implications for efforts to combat climate change denial and for other cases of public rejection of science. (shrink)

In a number of very influential publications, Epstein and Hoover (among other authors) have recently argued that a thoroughly micro-foundationalist approach towards economics is unconvincing for metaphysical reasons. However, as we show in this article, this metaphysical/social ontological approach to the debate fails to resolve the status of micro-foundations in the practice of economic modelling. To overcome this, we argue that endogenizing a model—that is, providing micro-foundations for it—correlates with making that model more complex. Specifically, we show that models with (...) more micro-foundations tend to have more parameters or variables. This matters, as there are well-established methodological reasons for preferring models with fewer parameters or variables—ceteris paribus. We therefore conclude that, from a practice-based point of view, micro-foundations are only defensible to the extent that they significantly improve the ability of the relevant model to fit the data of interest. In this way, we arrive at a practice-based, methodological reconceptualization of the debate surrounding the need for micro-foundations in economics. (shrink)

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

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 tremendous philosophical focus on how to characterize explanatory metaphysical dependence has eclipsed a number of other unresolved issued about scientific explanation. The purpose of this paper is taxonomical. I will outline a number of other questions about the nature of explanation and its role in science—eight, to be precise—and argue that each is independent. All of these topics have received some philosophical attention, but none nearly so much as it deserves. Furthermore, existing views on these topics have been obscured (...) by not distinguishing among these independent questions and, especially, by not separating them from the question of what metaphysical dependence relation is explanatory. Philosophical analysis of scientific explanation would be much improved by attending more carefully to these, and probably still other, elements of an account of explanation. (shrink)

How can a reflective scientist put forward an explanation using a model when they are aware that many of the assumptions used to specify that model are false? This paper addresses this challenge by making two substantial assumptions about explanatory practice. First, many of the propositions deployed in the course of explaining have a non-representational function. In particular, a proposition that a scientist uses and also believes to be false, i.e. an “idealization”, typically has some non-representational function in the practice, (...) such as the interpretation of some model or the specification of the target of the explanation. Second, when an agent puts forward an explanation using a model, they usually aim to remain agnostic about various features of the phenomenon being explained. In this sense, explanations are intended to be autonomous from many of the more fundamental features of such systems. I support these two assumptions by showing how they allow one to address a number of recent concerns raised by Bokulich, Potochnik and Rice. In addition, these assumptions lead to a defense of the view that explanations are wholly true that improves on the accounts developed by Craver, Mäki and Strevens. (shrink)

I address an objection to inference to the best explanation due to Bas C. van Fraassen, according to which explanatory virtues cannot confirm a theory, since they make the theory more informative and thus less likely to be true given the probability axioms. I try to show that van Fraassen’s argument, once made precise, is deductively invalid, and that even an ampliative version of the argument (i) implies, absurdly, that no theory is confirmed by its fit with empirical data; (ii) (...) fails to account for confirmatory closure under deduction; and (iii) falsely presupposes that a theory and its sub-theories can be competing explanations. (shrink)

Scientific disputes about how often different processes or patterns occur are relative frequency controversies. These controversies occur across the sciences. In some areas—especially biology—they are even the dominant mode of dispute. Yet they depart from the standard picture of what a scientific controversy is like. In fact, standard philosophical accounts of scientific controversies suggest that relative frequency controversies are irrational or lacking in epistemic value. This is because standard philosophical accounts of scientific controversies often assume that in order to be (...) rational, a scientific controversy must reach a resolution and be about a scientifically interesting question. Relative frequency controversies rarely reach a resolution, however, and some scientists and philosophers are skeptical that these controversies center on scientifically interesting questions. In this paper, I provide a novel account of the epistemic contribution that relative frequency controversies make to science. I show that these controversies are rational in the sense of furthering the epistemic aims of the scientific communities in which they occur. They do this despite rarely reaching a resolution, and independent of whether the controversies are about scientifically interesting questions. This means that assumptions and about what is required for a controversy to be rational are wrong. Controversies do not need to reach a resolution in order to be rational. And they do not need to be about anything scientifically interesting in order to make valuable epistemic contributions to science. (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)

Some theorists of normative explanation argue that we can make sense of debates between first-order moral theories such as consequentialism and its rivals only if we understand their explanations of why the right acts are right and the wrong acts are wrong as generative (e.g. grounding) explanations. Others argue that the standard form of normative explanation is, instead, some kind of unification. Neither sort of explanatory monism can account for all the explanations of particular moral facts that moral theorists seek (...) to state and defend. This paper argues that we can do better if we accept normative explanatory pluralism, the view that at least some particular explananda in normative inquiry have more than one type of correct complete explanation. Such pluralism is supported by what goes on in actual moral inquiry, parallels an independently plausible form of pluralism about scientific explanation, and can offer principled responses to central objections. (shrink)

The potential reducibility of chemical entities to their physical bases is a matter of dispute between ontological reductionists on one hand, and emergentists on the other. However, relevant debates typically revolve around the reducibility of so-called ‘higher-level’ chemical entities, such as molecules. Perhaps surprisingly, even committed proponents of emergence for these higher-level chemical entities appear to accept that the ‘lowest-level’ chemical entities – atomic species – are reducible to their physical bases. In particular, the microstructural view of chemical elements, actively (...) developed and defended by emergentists, appears to hold that the explanatory power of nuclear charge justifies being reductionist about atomic species. My first task in this paper is to establish that nuclear charge cannot ultimately provide explanations sufficient to justify a reductionist approach to atomic species, unless we abandon the persuasive intuition that the presence of an element in a substance ought to explain the properties of that substance. The ‘missing piece’ for explaining the properties of substances by way of their elemental constituents is the electronegativity values of participant atoms. But electronegativity is a strikingly disunified concept that appears distinctly unamenable to analysis by way of fundamental physical principles. Through evaluating the uncertain physical identity of electronegativity, as well as its widespread and indispensable epistemic utility in chemical practice, I argue that electronegativity provides compelling grounds to seriously consider emergence for atomic species. (shrink)

Brian Epstein has recently argued that a thoroughly microfoundationalist approach towards economics is unconvincing for metaphysical reasons. Generally, Epstein argues that for an improvement in the methodology of social science we must adopt social ontology as the foundation of social sciences; that is, the standing microfoundationalist debate could be solved by fixing economics’ ontology. However, as I show in this paper, fixing the social ontology prior to the process of model construction is optional instead of necessary and that metaphysical-ontological commitments (...) are often the outcome of model construction, not its starting point. By focusing on the practice of modeling in economics the paper provides a useful inroad into the debate about the role of metaphysics in the natural and social sciences more generally. (shrink)

Philosophers pursue a number of different explanatory projects when explaining various sorts of normative phenomena. For example, they may seek to explain why the right acts are right or why the things that are good for us are so, explain what it is for something to be obligatory, or explain the source of reasons for action. This chapter takes some steps towards understanding this variety. I first lay some general ground about explanation, suggest that explanations that are appropriate in normative (...) inquiry are objective in a certain sense, and discuss the relevant notion of the normative. I describe some key axes of debate about the form and the content of explanations that first-order normative inquiry (such as normative ethics) typically seeks to state and defend, such as whether normative principles are essential to first-order normative explanation and whether first-order normative explanations work by highlighting what grounds the normative phenomena that are being explained, or by unifying them with other seemingly disparate normative phenomena, or in some other way. I then discuss the function of explanation in normative inquiry and the question of whether normative explanation might be pluralist in various senses. More briefly I discuss how two other sorts of normative explanation that seem more concerned with the foundations of normative domains like ethics and practical reason (such as the source of reasons for action) and with explicating or analyzing the natures of normative properties might be understood and how they relate to first-order normative explanations. (shrink)

Scientific realism is a thesis about the success of science. Most traditionally: science has been so successful at prediction and guiding action because its best theories are true (or approximately true or increasing in their degree of truth). If science is in the business of doing its best to generate true theories, then we should turn to those theories for explanatory knowledge, predictions, and guidance of our actions and decisions. Views that are popular in contemporary philosophy of science about scientific (...) modeling and the centrality of idealization create several challenges for this traditional form of scientific realism. Yet the basic idea behind scientific realism that science has been and will continue to be epistemically successful is deeply appealing. This chapter explores the challenges posed by idealization and scientific modeling to motivate a scientific realism fully divorced from the idea that science is in the business of generating true theories. On the resulting view, the objects of scientific knowledge are causal patterns, so this knowledge only ever provides partial, simplified accounts of a complex reality. This variety of selective realism better accommodates the nature of our present-day scientific successes and offers an interpretation of scientific progress that resists the antirealist’s pessimism. (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)

The advancement of computing technology makes it possible to build extremely accurate digital reconstructions of brain circuits. Are such unprecedented levels of biological accuracy essential for brain simulations to play the roles they are expected to play in neuroscientific research? The main goal of this paper is to clarify this question by distinguishing between various roles played by large-scale simulations in contemporary neuroscience, and by reflecting about what makes a simulation biologically accurate. It is argued that large-scale simulations may play (...) model-oriented and prediction-oriented roles in brain research, and that the concept of biological accuracy can be interpreted as related to the plausibility of the theoretical model implemented in the simulation system, to the accuracy of the computer implementation, and to the level of details of the implemented model. Building on these observations and distinctions, it is argued that biological accuracy is not essential for a computer simulation to play the epistemic roles it is expected to play in brain research. (shrink)

The recent use of typicality in statistical mechanics for foundational purposes has stirred an important debate involving both philosophers and physicists. While this debate customarily focuses on technical issues, in this paper I try to approach the problem from an epistemological angle. The discussion is driven by two questions: (1) What does typicality add to the concept of measure? (2) What kind of explanation, if any, does typicality yield? By distinguishing the notions of `typicality-as-vast-majority' and `typicality-as-best-exemplar', I argue that the (...) former goes beyond the concept of measure. Furthermore, I also argue that typicality aims at providing us with a form of causal explanation of equilibrium. (shrink)

There is a widespread philosophical interpretation of natural selection in evolutionary theory: natural selection, like mutation, migration, and drift are seen as forces that propel the evolution of populations. Natural selection is thus a population level causal process. This account has been challenged by the Statistics, claiming that natural selection is not a population level cause but rather a statistical feature of a population. This paper examines the nature of the aforementioned ontological debate and the nature of statistical explanations given (...) by population genetics. I claim that the Modern Synthesis provides good explanations of the changes in trait structure of populations without appealing to detailed causal information about the individual trajectories of the members of a population. (shrink)

In the target article for this issue, Christie, Brusse, et al. [2022a] argue that Selected Effects Functions (SEF), at least as currently articulated, often do not explain biological traits. In res...

This dissertation aims to determine the optimal level of granularity for the variables used in probabilistic causal models. These causal models are useful for generating explanations in a number of scientific contexts. In Chapter 1, I argue that there is rarely a unique level of granularity at which a given phenomenon can be causally explained, thereby rejecting various causal exclusion arguments. In Chapter 2, I consider several recent proposals for measuring the explanatory power of causal explanations, and show that these (...) measures fail to track the comparative depth of explanations given at different levels of granularity. In Chapter 3, I offer a pragmatic account of how to partition the measure space of a causal variable so as to optimally explain its effect. My account uses the decision-theoretic notion of value of information, and indexes the relative depth of an explanation to a particular agent faced with a particular decision problem. Chapter 4 applies this same decisiontheoretic framework to answer the epistemic question of how to discover constitutive relationships in nature. In Chapter 5, I describe the formal details of the relationship between random variables that are meant to be coarse-grained and fine-grained representations of the same type of phenomenon. I use this formal framework to rebut a popular argument for the view that special science probabilities can be objective chances. Chapter 6 discusses challenges related to the causal interpretation of Bayes nets that use imprecise rather than precise probabilities. (shrink)