For over two decades now, Robert Batterman’s work has been important reading for anyone interested in emergence and reduction in the natural sciences. In Batterman’s first book, The Devil in the Details, he identified a varied collection of patterns of inference that exhibit what he called “asymptotic reasoning”: systematically eliminating or abstracting away details from the full description of a physical system given by fundamental physical theory. Batterman argued that recognizing that many details of a physical system are irrelevant to much of its dynamical behavior and, using asymptotic reasoning to eliminate those irrelevant details, often play an essential role in securing predictive and explanatory success in the physical sciences.Based on this study of asymptotic reasoning, Batterman argued that there are many cases in which the resources for explaining a physical phenomenon are not housed solely within fundamental physical theory. Nor are those resources housed solely within the less fundamental, superseded physical theory. Instead, explaining a large class of physical phenomena requires a third, hybrid theory that inhabits the “asymptotic borderlands” between the fundamental and superseded theories: a theory that abstracts away from select details of the fundamental theory while incorporating elements of the superseded theory. Batterman argued that such hybrid theories are typically necessary to explain multiply realized (what physicists call universal) patterns of behavior: identical behavior displayed by physical systems that are, in their fundamental details, importantly distinct.These two themes—the challenges of explaining universal patterns of behavior and the philosophical significance of intertheoretic borderlands—again figure centrally, if in rather different guise, in Batterman’s latest book A Middle Way. The book is framed around the following question: AUT: How can systems that are heterogeneous at some (typically) micro-scale exhibit the same pattern of behavior at the macro-scale?This question is a familiar one, but Batterman puts it to interesting use. While AUT has typically been asked of distinct systems exhibiting some identical pattern of behavior—for example, the fact that certain properties of water and iron behave identically when those systems undergo a phase transition—Batterman notes that a similar puzzle arises from the way we model single systems at different scales. Consider water, for example. At the scale of centimeters or larger, the behavior of water is modeled using the Navier-Stokes equations. This treats water as a homogeneous substance at all length scales: the Navier-Stokes equations make no distinction between the structure exhibited by water at 10 meters and at 10−100 meters. Of course, this is false: actual water is fundamentally a collection of discrete, interacting molecules, and this substructure is revealed at scales smaller than about 10−8 meters. So how is it that actual water, with all of its heterogeneous substructure, can exhibit the same behavior as a fictitious, perfectly homogeneous fluid at the scale of centimeters? How is it that the substructure of actual water appears not to matter when its behavior is modeled at sufficiently long length scales?Batterman’s approach begins with an argument that an answer to AUT cannot be found by examining only fundamental physical theories and hoping to extract from them “bottom-up” explanations of the shared behavior. Instead, the answer to AUT emerges from a study of the theories and methods used to model physical phenomena at the mesoscale. The mesoscale is a collective term for the range of intermediate scales that lie between the microscale and the macroscale. (In a steel beam, for example, the mesoscale encompasses the whole range of substructure that exists between 10−10 meters—about the scale of individual molecules—and scale of centimeters, where we model continuum phenomena like bending and shearing.) Batterman calls this collection of methods hydrodynamic methods and argues that, in the many systems to which they can be applied, they reveal an answer to AUT.Suppose you have a description of a physical system in the language of a fundamental physical theory—a description of a steel beam as a collection of molecules interacting with each other via some specified dynamics, for example. Your interest is in deriving a description of continuum phenomena like bending and shearing, which obey the Navier-Cauchy equations. One might hope that some complicated averaging procedure might work: choose little cubes of volume L3, compute a judiciously chosen average over the properties of the molecules in each cube, define a new, coarse-grained variable appropriate to the scale L′>L, and rinse and repeat until you have derived a continuum description of the steel beam from its fundamental, molecular description. Batterman emphasizes the problem with this: it almost never works. Importantly, it doesn’t work because systems like steel and water and wood are not homogeneous between the molecular scale and the continuum scales: they contains all sorts of impurities and cracks and other mesoscale structure that invalidate a naive averaging strategy. Enter hydrodynamic methods.In brief, these methods work as follows. Suppose that when examined at the mesoscale, our steel beam has disconnected blobs of impurities distributed throughout. Instead of choosing little cubes that misdiagnose the mesoscale structure, one characterizes that structure using correlation functions. If we choose two, or three, or n spatial points separated by a distance D in our steel beam, the appropriate correlation function gives the probability that molecules located at those two, three, or n spatial points lie within one of the impure blobs. A complete set of correlation functions encodes the geometric and topological structure of our steel beam at the mesoscale. One can then, in turn, define variables and dynamical equations characterizing the continuum phenomena of our steel beam using the correlation functions that accurately characterize the system’s mesoscale structure.These continuum variables represent the collective behavior of large collections of molecules, but they cannot be defined directly from the fundamental molecular description of our steel beam: instead, Batterman emphasizes, they can only be defined from the correlation functions used to characterize the mesoscale structure. Of crucial importance for Batterman is that these correlation functions are themselves mesoscale structures: properties of large collections of molecules that are only well defined at scales much larger than the fundamental, molecular scale. This forms the basis of Batterman’s rejection of “bottom-up” answers to AUT: only by taking the mesoscale structure of a physical system as the starting point can one connect the fundamental and continuum descriptions of physical system. Batterman devotes the core chapters 3 through 6 of A Middle Way to extended description of hydrodynamic methods (including an interesting historical chapter relating hydrodynamic methods to Einstein’s work on Brownian motion) and developing the argument for the primacy of mesoscale structure.So how does all of this answer AUT? It emerges from Batterman’s analysis of hydrodynamic methods that the information contained in the fundamental, molecular description of a physical system like a fluid or a metal contributes in a precisely specifiable and minimal fashion to its continuum behavior. Dynamical equations governing continuum phenomena, like the Navier-Stokes or Navier-Cauchy equations, typically contain undetermined parameters that encode properties like the viscosity of a fluid or the density of a metal. When one can calculate the values of those parameters using hydrodynamic methods, one finds that the only difference between the continuum equations for, say, water and olive oil is the value of those undetermined parameters. What this reveals, according to Batterman, is that the molecular details that distinguish olive oil from water, or a fictitious, perfectly homegeneous fluid from a real one exhibiting heterogeneous structure at the microscale, contribute to the continuum phenomena only insofar as they determine the value of a few parameters appearing in the continuum dynamical equations.Batterman’s exposition of hydrodynamic methods is technical and occasionally terse, and I found myself wishing the presentation in chapters 3 through 6 was more pedagogical. This would be less of an issue if A Middle Way addressed issues of interest only to specialists in the philosophy of physics. However, AUT is of general and long-standing philosophical interest, and it is no small feat that Batterman develops a compelling and novel answer. However, that answer depends importantly on technical details of hydrodynamic methods, and I expect that some readers will find themselves struggling at certain points in the presentation of those details.Batterman concludes A Middle Way by considering ontological consequences of his argument that mesoscale structure is indispensable for answering AUT. In particular, he argues that we should consider the correlation functions used to characterize mesoscale structure as natural kinds. By what standard? Batterman unsurprisingly rejects any philosophical account that links natural kinds to fundamentality, but he also denies that it is only pragmatic, or methodological, considerations that justify treating correlation functions as natural kinds. Instead, Batterman offers what he calls a “scientific” argument that leans heavily on a theorem of statistical physics, the fluctuation-dissipation theorem. In this context, the significance of the fluctuation-dissipation theorem is that it guarantees that under very general conditions, examining physical systems at the mesoscale will reveal nontrivial patterns of correlation between collections of molecules. Furthermore, we can use correlation functions to distinguish useless correlations, which dissipate quickly and have no interesting dynamics, from conserved quantities of a physical system (like the total magnetization of a bar of iron) that have nontrivial dynamics, are stable, and that can be used to characterize the system.Here again, Batterman proposes a novel and intriguing perspective on an old philosophical question. However, I found myself struggling to see where an advocate of a pragmatic standard for natural kinds, like James Woodward (2016) (who serves as Batterman’s representative for the position), would disagree with Batterman’s ostensibly distinct “scientific” argument. For example, it was hard to see much daylight between Batterman’s claim that correlation functions are natural kinds insofar as they “allow for much more effective modeling of the mesoscale regularities” (121) and Woodward’s (2016: 1057; cited by Batterman on p. 126) proposal that metaphysical criteria for natural properties be replaced “with a methodological investigation into which variables best serve various goals of inquiry.” This isn’t to say there is no such distinction to be drawn, but I also wasn’t convinced by Batterman’s presentation and would have appreciated expanded discussion of his “scientific” criterion for natural kinds.The book also contains brief and stimulating discussions of topics beyond what I have discussed here—of the metaphysics of levels, for example, and of a proposal that the ability to identify target systems for scientific study that are largely independent of their fundamental details is a precondition for the possibility of doing science—that should spur additional philosophical investigation. In summary, A Middle Way proposes technically sophisticated and philosophically novel answers to multiple questions of long-standing philosophical interest. I expect it to join Batterman’s previous book on the list of required reading for those interested in emergence, reduction, and intertheoretic relations in the natural sciences.

中文翻译：

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中间道路：多体物理的非基础方法

二十多年来，罗伯特·巴特曼的著作对于任何对自然科学的涌现和还原感兴趣的人来说都是重要的读物。在巴特曼的第一本书《细节中的魔鬼》中，他确定了一系列不同的推理模式，这些模式展示了他所谓的“渐近推理”：从基本物理理论给出的物理系统的完整描述中系统地消除或抽象出细节。巴特曼认为，认识到物理系统的许多细节与其动力学行为无关，并且使用渐近推理来消除这些不相关的细节，通常在确保物理科学的预测和解释成功方面发挥着至关重要的作用。在渐进推理中，巴特曼认为，在很多情况下，解释物理现象的资源不仅仅包含在基本物理理论中。这些资源也不仅仅包含在不太基础的、被取代的物理理论中。相反，解释一大类物理现象需要第三种混合理论，它位于基本理论和被取代理论之间的“渐近边界”：一种抽象出基本理论的选定细节，同时融入被取代理论的元素的理论。巴特曼认为，这种混合理论通常有必要解释多重实现的（物理学家称之为普遍的）行为模式：物理系统所表现出的相同行为，在其基本细节上是截然不同的。这两个主题——解释普遍模式的挑战巴特曼的最新著作《中间道路》中再次集中体现了理论间边界的行为和哲学意义，尽管是以相当不同的形式。这本书围绕以下问题展开：AUT：在某些（通常）微观尺度上异构的系统如何在宏观尺度上表现出相同的行为模式？这个问题是一个熟悉的问题，但巴特曼将其变得有趣使用。虽然 AUT 通常被要求表现出某些相同行为模式的不同系统（例如，当这些系统经历相变时，水和铁的某些属性表现相同），巴特曼指出，我们建模的方式也出现了类似的难题不同规模的单一系统。以水为例。在厘米或更大的尺度上，使用纳维-斯托克斯方程对水的行为进行建模。这将水视为所有长度尺度上的均质物质：纳维-斯托克斯方程对 10 米和 10−100 米处的水所表现出的结构没有区别。当然，这是错误的：实际的水从根本上来说是离散的、相互作用的分子的集合，并且这种子结构在小于约 10−8 米的尺度上被揭示。那么实际的水是怎样的呢？具有所有异质子结构，能否在厘米尺度上表现出与虚构的、完全均质的流体相同的行为？当水的行为在足够长的尺度上建模时，为什么实际水的底层结构似乎并不重要？巴特曼的方法始于这样一个论点：仅通过检查基本物理理论并希望从中提取无法找到 AUT 的答案对共同行为的“自下而上”解释。相反，AUT 的答案来自于对中尺度物理现象建模的理论和方法的研究。介观尺度是介于微观尺度和宏观尺度之间的中间尺度范围的统称。 （例如，在钢梁中，介观尺度涵盖了 10−10 米之间存在的整个子结构范围（大约是单个分子的尺度）和厘米尺度，我们在其中模拟弯曲和剪切等连续体现象。）巴特曼称这一系列方法是流体动力学方法，并认为，在它们可以应用的许多系统中，它们揭示了 AUT 的答案。假设您用基本物理理论的语言描述了一个物理系统，即对一个物理系统的描述。例如，钢梁是通过某些特定动力学相互作用的分子集合。您的兴趣在于导出对弯曲和剪切等连续介质现象的描述，这些现象遵循纳维-柯西方程。人们可能希望某种复杂的平均程序可能起作用：选择体积为 L3 的小立方体，计算每个立方体中分子属性的明智选择的平均值，定义一个适合规模 L'>L 的新的粗粒度变量，冲洗并重复，直到从钢梁的基本分子描述中得出钢梁的连续描述。巴特曼强调了这样做的问题：它几乎永远不会起作用。重要的是，它不起作用，因为像钢、水和木材这样的系统在分子尺度和连续尺度之间并不均匀：它们包含各种杂质和裂缝以及其他介观结构，这些结构使朴素的平均策略失效。进入流体动力学方法。简而言之，这些方法的工作原理如下。假设在介观尺度上进行检查时，我们的钢梁上分布着不连续的杂质斑点。人们不会选择误诊介观结构的小立方体，而是使用相关函数来表征该结构。如果我们选择钢梁中相隔距离 D 的两个、三个或 n 个空间点，则适当的相关函数给出位于这两个、三个或 n 个空间点的分子位于不纯斑点之一内的概率。一套完整的相关函数对钢梁在介观尺度上的几何和拓扑结构进行编码。然后，人们可以反过来，使用精确表征系统介观结构的相关函数定义表征钢梁连续介质现象的变量和动力学方程。这些连续介质变量代表大量分子的集体行为，但它们不能直接从基本分子描述中定义我们的钢梁：相反，巴特曼强调，它们只能根据用于表征介观结构的相关函数来定义。对于巴特曼来说至关重要的是，这些相关函数本身就是介观结构：大量分子集合的特性，只有在比基本分子尺度大得多的尺度上才能得到很好的定义。这构成了巴特曼拒绝AUT“自下而上”答案的基础：只有以物理系统的介观结构为出发点，才能将物理系统的基本描述和连续统描述联系起来。巴特曼在《中间道路》的核心章节 3 到 6 中对流体动力学方法进行了扩展描述（包括一个有趣的历史章节，将流体动力学方法与爱因斯坦的布朗运动工作联系起来），并提出了中尺度结构首要性的论点。这个答案 AUT？从巴特曼对流体动力学方法的分析中可以看出，流体或金属等物理系统的基本分子描述中包含的信息以精确可指定和最小的方式对其连续行为做出了贡献。控制连续体现象的动力学方程，如纳维-斯托克斯或纳维-柯西方程，通常包含未确定的参数，这些参数编码流体的粘度或金属的密度等属性。当人们可以使用流体动力学方法计算这些参数的值时，人们会发现水和橄榄油的连续方程之间的唯一区别是那些未确定的参数的值。根据巴特曼的说法，这揭示了区分橄榄油和水的分子细节，或者区分虚构的、完全同质的流体和在微观尺度上表现出异质结构的真实流体的分子细节，只有在它们决定价值的情况下才会对连续体现象做出贡献。连续介质动力学方程中出现的一些参数。巴特曼对流体动力学方法的阐述是技术性的，有时是简洁的，我发现自己希望第 3 章到第 6 章中的介绍更具教学意义。如果中间道路只解决物理学哲学专家感兴趣的问题，那么这就不是什么问题了。然而，AUT 具有普遍且长期的哲学意义，巴特曼提出了一个令人信服且新颖的答案，这绝非易事。然而，这个答案很大程度上取决于流体动力学方法的技术细节，我预计一些读者会发现自己在呈现这些细节的某些点上遇到了困难。巴特曼通过考虑他的论点的本体论后果得出了《中间道路》的结论，即中尺度结构对于回答 AUT 是必不可少的。特别是，他认为我们应该考虑用于将介观结构表征为自然类的相关函数。按什么标准？不出所料，巴特曼拒绝任何将自然类与基本性联系起来的哲学解释，但他也否认只有实用主义或方法论的考虑才能证明将相关函数视为自然类是合理的。相反，巴特曼提出了他所谓的“科学”论点，该论点很大程度上依赖于统计物理学定理，即涨落耗散定理。在这种情况下，涨落耗散定理的意义在于，它保证在非常一般的条件下，在介观尺度上检查物理系统将揭示分子集合之间的非平凡相关模式。此外，我们可以使用相关函数来区分无用的相关性，这些相关性会很快消散并且没有有趣的动力学，而物理系统的守恒量（例如铁棒的总磁化强度）具有非平凡的动力学，是稳定的，并且可以在这里，巴特曼再次对一个古老的哲学问题提出了一个新颖而有趣的观点。然而，我发现自己很难看出自然类实用标准的倡导者，比如詹姆斯·伍德沃德（James Woodward，2016）（他是巴特曼的代表），会在哪里不同意巴特曼表面上独特的“科学”论点。例如，巴特曼声称相关函数是自然类，因为它们“允许对中尺度规律进行更有效的建模”（121），而伍德沃德的观点（2016：1057；由巴特曼在第 14 页引用）之间很难看出多少相似之处。 126）建议“用方法论调查来取代自然属性的形而上学标准，以了解哪些变量最能服务于各种调查目标”。这并不是说没有这样的区别，但我也不相信巴特曼的演讲，并且希望对他的自然类“科学”标准进行更广泛的讨论。这本书还包含简短而刺激的讨论超出我在这里讨论的主题——例如，层次的形而上学，以及一项提议，即识别在很大程度上独立于其基本细节的科学研究目标系统的能力是进行科学研究的可能性的先决条件——应该激发更多的哲学研究。总之，《中间道路》为长期存在的哲学兴趣的多个问题提出了技术上复杂且哲学上新颖的答案。我希望它能与巴特曼的前一本书一起列入那些对自然科学中的涌现、还原和理论间关系感兴趣的人的必读书目中。