•  352
    On the explanatory role of mathematics in empirical science
    British Journal for the Philosophy of Science 61 (1): 1-25. 2010.
    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.
  •  344
    Game theoretic explanations and the evolution of justice
    with Justin D'Arms and Krzyzstof Gorny
    Philosophy of Science 65 (1): 76-102. 1998.
    Game theoretic explanations of the evolution of human behavior have become increasingly widespread. At their best, they allow us to abstract from misleading particulars in order to better recognize and appreciate broad patterns in the phenomena of human social life. We discuss this explanatory strategy, contrasting it with the particularist methodology of contemporary evolutionary psychology. We introduce some guidelines for the assessment of evolutionary game theoretic explanations of human beh…Read more
  •  313
    Idealization and modeling
    Synthese 169 (3): 427-446. 2009.
    This paper examines the role of mathematical idealization in describing and explaining various features of the world. It examines two cases: first, briefly, the modeling of shock formation using the idealization of the continuum. Second, and in more detail, the breaking of droplets from the points of view of both analytic fluid mechanics and molecular dynamical simulations at the nano-level. It argues that the continuum idealizations are explanatorily ineliminable and that a full understanding o…Read more
  •  288
    Emergence, Singularities, and Symmetry Breaking
    Foundations of Physics 41 (6): 1031-1050. 2011.
    This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world
  •  236
    Response to Belot’s “Whose Devil? Which Details?‘
    Philosophy of Science 72 (1): 154-163. 2005.
    I respond to Belot's argument and defend the view that sometimes `fundamental theories' are explanatorily inadequate and need to be supplemented with certain aspects of less fundamental `theories emeritus'.
  •  219
    Minimal Model Explanations
    with Collin C. Rice
    Philosophy of Science 81 (3): 349-376. 2014.
    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 distingui…Read more
  •  218
    On the specialness of special functions (the nonrandom effusions of the divine mathematician)
    British Journal for the Philosophy of Science 58 (2). 2007.
    This article attempts to address the problem of the applicability of mathematics in physics by considering the (narrower) question of what make the so-called special functions of mathematical physics special. It surveys a number of answers to this question and argues that neither simple pragmatic answers, nor purely mathematical classificatory schemes are sufficient. What is required is some connection between the world and the way investigators are forced to represent the world
  •  209
    Falling cats, parallel parking, and polarized light
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (4): 527-557. 2003.
    This paper addresses issues surrounding the concept of geometric phase or "anholonomy". Certain physical phenomena apparently require for their explanation and understanding, reference to toplogocial/geometric features of some abstract space of parameters. These issues are related to the question of how gauge structures are to be interpreted and whether or not the debate over their "reality" is really going to be fruitful.
  •  205
    Reduction and renormalization
    In Gerhard Ernst & Andreas Hüttemann (eds.), Time, Chance and Reduction: Philosophical Aspects of Statistical Mechanics, Cambridge University Press. pp. 159--179. 2006.
    This paper discusses the alleged reduction of Thermodynamics to Statistical Mechanics. It includes an historical discussion of J. Willard Gibbs' famous caution concerning the connections between thermodynamic properties and statistical mechanical properties---his so-called ``Thermodynamic Analogies.'' The reasons for Gibbs' caution are reconsidered in light of relatively recent work in statistical physics on the existence of the thermodynamic limit and the explanation of critical behavior using …Read more
  •  169
    This paper addresses a relatively common scientific (as opposed to philosophical) conception of intertheoretic reduction between physical theories. This is the sense of reduction in which one (typically newer and more refined) theory is said to reduce to another (typically older and coarser) theory in the limit as some small parameter tends to zero. Three examples of such reductions are discussed: First, the reduction of Special Relativity (SR) to Newtonian Mechanics (NM) as (v/c)20; second, the…Read more
  •  163
    This paper concerns the scale related decoupling of the physics of breaking drops and considers the phenomenon from the point of view of both hydrodynamics and molecular dynamics at the nanolevel. It takes the shape of droplets at breakup to be an example of a genuinely emergent phenomenon---one whose explanation depends essentially on the phenomenological (non-fundamental) theory of Navier-Stokes. Certain conclusions about the nature of "fundamental" theory are drawn.
  •  161
    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…Read more
  •  158
    Critical phenomena and breaking drops: Infinite idealizations in physics
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2): 225-244. 2004.
    Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to…Read more
  •  146
    Defining chaos
    Philosophy of Science 60 (1): 43-66. 1993.
    This paper considers definitions of classical dynamical chaos that focus primarily on notions of predictability and computability, sometimes called algorithmic complexity definitions of chaos. I argue that accounts of this type are seriously flawed. They focus on a likely consequence of chaos, namely, randomness in behavior which gets characterized in terms of the unpredictability or uncomputability of final given initial states. In doing so, however, they can overlook the definitive feature of …Read more
  •  109
    Asymptotics and the role of minimal models
    British Journal for the Philosophy of Science 53 (1): 21-38. 2002.
    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.
  •  107
    Discussions of the foundations of Classical Equilibrium Statistical Mechanics (SM) typically focus on the problem of justifying the use of a certain probability measure (the microcanonical measure) to compute average values of certain functions. One would like to be able to explain why the equilibrium behavior of a wide variety of distinct systems (different sorts of molecules interacting with different potentials) can be described by the same averaging procedure. A standard approach is to appea…Read more
  •  104
    Multiple realizability and universality
    British Journal for the Philosophy of Science 51 (1): 115-145. 2000.
    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 ph…Read more
  •  92
    This paper considers the relationship between continuum hydrodynamics and discrete molecular dynamics in the context of explaining the behavior of breaking droplets. It is argued that the idealization of a fluid as a continuum is actually essential for a full explanation of the drop breaking phenomenon and that, therefore, the less "fundamental," emergent hydrodynamical theory plays an ineliminable role in our understanding
  •  82
    A ‘Modern’ Attitude Towards Scientific Understanding
    The Monist 83 (2): 228-257. 2000.
    In a recent book on applied mathematics A. C. Fowler offers the following description of what is involved in mathematical modeling
  •  75
    Irreversibility and statistical mechanics: A new approach?
    Philosophy of Science 57 (3): 395-419. 1990.
    I discuss a broad critique of the classical approach to the foundations of statistical mechanics (SM) offered by N. S. Krylov. He claims that the classical approach is in principle incapable of providing the foundations for interpreting the "laws" of statistical physics. Most intriguing are his arguments against adopting a de facto attitude towards the problem of irreversibility. I argue that the best way to understand his critique is as setting the stage for a positive theory which treats SM as…Read more
  •  60
    The inconsistency of Physics
    Synthese 191 (13): 2973-2992. 2014.
    This paper discusses a conception of physics as a collection of theories that, from a logical point of view, is inconsistent. It is argued that this logical conception of the relations between physical theories is too crude. Mathematical subtleties allow for a much more nuanced and sophisticated understanding of the relations between different physical theories
  •  58
    Explanatory instability
    Noûs 26 (3): 325-348. 1992.
  •  57
    This paper addresses the recent resurgence of Nagel style reduction in the philosophical literature. In particular, it considers the so-called multiple realizability objection to reductionism presented most forcefully by Sober in 1999. It is argued that this objection misses the point of multiple realizability and that there remain serious problems for reductionist methodologies in science.
  •  54
    This paper aims to draw attention to an explanatory problem posed by the existence of multiply realized or universal behavior exhibited by certain physical systems. The problem is to explain how it is possible that systems radically distinct at lower-scales can nevertheless exhibit identical or nearly identical behavior at upper-scales. Theoretically this is reflected by the fact that continuum theories such as fluid mechanics are spectacularly successful at predicting, describing, and explainin…Read more
  •  49
    The Tyranny of Scales
    In The Oxford handbook of philosophy of physics, Oxford University Press. pp. 255-286. 2013.
    This paper examines a fundamental problem in applied mathematics. How can one model the behavior of materials that display radically different, dominant behaviors at different length scales. Although we have good models for material behaviors at small and large scales, it is often hard to relate these scale-based models to one another. Macroscale models represent the integrated effects of very subtle factors that are practically invisible at the smallest, atomic, scales. For this reason it has b…Read more
  •  49
    I discuss recent work in ergodic theory and statistical mechanics, regarding the compatibility and origin of random and chaotic behavior in deterministic dynamical systems. A detailed critique of some quite radical proposals of the Prigogine school is given. I argue that their conclusion regarding the conceptual bankruptcy of the classical conceptions of an exact microstate and unique phase space trajectory is not completely justified. The analogy they want to draw with quantum mechanics is not …Read more
  •  36
    Lawrence Sklar philosophy and the foundations of dynamics
    British Journal for the Philosophy of Science 66 (3): 701-705. 2015.
  •  35
    The Oxford Handbook of Philosophy of Physics (edited book)
    Oxford University Press USA. 2013.
    This Handbook provides an overview of many of the topics that currently engage philosophers of physics. It surveys new issues and the problems that have become a focus of attention in recent years. It also provides up-to-date discussions of the still very important problems that dominated the field in the past.
  •  35
    Universality and RG Explanations
    Perspectives on Science 27 (1): 26-47. 2019.
    In its broadest sense, "universality" is a technical term for something quite ordinary. It refers to the existence of patterns of behavior by physical systems that recur and repeat despite the fact that in some sense the situations in which these patterns recur and repeat are different. Rainbows, for example, always exhibit the same pattern of spacings and intensities of their bows despite the fact that the rain showers are different on each occasion. They are different because the shapes of the…Read more