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)

Several articles have recently appeared arguing that there really are no viable alternatives to mechanistic explanation in the biological sciences. This claim is meant to hold both in principle and in practice. The basic claim is that any explanation of a particular feature of a biological system, including dynamical explanations, must ultimately be grounded in mechanistic explanation. There are several variations on this theme, some stronger and some weaker. In order to avoid equivocation and miscommunication, in section 1 we will (...) argue that mechanistic explanation is defined by localization and decomposition. In section 2 we will argue that systems neuroscience contains explanations that violate both localization and decomposition on any non-trivial construal of these concepts. Therefore, in section 3 we conclude the mechanistic model of explanation either needs to stretch to now include explanations wherein localization or decomposition fail, or acknowledge that there are counter-examples to mechanistic explanation in the biological sciences. We will also consider consequences and possible replies on the part of the mechanist in section 3. (shrink)

An analysis of two heuristic strategies for the development of mechanistic models, illustrated with historical examples from the life sciences. In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in divergent (...) explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility—the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized. When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993. (shrink)

It is shown that three common conditions for scientific explanations are violated by a widely used class of domain-independent explanations. These explanations can accommodate both complex and noncomplex systems and do not require the use of detailed models of system-specific processes for their effectiveness, although they are compatible with such model-based explanations. The approach also shows how a clean separation can be maintained between mathematical representations and empirical content.

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)

While mechanistic explanation and, to a lesser extent, nomological explanation are well-explored topics in the philosophy of biology, topological explanation is not. Nor is the role of diagrams in topological explanations. These explanations do not appeal to the operation of mechanisms or laws, and extant accounts of the role of diagrams in biological science explain neither why scientists might prefer diagrammatic representations of topological information to sentential equivalents nor how such representations might facilitate important processes of explanatory reasoning unavailable to (...) scientists who restrict themselves to sentential representations. Accordingly, relying upon a case study about immune system vulnerability to attacks on CD4+ T-cells, I argue that diagrams group together information in a way that avoids repetition in representing topological structure, facilitate identification of specific topological properties of those structures, and make available to controlled processing explanatorily salient counterfactual information about topological structures, all in ways that sentential counterparts of diagrams do not. (shrink)

Several articles have recently appeared arguing that there really are no viable alternatives to mechanistic explanation in the biological sciences (Kaplan and Bechtel; Kaplan and Craver). We argue that mechanistic explanation is defined by localization and decomposition. We argue further that systems neuroscience contains explanations that violate both localization and decomposition. We conclude that the mechanistic model of explanation needs to either stretch to now include explanations wherein localization or decomposition fail or acknowledge that there are counterexamples to mechanistic explanation (...) in the biological sciences. (shrink)

The aim of the paper is to introduce some of the history and key concepts of network science to a philosophical audience, and to highlight a crucial—and often problematic—presumption that underlies the network approach to complex systems. Network scientists often talk of “the structure” of a given complex system or phenomenon, which encourages the view that there is a unique and privileged structure inherent to the system, and that the aim of a network model is to delineate this structure. I (...) argue that this sort of naïve realism about structure is not a coherent or plausible position, especially given the multiplicity of types of entities and relations that can feature as nodes and links in complex networks. (shrink)

Philosophers of science increasingly recognize the importance of idealization: the intentional introduction of distortion into scientific theories. Yet this recognition has not yielded consensus about the nature of idealization. e literature of the past thirty years contains disparate characterizations and justifications, but little evidence of convergence towards a common position.

This paper argues that besides mechanistic explanations, there is a kind of explanation that relies upon “topological” properties of systems in order to derive the explanandum as a consequence, and which does not consider mechanisms or causal processes. I first investigate topological explanations in the case of ecological research on the stability of ecosystems. Then I contrast them with mechanistic explanations, thereby distinguishing the kind of realization they involve from the realization relations entailed by mechanistic explanations, and explain how both (...) kinds of explanations may be articulated in practice. The second section, expanding on the case of ecological stability, considers the phenomenon of robustness at all levels of the biological hierarchy in order to show that topological explanations are indeed pervasive there. Reasons are suggested for this, in which “neutral network” explanations are singled out as a form of topological explanation that spans across many levels. Finally, I appeal to the distinction of explanatory regimes to cast light on a controversy in philosophy of biology, the issue of contingence in evolution, which is shown to essentially involve issues about realization. (shrink)

I defend an account of explanatory depth according to which explanations in the non-fundamental sciences can be deeper than explanations in fundamental physics.

Two widely accepted assumptions within cognitive science are that (1) the goal is to understand the mechanisms responsible for cognitive performances and (2) computational modeling is a major tool for understanding these mechanisms. The particular approaches to computational modeling adopted in cognitive science, moreover, have significantly affected the way in which cognitive mechanisms are understood. Unable to employ some of the more common methods for conducting research on mechanisms, cognitive scientists’ guiding ideas about mechanism have developed in conjunction with their (...) styles of modeling. In particular, mental operations often are conceptualized as comparable to the processes employed in classical symbolic AI or neural network models. These models, in turn, have been interpreted by some as themselves intelligent systems since they employ the same type of operations as does the mind. For this paper, what is significant about these approaches to modeling is that they are constructed specifically to account for behavior and are evaluated by how well they do so—not by independent evidence that they describe actual operations in mental mechanisms. (shrink)

Every Thing Must Go aruges that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it ...

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.

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)

Proponents of mechanistic explanation all acknowledge the importance of organization. But they have also tended to emphasize specificity with respect to parts and operations in mechanisms. We argue that in understanding one important mode of organization—patterns of causal connectivity—a successful explanatory strategy abstracts from the specifics of the mechanism and invokes tools such as those of graph theory to explain how mechanisms with a particular mode of connectivity will behave. We discuss the connection between organization, abstraction, and mechanistic explanation and (...) illustrate our claims by looking at an example from recent research on so-called network motifs. (shrink)

To understand the behavior of a complex system, you must understand the interactions among its parts. Doing so is difficult for non-decomposable systems, in which the interactions strongly influence the short-term behavior of the parts. Science's principal tool for dealing with non-decomposable systems is a variety of probabilistic analysis that I call EPA. I show that EPA's power derives from an assumption that appears to be false of non-decomposable complex systems, in virtue of their very non-decomposability. Yet EPA is extremely (...) successful. I aim to find an interpretation of EPA's assumption that is consistent with, indeed that explains, its success. (shrink)