The optimality approach to modeling natural selection has been criticized by many biologists and philosophers of biology. For instance, Lewontin (1979) argues that the optimality approach is a shortcut that will be replaced by models incorporating genetic information, if and when such models become available. In contrast, I think that optimality models have a permanent role in evolutionary study. I base my argument for this claim on what I think it takes to best explain an event. In certain contexts, optimality (...) and game-theoretic models best explain some central types of evolutionary phenomena. ‡Thanks to Michael Friedman, Helen Longino, Michael Weisberg, and especially Elliott Sober for comments on earlier drafts of this paper. †To contact the author, please write to: Department of Philosophy, Stanford University, Stanford, CA 94305-2155; e-mail: [email protected]. (shrink)

A traditional view of mathematical modeling holds, roughly, that the more details of the phenomenon being modeled that are represented in the model, the better the model is. This paper argues that often times this ‘details is better’ approach is misguided. One ought, in certain circumstances, to search for an exactly solvable minimal model—one which is, essentially, a caricature of the physics of the phenomenon in question.

This paper concerns what Jerry Fodor calls a 'metaphysical mystery': How can there by macroregularities that are realized by wildly heterogeneous lower level mechanisms? But the answer to this question is not as mysterious as many, including Jaegwon Kim, Ned Block, and Jerry Fodor might think. The multiple realizability of the properties of the special sciences such as psychology is best understood as a kind of universality, where 'universality' is used in the technical sense one finds in the physics literature. (...) It is argued that the same explanatory strategy used by physicists to provide understanding of universal behavior in physics can be used to explain how special science properties can be heterogeneously multiply realized. (shrink)

Roald Hoffmann and other theorists claim that we ought to use highly idealized chemical models (“qualitative models”) in order to increase our understanding of chemical phenomena, even though other models are available which make more highly accurate predictions. I assess this norm by examining one of the tradeoffs faced by model builders and model users—the tradeoff between precision and generality. After arguing that this tradeoff obtains in many cases, I discuss how the existence of this tradeoff can help us defend (...) Hoffmann's norm for modelling. (shrink)

even if an equilibrium is asymptotically stable, that is no guarantee that the system will reach that equilibrium unless we know that the system's initial state is sufficiently close to the equilibrium. Global stability of an equilibrium, when we have it, gives the equilibrium a much more powerful explanatory role. An equilibrium is globally asymptotically stable if the dynamics carries every possible initial state in the interior of the state space to that equilibrium. If an equilibrium is globally stable, it (...) can have.. (shrink)

It has been argued, most trenchantly by Nancy Cartwright, that the diversity of the concepts and regularities we actually use to describe nature and predict and explain its behavior leaves us with no reason to believe that our foundational physical theories actually "apply" outside of delicately contrived systems within the laboratory. This paper argues that, diversity of method notwithstanding, there is indeed good reason to think that the foundational laws of physics are universal in their scope.

The official model of explanation proposed by the logical empiricists, the covering law model, is subject to familiar objections. The goal of the present paper is to explore an unofficial view of explanation which logical empiricists have sometimes suggested, the view of explanation as unification. I try to show that this view can be developed so as to provide insight into major episodes in the history of science, and that it can overcome some of the most serious difficulties besetting the (...) covering law model. (shrink)

To explain the phenomena in the world of our experience, to answer the question “why?” rather than only the question “what?”, is one of the foremost objectives of all rational inquiry; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science, there exists considerable difference of opinion as to the function (...) and the essential characteristics of scientific explanation. In the present essay, an attempt will be made to shed some light on these issues by means of an elementary survey of the basic pattern of scientific explanation and a subsequent more rigorous analysis of the concept of law and of the logical structure of explanatory arguments. (shrink)

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Reductionism is often understood to include two theses: (1) every singular occurrence that the special sciences can explain also can be explained by physics; (2) every law in a higher-level science can be explained by physics. These claims are widely supposed to have been refuted by the multiple realizability argument, formulated by Putnam (1967, 1975) and Fodor (1968, 1975). The present paper criticizes the argument and identifies a reductionistic thesis that follows from one of the argument's premises.

Physics tells us what is objectively there. It has no place for the colours of things. So colours are not objectively there. Hence, if there is such a thing at all, colour is mind-dependent. This argument forms the background to disputes over whether common sense makes a mistake about colours. It is assumed that..

Ceteris-paribus clauses are nothing to worry about; aceteris-paribus qualifier is not poisonously indeterminate in meaning. Ceteris-paribus laws teach us that a law need not be associated straightforwardly with a regularity in the manner demanded by regularity analyses of law and analyses of laws as relations among universals. This lesson enables us to understand the sense in which the laws of nature would have been no different under various counterfactual suppositions — a feature even of those laws that involve no ceteris-paribus (...) qualification and are actually associated with exceptionless regularities. Ceteris-paribus generalizations of an‘inexact science’ qualify as laws of that science in virtue of their distinctive relation to counterfactuals: they form a set that is stable for the purposes of that field. (Though an accident may possess tremendous resilience under counterfactual suppositions, the laws are sharply distinguished from the accidents in that the laws are collectively as resilient as they could logically possibly be.) The stability of an inexact science's laws may involve their remaining reliable even under certain counterfactual suppositions violating fundamental laws of physics. The ceteris-paribus laws of an inexact science may thus possess a kind of necessity lacking in the fundamental laws of physics. A nomological explanation supplied by an inexact science would then be irreducible to an explanation of the same phenomenon at the level of fundamental physics. Island biogeography is used to illustrate how a special science could be autonomous in this manner. (shrink)

The two major modern accounts of explanation are the causal and unification accounts. My aim in this paper is to provide a kind of unification of the causal and the unification accounts, by using the central technical apparatus of the unification account to solve a central problem faced by the causal account, namely, the problem of determining which parts of a causal network are explanatorily relevant to the occurrence of an explanandum. The end product of my investigation is a causal (...) account of explanation that has many of the advantages of the unification account. (shrink)

In this paper I defend fundamental physical laws from the arguments mounted by Nancy Cartwright in her (1999) book The Dappled World (and other publications). I argue, positively, that we have a good deal of evidence for mathematical laws—not just causal capacities—underlying many natural phenomena. I also argue, negatively, that Cartwright's main arguments unfairly demand that a fundamentalist be a strong reductionist.

In a recent book on applied mathematics A. C. Fowler offers the following description of what is involved in mathematical modeling.

Individualists claim that wide explanations in psychology are problematic. I argue that wide psychological explanations sometimes have greater explanatory power than individualistic explanations. The aspects of explanatory power I focus on are causal depth and theoretical appropriateness. Reflection on the depth and appropriateness of other wide explanations of behavior, such as evolutionary explanations, clarifies why wide psychological explanations sometimes have more causal depth and theoretical appropriateness than narrow psychological explanations. I also argue for the rejection of eliminative materialism.

Despite their best efforts, scientists may be unable to construct models that simultaneously exemplify every theoretical virtue. One explanation for this is the existence of tradeoffs: relationships of attenuation that constrain the extent to which models can have such desirable qualities. In this paper, we characterize three types of tradeoffs theorists may confront. These characterizations are then used to examine the relationships between parameter precision and two types of generality. We show that several of these relationships exhibit tradeoffs and discuss (...) what consequences those tradeoffs have for theoretical practice. (shrink)

It is widely held that the size of a probability makes no difference to the quality of a probabilistic explanation. I argue that explanatory practice in statistical physics belies this claim. The claim has gained currency only because of an impoverished conception of probabilistic processes and an unwarranted assumption that all probabilistic explanations have a single form.

A common argument against explanatory reductionism is that higher‐level explanations are sometimes or always preferable because they are more general than reductive explanations. Here I challenge two basic assumptions that are needed for that argument to succeed. It cannot be assumed that higher‐level explanations are more general than their lower‐level alternatives or that higher‐level explanations are general in the right way to be explanatory. I suggest a novel form of pluralism regarding levels of explanation, according to which explanations at different (...) levels are preferable in different circumstances because they offer different types of generality, which are appropriate in different circumstances of explanation. (shrink)

In the course of defending his view of the relation between the special sciences and physics from Jaegwon Kim’s objections Jerry Fodor asks “So then, why is there anything except physics?” By which he seems to mean to ask if physics is fundamental and complete in its domain how can there be autonomous special science laws. Fodor wavers between epistemological and metaphysical understandings of the autonomy of the special sciences. In my paper I draw out the metaphysical construal of his (...) view and argue that while in a sense it answers Fodor’s question it is immensely implausible. (shrink)

Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do (...) science. This account successfully reconciles theoretical indispensability and metaphysical dispensability and has important consequences for both advocates and critics of indispensability arguments for platonism about mathematics. (shrink)

The multiple-realizability argument has been the mainstay ofanti-reductionist consensus in philosophy of mind for the past thirty years. Reductionist opposition to it has sometimes taken the form of the Disjunctive Move: If mental types are multiply-realizable, they are not coextensive with physical types; they might nevertheless be coextensive with disjunctionsof physical types, and those disjunctions could still underwrite psychophysical reduction. Among anti-reductionists, confidence is high that the Disjunctive Move fails; arguments to this effect, however, often leave something to be desired. (...) I raise difficulties for one anti-reductionist response to the DisjunctiveMove, the Explanatory Response. (shrink)

Many of the things that we try to explain, in both our common sense and our scientific engagement with the world, are capable of being explained more or less finely: that is, with greater or lesser attention to the detail of the producing mechanism. A natural assumption, pervasive if not always explicit, is that other things being equal, the more finegrained an explanation, the better. Thus, Jon Elster, who also thinks there are instrumental reasons for wanting a more fine-grained explanation, (...) assumes that in any case the mere fact of getting nearer the detail of production makes such an explanation intrinsically superior: “a more detailed explanation is also an end in itself”. Michael Taylor agrees: “A good explanation should be, amongst other things, as fine-grained as possible.”. (shrink)

This paper discusses the explanatory significance of the equilibrium concept in the context of an example of extremely complicated dynamical behavior. In particular, numerical evidence is presented for the existence of chaotic dynamics on a "strange attractor" in the evolutionary game dynamics introduced by Taylor and Jonker [also known as the "replicator dynamics"]. This phenomenon is present already in four strategy evolutionary games where the dynamics takes place in a simplex in three dimensional space-the lowest number of dimensions in which (...) such a strange attractor is possible. From a dynamical point of view, it is the attractor-rather than the equilibrium-that is of prime interest. (shrink)

This paper discusses some issues concerning the relationship between the mental and the physical, including the so-called causal exclusion argument, within the framework of a broadly interventionist approach to causation.