Modelers often rely on robustness analysis, the search for predictions common to several independent models. Robustness analysis has been characterized and championed by Richard Levins and William Wimsatt, who see it as central to modern theoretical practice. The practice has also been severely criticized by Steven Orzack and Elliott Sober, who claim that it is a nonempirical form of confirmation, effective only under unusual circumstances. This paper addresses Orzack and Sober's criticisms by giving a new account of robustness analysis and (...) showing how the practice can identify robust theorems. Once the structure of robust theorems is clearly articulated, it can be shown that such theorems have a degree of confirmation, despite the lack of direct empirical evidence for their truth. (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)

Late nineteenth‐century opponents of atomism questioned whether the evidence required any notion of an atom. In this spirit, Duhem developed an account of the import of chemical formulas that is clearly neutral on the atomic question rather than antiatomistic. The argument is supplemented with specific inadequacies of atomic theories of chemical combination and considerably strengthened by the theory of chemical combination provided by thermodynamics. Despite possible counterevidence available at the time, which should have tempered some of Duhem's concluding remarks, there (...) was no atomic theory of chemical combination, which is wholly a product of the twentieth century. †To contact the author, please write to: Department of Philosophy, University of Stockholm, SE‐106 91 Stockholm, Sweden; e‐mail: [email protected]. (shrink)

Because most chemical reactions, by definition, cannot avoid breaking of bonds, weakly bonded species exist fleetingly in almost every chemical change. Historically, chemical quantum mechanics was aimed at explaining the nature of strong bonds. The theory involved a number of approximations to the full solution of the Schrödinger equation. The study of non‐Kekulé molecules provides an opportunity to test whether modern quantum chemical computations are competent to deal with the nature of molecules with very weak bonds. †To contact the author, (...) please write to: Department of Chemistry, Yale University, New Haven, CT: 06520‐8107; e‐mail: [email protected]. (shrink)

This dissertation examines how we may meaningfully attribute explanatoriness to theoretical structures and in turn, how such attributions can, and should, influence theory assessment generally. In this context, I argue against "inference to the best explanation" accounts of explanatory power as well as the deflationary "answers to why questions" proposal of van Fraassen. Though my analysis emphases the role of unification in explanation, I demonstrate ways in which Kitcher's particular account is insufficient. The suggested alternative takes explanatory power to be (...) a measure of theory intelligibility; thus, its value resides in making theories easy to probe, communicate, and ultimately modify. ;An underlying goal of the discussion is to demonstrate, even for a small set of examples, that not all components of rational assessment distill down, in one way or another, to evaluations of a theory's empirical adequacy. Instead, the merits of explanatory structures are argued to be forward-looking, meaning that they hold the potential to contribute significantly to theory development either by providing directives for theoretical modification, perhaps indirectly by guiding empirical investigation, or by facilitating various means of inferential error control. ;The dissertation's central case study concerns the development of twentieth century quantum mechanical theories of the chemical bond, provocative territory because of the diversity of models and representations developed for incorporating a computationally challenging, and potentially intractable, fundamental theory into pre-existing chemical theory and practice. Explicit mathematical techniques as well as various graphical, schematic, and diagrammatic models are examined in some detail. Ultimately these theoretical structures serve as the landscape for exploring, in a preliminary fashion, the influence of representational format on inferential capacities generally. Although the connection between representation and explanation is seldom emphasized, this dissertation offers evidence of the high cost of such neglect. (shrink)