In this field guide, I distinguish five separate senses with which the term ‘mechanism’ is used in contemporary philosophy of science. Many of these senses have overlapping areas of application but involve distinct philosophical claims and characterize the target mechanisms in relevantly different ways. This field guide will clarify the key features of each sense and introduce some main debates, distinguishing those that transpire within a given sense from those that are best understood as concerning two distinct senses. The ‘new (...) mechanisms’ sense is the primary sense from which other senses will be distinguished. In part II of this field guide, I consider three further senses of the term that are ontologically ‘flat’ or at least not explicitly hierarchical in character: equations in structural equation models of causation, causal-physical processes, and information-theoretic constraints on states available to systems. After characterizing each sense, I clarify its ontological commitments, its methodological implications, how it figures in explanations, its implications for reduction, and the key manners in which it differs from other senses of mechanism. I conclude that there is no substantive core meaning shared by all senses, and that debates in contemporary philosophy of science can benefit from clarification regarding precisely which sense of mechanism is at stake. (shrink)

one takes to be the most salient, any pair could be judged more similar to each other than to the third. Goodman uses this second problem to showthat there can be no context-free similarity metric, either in the trivial case or in a scientifically ...

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a (...) scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics. (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 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.

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)

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.

The Enhanced Indispensability Argument (Baker [ 2009 ]) exemplifies the new wave of the indispensability argument for mathematical Platonism. The new wave capitalizes on mathematics' role in scientific explanations. I will criticize some analyses of mathematics' explanatory function. In turn, I will emphasize the representational role of mathematics, and argue that the debate would significantly benefit from acknowledging this alternative viewpoint to mathematics' contribution to scientific explanations and knowledge.

Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...) potential future directions of research for each side in the debate over the existence of abstract mathematical objects. (shrink)

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

In semiclassical mechanics one finds explanations of quantum phenomena that appeal to classical structures. These explanations are prima facie problematic insofar as the classical structures they appeal to do not exist. Here I defend the view that fictional structures can be genuinely explanatory by introducing a model-based account of scientific explanation. Applying this framework to the semiclassical phenomenon of wavefunction scarring, I argue that not only can the fictional classical trajectories explain certain aspects of this quantum phenomenon, but also that (...) an explanation that does not make reference to these classical structures is, in a certain sense, deficient. (shrink)

Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...) issues in the philosophy of mathematics; in particular it may help platonists respond to a recent challenge by Joseph Melia concerning the force of the Indispensability Argument. (shrink)

Theorizing in ecology and evolution often proceeds via the construction of multiple idealized models. To determine whether a theoretical result actually depends on core features of the models and is not an artifact of simplifying assumptions, theorists have developed the technique of robustness analysis, the examination of multiple models looking for common predictions. A striking example of robustness analysis in ecology is the discovery of the Volterra Principle, which describes the effect of general biocides in predator-prey systems. This paper details (...) the discovery of the Volterra Principle and the demonstration of its robustness. It considers the classical ecology literature on robustness and introduces two individual-based models of predation, which are used to further analyze the Volterra Principle. The paper also introduces a distinction between parameter robustness, structural robustness, and representational robustness, and demonstrates that the Volterra Principle exhibits all three kinds of robustness. *Received September 2006; revised May 2007. ‡Earlier versions of this paper were presented at the Australasian Association of Philosophy, the London School of Economics, and the University of Bristol. The authors wish to thank those audiences as well as Patrick Forber, Ken Waters, Deena Skolnick Weisberg, Uri Wilensky, and Bill Wimsatt for many helpful comments. Special thanks to Giacomo Sillari for his assistance in translating Volterra's original paper and his insightful thoughts about Volterra's aims and methods. Some of the research in this paper was supported by NSF grant SES-0620887 to MW. †To contact the authors, please write to: Michael Weisberg, Department of Philosophy, University of Pennsylvania, 433 Logan Hall, Philadelphia, PA 19104; e-mail: [email protected]; Kenneth Reisman, Pluribo, Inc., 100 Park Avenue, Suite 1600, New York, NY 10017; e-mail: [email protected]. (shrink)

In this paper I discuss the relationship between model, theories, and laws in the practice of experimental scale modeling. The methodology of experimental scale modeling, also known as physical similarity, differs markedly from that of other kinds of models in ways that are important to issues in philosophy of science. Scale models are not discussed in much depth in mainstream philosophy of science. In this paper, I examine how scale models are used in making inferences. The main question I address (...) in this talk is ``How are fundamental laws involved in the construction of, and inferences drawn from, experimental scale models?'' We shall see that there is a refreshing alternative to the mainstream view that models can serve only as intermediaries between theory and experiment. Using the methodology of scale models, one can use observations on one piece of the world to make inferences about another piece of the world, without involving an intermediate abstract model about which one reasons. The philosophical significance of that point to philosophy of science is that the method of physical similarity, which provides the basis for inferences based upon scale models, is a qualitatively different way in which fundamental laws can be used in analogical reasoning that is truly informative. Finally, as this method provides a formal basis for case-based reasoning, it may be helpful in formalizing methods used in some of the so-called ``special sciences''. (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)

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)