In the postscripts to “A Subjectivist’s Guide to Objective Chance,” David Lewis (1986: 118) wrote: “To the question how chance can be reconciled with determinism, …my answer is: it can’t be done.” But a number of philosophers have tried, in the past thirty years or so, to show that Lewis was mistaken. Motives for doing so are not hard to find. Classical gambling systems such as coin flips and dice rolls, to which we ascribe objective probabilities, are arguably deterministic in their dynamics, or nearly so; and one of the two huge areas of physics in which objective probabilities play a crucial role, statistical mechanics, is based on fully deterministic underlying dynamics. Finding a clear account of such probabilities that makes them objective, yet compatible with determinism, has been a chief goal of philosophy of probability, with novel proposals having been defended by David Albert (2000), Barry Loewer (2001), Michael Strevens (2003), Aidan Lyon (2010), Jenann Ismael (2009, 2011), Jonathan Cohen and Craig Callender (2009), and myself (Hoefer 2019), among others.Beyond Chance and Credence (hereafter, BCC) develops and defends an approach to objective probability that Myrvold first presented in a 2012 article: epistemic chance. It is a notion that blends physical objectivity with epistemic considerations about the credences of cognitively limited agents such as human beings. But the name, and this description, may seem to suggest a fifty-fifty mix of objectivity and subjectivity, and that is very far from the truth. Epistemic chances are essentially determined by the physical dynamics, and hence are as objective as anyone should wish. In BCC, Myrvold has given us the best account yet of how objective probabilities can exist for the behaviors of (at least many of the) physical systems whose dynamics is deterministic. But BCC offers much more than that as well.BCC begins with a historical overview of the introduction of probabilistic considerations into physics, and the resultant problem of how to understand such probabilities when applied to deterministic systems. Myrvold is far more careful to get the history right than most philosophers of physics (or probability) tend to be, giving the reader a first taste of the rigor and clarity that will be maintained throughout the book. Chapter 2 introduces the notions of chance and of credence (agents’ subjective probabilities), offering a more sophisticated introduction to the latter than many readers will ever have seen. With these concepts in hand, BCC returns to the historical narrative begun in chapter 1, and to how the ideas of treating probabilities as either purely epistemic, or as frequency-based, arose in the nineteenth and twentieth centuries. Chapter 3 explains why the probabilities we want to have for deterministic dynamical systems can neither be understood along classical lines (based on equiprobable cases or principles of indifference), nor as purely subjective credences, nor along frequentist lines. This chapter’s arguments are far more compelling than the laundry list of familiar objections that one typically finds in discussions of early approaches to probability.Chapters 4 and 5 are the conceptual core of BCC, introducing the reader to the fundamental ideas of epistemic chance (hereafter, EC). Chapter 4 introduces a mathematical example of a deterministic dynamical system, one that Myrvold then uses in several subsequent chapters to illustrate key features of EC: the “parabola gadget.” This is a system in which a point-sized ball moves according to a set of rules that make the ball follow a series of vertical and horizontal movements (see fig. 1).A single iteration of the dynamics takes the ball from some starting point on the diagonal and moves it vertically until it meets the parabola, and then horizontally until the diagonal is met once more. This system amplifies any uncertainty regarding the initial position of the ball fairly quickly, so in case one has such uncertainty, one wants to use probabilistic considerations to figure out how likely the ball is to be in a given interval of the x axis after n iterations of the gadget’s operation. Equal-sized intervals of x turn out not to be equiprobable as locations where the ball may be found, after the gadget has run for a while—not by a long way! Figure 2 shows the kind of frequency distributions that running the gadget tends to produce after many iterations, almost no matter where the ball starts from.1As Myrvold shows, there is an invariant distribution of the parabola gadget dynamics, U-shaped as seen roughly in figure 2, and precisely in figure 3 below, toward which almost any initial probability distribution over the initial x-condition evolves fairly rapidly as n increases. For this reason, the gadget can be said to be a dynamical system for which epistemic chances exist—chances of the ball being found in a given interval of x-value at the end of an iteration, if the gadget has been running for a while.The invariance of the distribution in figure 3 is the key to understanding what an epistemic chance is. Consider a rational agent who does not know the precise initial condition with which a gadget has been set in motion. Perhaps the agent knows only that it was very near to 0.6; perhaps she knows that it was between 0.2 and 0.8, and more likely near the middle than the extremes of these values, but nothing else; perhaps she knows nothing at all about where it started. Her credences would be representable by something like a sharply peaked Gaussian centered on x=0.6, or perhaps a narrow, flat-topped bar centered on x=0.6, in the first case; a gently peaked hump-shaped curve from 0.2 to 0.8, perhaps, in the second case; and a flat plateau from 0 to 1 in the third. Suppose that the agent is asked to make bets on which decile the ball will be found in after five hundred iterations of the gadget dynamics. Crucially, if any of these three agents update their credences about the ball’s location by starting from their initial credence distribution and evolving it forward under the dynamics, the updated credence distribution will look, at a coarse-grained level, very, very similar to the shape of figure 3. All three agents’ credences about (for example) how likely the ball is to be found between x=0.3 and 0.4 will, to a high degree of approximation, be the same. The dynamics of the parabola gadget, in other words, imposes “the right” credences on agents who have almost any reasonable initial credence distribution over possible initial x-values and who update those credences in light of the gadget’s known dynamics. These “right” credences that such rational agents end up closely approximating are precisely the epistemic chances (ECs) for the x-values of balls in a long-running parabola gadget.The features described above are not, fortunately, restricted to parabola gadgets. As Myrvold demonstrates in chapter 8, equilibration in thermodynamical systems can be understood as a dynamical process that maps very diverse (but not unreasonable) credences about the initial microstate of the system into agreement as to the probabilities of coarse-grained final states of the system. More generally, statistical mechanical probabilities can be understood as epistemic chances arising from the deterministic dynamics (Newtonian, for classical Statistical Mechanics [SM]). With the tool of ECs—and a long career’s worth of accumulated wisdom concerning the philosophy of SM—Myrvold achieves wonderful results in chapter 8. Myrvold shows why we do not need to invoke a “Past Hypothesis” to let us explain why systems around us evolve to higher entropy conditions rather than lower.2 More generally, chapter 8 offers satisfying solutions to many of the main philosophical problems regarding classical SM. (On the way, chapters 6 and 7 give clear, compact, and elegant introductions to thermodynamics and classical SM, respectively; these are didactic gems in their own right, and an invaluable resource for future philosophy of physics.)Coming back to epistemic chances in general, a few further remarks will help to situate Myrvold’s approach compared to others, and to highlight its strengths and limitations. As Myrvold stresses, ECs have an epistemic side to them, which is ineliminable and not problematic. I would stress that their objectivity is what makes them well suited to play the role of objective chances—an objectivity that is exactly as strong as the objectivity of the dynamics of the systems to which they attach. Myrvold, who is (unlike me) willing to contemplate that there might be brute/primitive objective chances in the world (perhaps associated to brute probabilistic physical laws), does not want to consider his ECs to be objective chances. Nevertheless, within their domains, they can serve all the purposes that objective chances are taken to serve. One of the nice points of Myrvold’s account is his quick but plausible demonstration that ECs satisfy a close analogue of Lewis’s Principal Principle.The strengths of the EC approach come, however, with a corresponding limitation: the account only extends to chances regarding the behaviors of systems that are governed by the right sort of dynamics. Myrvold does not try to delimit the scope of the approach, other than by discussing it in connection with SM (both classical and quantum), and in connection with standard Quantum Mechanics itself, about which more in a moment. One may wonder: does it cover the whole range of classical gambling systems? It seems very likely that roulette wheels have a dynamics with the requisite features, and probably dice rolling also. About coin flips I am not so sure, since it is not clear that the dynamics will substantially wash out bumpy initial credences enough to make the entire class of reasonable initial credences converge to near 50 percent credence in H and T. And about chances in card games—for example, the chance of drawing to an inside straight in draw poker—it seems to me unlikely that the wide variety of deck-shuffling methods found in the real world can all be treated as kinds of dynamical systems with ECs arising from the dynamics. Looking beyond gambling systems, many other kinds of probabilities that we treat as at least quasi-objective, such as probabilities of being involved in a car accident, or of suffering a cancerous mutation in a lung cell, or recombination probabilities in genetics, are probably not amenable to treatment as ECs. So, while EC does cover many of the most central and important probabilities found in physics and in a wide class of dynamical systems, it is not apt for use in every context. By contrast, Humean Best Systems approaches to chance (e.g., Cohen and Callender 2009; Loewer 2001; Hoefer 2019), by making chances supervene on actual events themselves rather than on dynamical systems having certain mathematical features, are arguably better able to encompass the full range of contexts in which we postulate objective probabilities in science and in daily life.3The past few decades have seen an explosion of new work in the philosophy of probability, and Beyond Chance and Credence is without doubt one of the very best contributions to the field. Myrvold has crafted a novel, elegant account of objective probabilities. It may have a restricted domain of applicability, but within that domain its achievements are remarkable.

中文翻译：

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超越机会和信任


在《客观机会的主观主义者指南》的后记中，大卫·刘易斯（David Lewis，1986：118）写道：“对于机会如何与决定论相调和的问题，……我的答案是：这是不可能的。”但在过去三十年左右的时间里，许多哲学家试图证明刘易斯是错误的。这样做的动机并不难找到。经典的赌博系统，例如抛硬币和掷骰子，我们将其归因于客观概率，其动态可以说是确定性的，或者几乎是确定性的；客观概率在物理学中发挥着至关重要作用的两大领域之一——统计力学——是基于完全确定性的基础动力学。找到对此类概率的清晰解释，使其客观且与决定论兼容，一直是概率哲学的主要目标，大卫·阿尔伯特（David Albert，2000）、巴里·洛厄尔（Barry Loewer，2001）、迈克尔·斯特文斯（Michael Strevens，2003）都为新颖的提议辩护。 ）、Aidan Lyon（2010）、Jenann Ismael（2009、2011）、Jonathan Cohen 和 Craig Callender（2009）以及我自己（Hoefer 2019）等。Beyond Chance and Credence（以下简称 BCC）开发并捍卫了一种方法Myrvold 在 2012 年的一篇文章中首次提出了客观概率：认知机会。这个概念将物理客观性与对人类等认知受限主体的可信度的认知考虑相结合。但这个名字和这个描述似乎暗示了客观性和主观性的五五十种混合，而这与事实相去甚远。认知机会本质上是由物理动力学决定的，因此正如任何人所希望的那样客观。 在《BCC》中，米尔沃德为我们提供了关于动态确定性的（至少许多）物理系统的行为如何存在客观概率的最佳解释。但 BCC 提供的远不止这些。BCC 首先概述了将概率考虑引入物理学的历史概述，以及由此产生的问题，即在应用于确定性系统时如何理解此类概率。与大多数物理学（或概率）哲学家相比，米尔沃德在正确地讲述历史方面要小心得多，让读者第一次感受到整本书将保持的严谨性和清晰度。第二章介绍了机会和可信度（主体的主观概率）的概念，对后者提供了比许多读者所见过的更复杂的介绍。掌握了这些概念后，BCC 回到了第一章开始的历史叙述，以及将概率视为纯粹认知的或基于频率的想法是如何在 19 世纪和 20 世纪出现的。第三章解释了为什么我们想要的确定性动力系统的概率既不能沿着经典路线（基于等概率情况或冷漠原则）来理解，也不能作为纯粹的主观可信度，也不能沿着频率主义路线来理解。本章的论点比人们在讨论早期概率方法时通常会发现的一长串熟悉的反对意见更有说服力。第 4 章和第 5 章是 BCC 的概念核心，向读者介绍了认知机会的基本思想（此后，欧共体）。 第 4 章介绍了一个确定性动力系统的数学示例，Myrvold 在随后的几章中使用了这个示例来说明 EC 的关键特征：“抛物线小工具”。在这个系统中，点大小的球根据一组规则移动，这些规则使球遵循一系列垂直和水平运动（见图 1）。动态的单次迭代使球从某个起点开始并垂直移动它直到遇到抛物线，然后水平移动直到再次遇到对角线。该系统相当快地放大了有关球初始位置的任何不确定性，因此，如果存在这种不确定性，则需要使用概率考虑因素来计算在 n 次迭代后球位于 x 轴给定区间内的可能性有多大小工具的操作。在小工具运行一段时间后，相同大小的 x 间隔与可能找到球的位置并不等概率 - 不是很远！图 2 显示了运行该小工具在多次迭代后往往会产生的频率分布类型，几乎无论球从哪里开始。1正如 Myrvold 所示，抛物线小工具动力学存在一个不变的分布，大致呈 U 形，如图所示如图 2 所示，确切地说是下面的图 3 所示，随着 n 的增加，初始 x 条件上的几乎任何初始概率分布都会相当迅速地演变。因此，小工具可以说是一个存在认知机会的动态系统——如果小工具已经运行了一段时间，则在迭代结束时在给定的 x 值区间内找到球的机会。图 3 中分布的不变性是理解什么是认知机会的关键。考虑一个理性代理人，他不知道小工具启动的精确初始条件。也许代理只知道它非常接近 0.6；也许她知道它在 0.2 到 0.8 之间，并且更有可能接近这些值的中间值而不是极端值，但除此之外一无所知；也许她根本不知道事情是从哪里开始的。在第一种情况下，她的可信度可以用以 x=0.6 为中心的尖峰高斯函数来表示，或者可以用以 x=0.6 为中心的窄平顶条来表示；在第二种情况下，可能是从 0.2 到 0.8 的平缓的峰形驼峰曲线；第三个是从 0 到 1 的平坦平台。假设代理被要求对小工具动力学进行 500 次迭代后球会出现在哪个十分位进行打赌。至关重要的是，如果这三个代理中的任何一个通过从最初的信任分布开始并在动态下向前发展来更新他们关于球位置的信任，则更新后的信任分布在粗粒度级别上看起来将非常非常类似于图 3 的形状。所有三个代理关于（例如）在 x=0.3 和 0.4 之间找到球的可能性的可信度在高度近似下是相同的。换句话说，抛物线小工具的动态将“正确”的信任强加给代理，这些代理在可能的初始 x 值上几乎具有任何合理的初始信任分布，并且根据小工具的已知动态更新这些信任。 这些理性智能体最终非常接近的“正确”可信度正是长期运行的抛物线小工具中球的 x 值的认知机会 (EC)。幸运的是，上述功能并不局限于抛物线小工具。正如 Myrvold 在第 8 章中所论证的那样，热力学系统中的平衡可以理解为一个动态过程，它将关于系统初始微观状态的非常多样化（但并非不合理）的可信度映射到与系统粗粒度最终状态的概率一致的过程。更一般地说，统计力学概率可以理解为由确定性动力学（牛顿，经典统计力学 [SM]）产生的认知机会。借助 EC 工具，以及长期职业生涯中积累的关于 SM 哲学的智慧，Myrvold 在第 8 章中取得了出色的成果。Myrvold 展示了为什么我们不需要援引“过去的假设”来解释为什么我们周围的系统演化到更高而不是更低的熵条件。2 更一般地说，第 8 章为许多有关经典 SM 的主要哲学问题提供了令人满意的解决方案。 （顺便说一句，第 6 章和第 7 章分别对热力学和经典 SM 进行了清晰、紧凑和优雅的介绍；这些本身就是教学瑰宝，也是未来物理哲学的宝贵资源。）回到认知机会总的来说，一些进一步的评论将有助于将 Myrvold 的方法与其他方法进行比较，并强调其优点和局限性。正如 Myrvold 所强调的，EC 有认知方面的一面，这是不可消除的，也没有问题。 我要强调的是，它们的客观性使它们非常适合发挥客观机会的作用——这种客观性与它们所依附的系统动力学的客观性一样强。麦沃尔德（与我不同）愿意考虑世界上可能存在残酷/原始的客观机会（可能与残酷的概率物理定律有关），但他不想将他的 EC 视为客观机会。然而，在他们的领域内，他们可以达到客观机会所达到的所有目的。 Myrvold 的解释的优点之一是他快速而合理地证明了 EC 满足刘易斯主要原理的近似模拟。然而，EC 方法的优点也有相应的限制：该解释仅扩展到关于以下行为的机会：由正确的动态控制的系统。米尔沃德并没有试图界定该方法的范围，除了结合 SM（经典和量子）以及标准量子力学本身进行讨论（稍后会详细介绍）。人们可能会想：它是否涵盖了所有经典赌博系统？轮盘赌轮似乎很可能具有具有必要功能的动态性，并且可能还具有滚动骰子的功能。关于硬币翻转，我不太确定，因为尚不清楚动态是否会充分消除崎岖不平的初始可信度，足以使整个类别的合理初始可信度收敛到 H 和 T 中接近 50% 的可信度。 至于纸牌游戏中的机会——例如，在抽牌扑克中抽到内侧顺子的机会——在我看来，现实世界中发现的各种各样的洗牌方法不太可能都被视为一种动态系统ECs 是由动态产生的。除了赌博系统之外，我们认为至少是准客观的许多其他类型的概率，例如卷入车祸的概率，或肺细胞中发生癌性突变的概率，或遗传学中的重组概率，都可能是不适合作为 EC 进行治疗。因此，虽然 EC 确实涵盖了物理学和各种动力系统中发现的许多最核心和最重要的概率，但它并不适合在所有情况下使用。相比之下，休谟最佳系统接近机会（例如，Cohen 和 Callender 2009；Loewer 2001；Hoefer 2019），通过使机会出现在实际事件本身而不是具有某些数学特征的动力系统上，可以说能够更好地涵盖全部我们在科学和日常生活中假设客观概率的一系列背景。3在过去的几十年里，概率哲学领域的新工作激增，《超越机会和可信度》无疑是对该领域最好的贡献之一。米尔沃德对客观概率进行了新颖、优雅的描述。它的适用范围可能有限，但在该领域内它的成就是显着的。