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.

This paper is an empirical critique of causal accounts of scientific explanation. Drawing on explanations which rely on nonlinear dynamical modeling, I argue that the requirement of causal relevance is both too strong and too weak to be constitutive of scientific explanation. In addition, causal accounts obscure how the process of mathematical modeling produces explanatory information. I advance three arguments for the inadequacy of causal accounts. First, I argue that explanatorily relevant information is not always information about causes, even in (...) cases where the explanandum has an identifiable causal history. Second, I argue that treating theoretical explanations as reductions from general causal laws does not accurately describe the types of "top-down" explanations typical of dynamical modeling. Finally, I argue that causal/mechanical accounts of explanation are intrinsically vulnerable to the irrelevance problem. (shrink)

How do novel scientific concepts arise? In Creating Scientific Concepts, Nancy Nersessian seeks to answer this central but virtually unasked question in the problem of conceptual change. She argues that the popular image of novel concepts and profound insight bursting forth in a blinding flash of inspiration is mistaken. Instead, novel concepts are shown to arise out of the interplay of three factors: an attempt to solve specific problems; the use of conceptual, analytical, and material resources provided by the cognitive-social-cultural (...) context of the problem; and dynamic processes of reasoning that extend ordinary cognition. Focusing on the third factor, Nersessian draws on cognitive science research and historical accounts of scientific practices to show how scientific and ordinary cognition lie on a continuum, and how problem-solving practices in one illuminate practices in the other. (shrink)

This paper examines a case of failed interdisciplinary collaboration, between experimental stem cell research and theoretical systems biology. Recently, two groups of theoretical biologists have proposed dynamical systems models as a basis for understanding stem cells and their distinctive capacities. Experimental stem cell biologists, whose work focuses on manipulation of concrete cells, tissues and organisms, have largely ignored these proposals. I argue that ‘failure to communicate’ in this case is rooted in divergent views of explanation: the theoretically-inclined modelers are committed (...) to a version of the covering-law view, while experimental stem cell biologists aim at mechanistic explanations. I propose a way to reconcile these two explanatory approaches to cell development, and discuss the significance of this result for interdisciplinary collaboration in systems biology and beyond. (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)

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)

Recently philosophers of science have begun to pay more attention to the use of highly idealized mathematical models in scientific theorizing. An important example of this kind of highly idealized modeling is the widespread use of optimality models within evolutionary biology. One way to understand the explanations provided by these models is as a censored causal explanation: an explanation that omits certain causal factors in order to focus on a modular subset of the causal processes that led to the explanandum. (...) In this paper, I first argue that the censored causal model approach fails to establish a permanent explanatory role for optimality models in biology and mischaracterizes the explanatory virtues of biological optimality modeling. In addition, I argue that many biological optimality explanations cannot be characterized as censored causal explanations. In response, I propose an alternative approach that analyzes optimality models’ reliance on synchronically representing a system’s constraints and tradeoffs as well as their employment of various kinds of idealization in order to provide equilibrium explanations. (shrink)

Using as case studies two early diagrams that represent mechanisms of the cell division cycle, we aim to extend prior philosophical analyses of the roles of diagrams in scientific reasoning, and specifically their role in biological reasoning. The diagrams we discuss are, in practice, integral and indispensible elements of reasoning from experimental data about the cell division cycle to mathematical models of the cycle’s molecular mechanisms. In accordance with prior analyses, the diagrams provide functional explanations of the cell cycle and (...) facilitate the construction of mathematical models of the cell cycle. But, extending beyond those analyses, we show how diagrams facilitate the construction of mathematical models, and we argue that the diagrams permit nomological explanations of the cell cycle. We further argue that what makes diagrams integral and indispensible for explanation and model construction is their nature as locality aids: they group together information that is to be used together in a way that sentential representations do not. (shrink)

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)

This paper explores the question of whether all or most explanations in biology are, or ideally should be, ‘mechanistic’. I begin by providing an account of mechanistic explanation, making use of the interventionist ideas about causation I have developed elsewhere. This account emphasizes the way in which mechanistic explanations, at least in the biological sciences, integrate difference‐making and spatio‐temporal information, and exhibit what I call fine‐tunedness of organization. I also emphasize the role played by modularity conditions in mechanistic explanation. I (...) will then argue, in agreement with John Dupré, that, given this account, it is plausible that many biological systems require explanations that are relatively non‐mechanical or depart from expectations one associates with the behaviour of machines. (shrink)

Due to the variation, contingency and complexity of living systems, biology is often taken to be a science without fundamental theories, laws or general principles. I revisit this question in light of the quest for design principles in systems biology and show that different views can be reconciled if we distinguish between different types of generality. The philosophical literature has primarily focused on generality of specific models or explanations, or on the heuristic role of abstraction. This paper takes a different (...) approach in emphasizing a theory-constituting role of general principles. Design principles signify general dependency-relations between structures and functions, given a set of formally defined constraints. I contend that design principles increase our understanding of living systems by relating specific models to general types. The categorization of types is based on a delineation of the scope of biological possibilities, which serves to identify and define the generic features of classes of systems. To characterize the basis for general principles through generic abstraction and reasoning about possibility spaces, I coin the term constraint-based generality. I show that constraint-based generality is distinct from other types of generality in biology, and argue that general principles play a unifying role that does not entail theory reduction. (shrink)

This paper is concerned with reasonings that purport to explain why certain organisms have certain traits by showing that their actual design is better than contrasting designs. Biologists call such reasonings 'functional explanations'. To avoid confusion with other uses of that phrase, I call them 'design explanations'. This paper discusses the structure of design explanations and how they contribute to scientific understanding. Design explanations are contrastive and often compare real organisms to hypothetical organisms that cannot possibly exist. They are not (...) causal but appeal to functional dependencies between an organism's different traits. These explanations point out that because an organism has certain traits, it cannot be alive if the trait to be explained were replaced by a specified alternative. They can be understood from a mechanistic point of view as revealing the constraints on what mechanisms can be alive. (shrink)

Kaplan and Craver claim that all explanations in neuroscience appeal to mechanisms. They extend this view to the use of mathematical models in neuroscience and propose a constraint such models must meet in order to be explanatory. I analyze a mathematical model used to provide explanations in dynamical systems neuroscience and indicate how this explanation cannot be accommodated by the mechanist framework. I argue that this explanation is well characterized by Batterman’s account of minimal model explanations and that it demonstrates (...) how relationships between explanatory models in neuroscience and the systems they represent is more complex than has been appreciated. (shrink)

Discovery proceeds in stages of construction, evaluation, and revision. Each of these stages is constrained by what is known or conjectured about what is being discovered. A new characterization of mechanism aids in specifying what is to be discovered when a mechanism is sought. Guidance in discovering mechanisms may be provided by the reasoning strategies of schema instantiation, modular subassembly, and forward/backward chaining. Examples are found in mechanisms in molecular biology, biochemistry, immunology, and evolutionary biology.

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical (...) equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena, where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism’s ability to respond to perturbations. I offer general conclusions for philosophical accounts of explanation. (shrink)

Stem cell biology and systems biology are two prominent new approaches to studying cell development. In stem cell biology, the predominant method is experimental manipulation of concrete cells and tissues. Systems biology, in contrast, emphasizes mathematical modeling of cellular systems. For scientists and philosophers interested in development, an important question arises: how should the two approaches relate? This essay proposes an answer, using the model of Waddington’s landscape to triangulate between stem cell and systems approaches. This simple abstract model represents (...) development as an undulating surface of hills and valleys. Originally constructed by C. H. Waddington to visually explicate an integrated theory of genetics, development and evolution, the landscape model can play an updated unificatory role. I examine this model’s structure, representational assumptions, and uses in all three contexts, and argue that explanations of cell development require both mathematical models and concrete experiments. On this view, the two approaches are interdependent, with mathematical models playing a crucial but circumscribed role in explanations of cell development. (shrink)

Explaining the complex dynamics exhibited in many biological mechanisms requires extending the recent philosophical treatment of mechanisms that emphasizes sequences of operations. To understand how nonsequentially organized mechanisms will behave, scientists often advance what we call dynamic mechanistic explanations. These begin with a decomposition of the mechanism into component parts and operations, using a variety of laboratory-based strategies. Crucially, the mechanism is then recomposed by means of computational models in which variables or terms in differential equations correspond to properties of (...) its parts and operations. We provide two illustrations drawn from research on circadian rhythms. Once biologists identified some of the components of the molecular mechanism thought to be responsible for circadian rhythms, computational models were used to determine whether the proposed mechanisms could generate sustained oscillations. Modeling has become even more important as researchers have recognized that the oscillations generated in individual neurons are synchronized within networks; we describe models being employed to assess how different possible network architectures could produce the observed synchronized activity. (shrink)

Discovery proceeds in stages of construction, evaluation, and revision. Each of these stages is constrained by what is known or conjectured about what is being discovered. A new characterization of mechanism aids in specifying what is to be discovered when a mechanism is sought. Guidance in discovering mechanisms may be provided by the reasoning strategies of schema instantiation, modular subassembly, and forward/backward chaining. Examples are found in mechanisms in molecular biology, biochemistry, immunology, and evolutionary biology.

Relations between physics and biology have been always difficult. One reason is that physical approaches to the phenomena of life have frequently been conceived by their authors as alternatives to biological explanations. My argument is that molecular descriptions and explanations have been pushed so far that they have reached their limits: these limits constitute a favourable niche in which physical explanations can develop. I will focus on the field of molecular and cell biology and give many examples of these recent (...) physical studies made possible by the precision of molecular observations. The nature of these niches is probably diverse. I consider that it is too early to have a global view of the interactions between biological and physical explanations, and to organize them into different categories. Such interactions are not new within the life sciences: the history of biology reveals a complex, permanently moving landscape of interactions between biological and physical explanations. (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)

ABSTRACT There is a new argument form within theoretical biology. This form takes as input competing explanatory models; it yields as output the conclusion that one of these models is more plausible than the others. The driving force for this argument form is an analysis showing that one model exhibits more parametric robustness than its competitors. This article examines these inferences to the more robust explanation, analysing them as variants of inference to the best explanation. The article defines parametric robustness (...) and distinguishes it from more familiar kinds of robustness. The article also argues that parametric robustness is an explanatory virtue not subsumed by more familiar explanatory virtues, and that the plausibility verdicts in the conclusions of inferences to the more robust explanations are best interpreted as guidance for research activity, rather than claims about likely truth. 1Introducing Inference to the More Robust Explanation 2Inference to the More Robust Explanation in the Study of Apoptosis 2.1Regulating apoptosis 2.2Competing models and evidential indecision 2.3Measuring robustness 2.4Robustness as a guide to plausibility 2.5Varieties of robustness 3Inference to the More Robust Explanation as Inference to the Best Explanation 3.1The structure of inference to the best explanation 3.2Parametric robustness as an explanatory virtue rather than an explanandum 3.3Relation of parametric robustness to other explanatory virtues 4Epistemological Significance of Inference to the More Robust Explanation 4.1Plausibility in practice 4.2Plausibility in principle 5Conclusion. (shrink)

With the emergence of systems biology the notion of organizing principles is being highlighted as a key research aim. Researchers attempt to ‘reverse engineer’ the functional organization of biological systems using methodologies from mathematics, engineering and computer science while taking advantage of data produced by new experimental techniques. While systems biology is a relatively new approach, the quest for general principles of biological organization dates back to systems theoretic approaches in early and mid-20th century. The aim of this paper is (...) to draw on this historical background in order to increase the understanding of the motivation behind the systems theoretic approach and to clarify different epistemic aims within systems biology. We pinpoint key aspects of earlier approaches that also underlie the current practice. These are i) the focus on relational and system-level properties, ii) the inherent critique of reductionism and fragmentation of knowledge resulting from overspecialization, and iii) the insight that the ideal of formulating abstract organizing principles is complementary to, rather than conflicting with, the aim of formulating detailed explanations of biological mechanisms. We argue that looking back not only helps us understand the current practice but also points to possible future directions for systems biology. (shrink)

Due to the variation, contingency and complexity of living systems, biology is often taken to be a science without fundamental theories, laws or general principles. I revisit this question in light of the quest for design principles in systems biology and show that different views can be reconciled if we distinguish between different types of generality. The philosophical literature has primarily focused on generality of specific models or explanations, or on the heuristic role of abstraction. This paper takes a different (...) approach in emphasizing a theory-constituting role of general principles. Design principles signify general dependencyrelations between structures and functions, given a set of formally defined constraints. I contend that design principles increase our understanding of living systems by relating specific models to general types. The categorization of types is based on a delineation of the scope of biological possibilities, which serves to identify and define the generic features of classes of systems. To characterize the basis for general principles through generic abstraction and reasoning about possibility spaces, I coin the term constraint-based generality. I show that constraintbased generality is distinct from other types of generality in biology, and argue that general principles play a unifying role that does not entail theory reduction. (shrink)

Evolutionary systems biology (ESB) aims to integrate methods from systems biology and evolutionary biology to go beyond the current limitations in both fields. This article clarifies some conceptual difficulties of this integration project, and shows how they can be overcome. The main challenge we consider involves the integration of evolutionary biology with developmental dynamics, illustrated with two examples. First, we examine historical tensions between efforts to define general evolutionary principles and articulation of detailed mechanistic explanations of specific traits. Next, these (...) tensions are further clarified by considering a recent case from another field focused on developmental dynamics: stem cell biology. In the stem cell case, incompatible explanatory aims block integration. Experimental approaches aim at mechanistic explanation while dynamical system models offer explanation in terms of general principles. We then discuss an ESB case in which integration succeeds: search for general attractors using a dynamical systems framework synergizes with the experimental search for detailed mechanisms. Contrasts between the positive and negative cases suggest general lessons for achieving an integrated understanding of developmental and evolutionary dynamics. The key integrative move is to acknowledge two complementary aims, both relevant to explanation: identifying the space of possible dynamic states and trajectories, and mechanistic understanding of causal interactions underlying a specific phenomenon of interest. These two aims can support one another in a joint project characterizing dynamic aspects of evolving lineages. This more inclusive project can lead to insights that cannot be reached by either approach in isolation. (shrink)

Design thinking in general, and optimality modeling in particular, have traditionally been associated with adaptationism—a research agenda that gives pride of place to natural selection in shaping biological characters. Our goal is to evaluate the role of design thinking in non-evolutionary analyses. Specifically, we focus on research into abstract design principles that underpin the functional organization of extant organisms. Drawing on case studies from engineering-inspired approaches in biology we show how optimality analysis, and other design-related methods, play a specific methodological (...) role that is tangential to the study of adaptation. To account for the role of these reasoning strategies in contemporary biology, we therefore suggest a reevaluation of the connection between design thinking and adaptationism. (shrink)