I defend a weak version of the Pigou-Dalton principle for chances. The principle says that it is better to increase the survival chance of a person who is more likely to die rather than a person who is less likely to die, assuming that the two people do not differ in any other morally relevant respect. The principle justifies plausible moral judgements that standard ex post views, such as prioritarianism and rank-dependent egalitarianism, cannot accommodate. However, the principle can be justified (...) by the same reasoning that has recently been used to defend the core axiom of ex post prioritarianism and egalitarianism, namely, Pigou-Dalton for well-being. The arguably biggest challenge for proponents of Pigou-Dalton for chances is that it violates State Dominance for social prospects. However, I argue that we have independent reason for rejecting State Dominance for social prospects, since it prevents a social planner from properly respecting people's preferences. (shrink)

This chapter focuses on the relations between objective probabilities in physical theories at different levels. In general philosophy of probability, it is frequently assumed that a fundamental deterministic theory cannot support probabilistic phenomena at any higher level, or more generally that there cannot be non-trivial probabilities in higher-level theories that are not encoded in probabilities at the lower level. These assumptions face significant challenges from some well-understood physical theories – I focus on statistical mechanics and Bohmian mechanics – where a (...) deterministic description at some lower level gives rise to an effectively probabilistic theory at some higher level; in each case, constraints arising from an objective physical limitation on the acquisition of evidence concerning the lower level plays a crucial role in supporting the higher-level probabilities. (shrink)

This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on (...) and summarize the highlights of the individual contributions. (shrink)

The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. von Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may not be part (...) of the best system, e.g. if a broad class of random devices is not often used. Spielraum probabilities have the potential to provide illuminating explanations of frequencies with which outcomes of trials on gambling devices arise. They ultimately fail to account for such frequencies though because they are compatible with frequencies that grossly differ from the values of the respective probabilities. I thus follow recent proposals by M. Strevens and M. Abrams and strengthen the definition of Spielraum probabilities by adding a further condition that restricts some actual frequencies. The resulting account remains limited in scope, but stands objections raised against it in the recent literature: it is neither circular nor based upon arbitrary choices of a measure or of physical variables. Nor does it lack any explanatory power. (shrink)

Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which appear to square the circle by being chancy and deterministic at once, and the appearance is backed by well-confirmed scientific theories such as statistical mechanics which also seem to provide us with chances for deterministic processes. Is this possible, and if so how? In this essay I discuss this question for probabilities as they occur in the (...) empirical sciences, setting aside metaphysical questions in connection with free will, divine intervention and determinism in history. (shrink)

How should we give accounts of scientific modal relations? According to the Humean, we should do so by considering the role of such relations in our lives and scientific theorizing. For example, to give a Humean account of chance, we need to identity a non-modal relation that can play the ‘role’ of chance—typically that of guiding credences and scientifically explaining events. Defenders of Humean accounts claim to be uniquely well placed to meet this aim. Humean chances are objective, and so (...) suitable for explaining. Humean chances reduce to patterns in actual events in a way that limits the possible divergence between relative frequencies and chances. So, they argue, Humean chances can uniquely be shown to satisfy chance−credence principles. I’ll argue that Humeans have no special advantage. When used in scientific contexts, Humean chances must be allowed to diverge from the relative frequencies. So, when considering the scientific question of whether agents who align their credences to the chances will do well, it is merely probable that they will. This scientific use of chance undercuts the Humean’s claimed advantage over their rivals. This undercutting also points to a deeper tension in Humeanism: Humeans must either give up the aim of recovering scientific practice, or live with a disunity between science and metaphysics. While a focus on function is laudable, the motivation for being Humean must come from elsewhere. (shrink)

In an illuminating article, Claus Beisbart argues that the recently-popular thesis that the probabilities of statistical mechanics (SM) are Best System chances runs into a serious obstacle: there is no one axiomatization of SM that is robustly best, as judged by the theoretical virtues of simplicity, strength, and fit. Beisbart takes this 'no clear winner' result to imply that the probabilities yielded by the competing axiomatizations simply fail to count as Best System chances. In this reply, we express sympathy for (...) the 'no clear winner' thesis. However, we argue that an importantly different moral should be drawn from this. We contend that the implication for Humean chances is not that there are no SM chances, but rather that SM chances fail to be sharp. (shrink)

Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract Principal Principle is both weakly and strongly consistent. The Abstract Principal Principle is strengthened by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined. It is shown that the Stable Abstract Principal Principle is weakly consistent. Strong consistency of the Stable Abstract Principal principle remains an open (...) question. (shrink)

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

I claim that objective consequentialism faces a problem stemming from the existence in some situations of a plurality of chances relevant to the outcomes of an agent’s acts. I suggest that this phenomenon bears structural resemblance to the well-known Reference Class problem. I outline a few ways in which one could attempt to deal with the issue, suggesting that it is the higher-level chance that should be employed by OC.

Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather than (...) on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert’s time-dependent projection operator formalism. This allows to better understand how general proposals for understanding probability in statistical mechanics, namely quantum approaches and almost-objective probabilities, can be accomodated in the MZ formalism. Moreover, I will provide a detailed physical analysis, based on the MZ formalism, of various proposals from the philosophical literature, such as Robertson’s theory of justifying coarse-graining via autonomous macrodynamics, Myrvold’s problem of explaining autonomous macrodynamics, and Wallace’s simple dynamical conjecture. (shrink)

How should contractualists assess the permissibility of risky actions? Both main views on the question, ex ante and ex post, fail to distinguish between different kinds of risk. In this article, I argue that this overlooks a third alternative that I call “objective ex ante contractualism”. Objective ex ante substitutes discounting complaints by epistemic risk in favor of discounting by objective risk. I further argue in favor of this new view. Objective ex ante contractualism provides the best model of justifiability (...) to each. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology (...) and to the quantum measurement problem. (shrink)

We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...) supervening on lower-level ones. We show that the distinction between objective chance and epistemic probability can be drawn, and operationalized, at every level of description. There is, therefore, not a single distinction between objective and epistemic probability, but a family of such distinctions. (shrink)

Several authors have argued that non-extreme probabilities used in special sciences such as chemistry and biology can be objective chances, even if the true microphysical description of the world is deterministic. This article examines an influential version of this argument and shows that it depends on a particular methodology for defining the relationship between coarse-grained and fine-grained events. An alternative methodology for coarse-graining is proposed. This alternative methodology blocks this argument for the existence of emergent chances, and makes better sense (...) of two well-known subjects of philosophical discussion: the Miners Puzzle and Simpson’s Paradox. (shrink)

One currently popular view about the nature of objective probabilities, or objective chances, is that they – or some of them, at least – are primitive features of the physical world, not reducible to anything else nor explicable in terms of frequencies, degrees of belief, or anything else. In this paper I explore the question of what the semantic content of primitive chance claims could be. Every attempt I look at to supply such content either comes up empty-handed, or begs (...) important questions against the skeptic who doubts the meaningfulness of primitive chance claims. In the second half of the paper I show that, by contrast, there are clear, and clearly contentful, ways to understand objective chance claims if we ground them on deterministic physical underpinnings. (shrink)

Our beliefs can have, or fail to have, a significant epistemic virtue: they can be true. What about our partial beliefs – that is, credences or subjective probabilities? Is there an epistemic virtue that credences can have or fail to have, whose nature or role with respect to credences is analogous to the role that truth has with respect to full beliefs? Van Fraassen argued in the 1980s that there is indeed such an analog virtue, and he claimed that it (...) is calibration: our credences should match, or be in tune with, some appropriately chosen frequencies of events. For example, if your credence in the proposition ‘It will rain today’ is 0.3 for any day that starts out like today did, and in fact it does rain on approximately 30% of such days, then your credence level is well‐calibrated, and is vindicated by the actual frequency of rain.In an unpublished paper Alan Hájek rejects this calibrationist answer, and proposes instead that having credences in agreement with the relevant objective chances is what it is to have vindicated credences, in the relevant sense analogous to truth for full beliefs. Although there are problems that afflict both van Fraassen's and Hájek's proposals, I will argue that Hájek and the calibrationist are both largely right – although the calibrationist answer is at bottom more right. In section I will propose an account of being in tune with the world that divides types of propositions into a few different classes; for one of those classes, Hájek's answer is exactly right, while for the others the calibrationist account gives the right answer. (shrink)

According to influential views the probabilities in classical statistical mechanics and other special sciences are objective chances, although the underlying mechanical theory is deterministic, since the deterministic low level is inadmissible or unavailable from the high level. Here two intuitions pull in opposite directions: One intuition is that if the world is deterministic, probability can only express subjective ignorance. The other intuition is that probability of high-level phenomena, especially thermodynamic ones, is dictated by the state of affairs in the world. (...) We argue in support of this second intuition and we show that in fact there are two different ways in which high-level probability describes matters of fact, even if the underlying microscopic reality is deterministic. Our analysis is novel, but supports approaches by, e.g., Loewer, Albert, Frigg and Hoefer, List and Pivato. In particular, the reductive view we propose here can be seen as a naturalization of the above approaches. We consider consequences of our result for nonreductive physicalist approaches, such as functionalism, that admit multiple realization of the kinds that appear in the special sciences by physical kinds. We show that nonreductive physicalism implies the existence of nonphysical matters of fact. (shrink)

We give a general background describing how the notion of levels of reality comes about in contemporary nonreductive approaches to the special sciences, what the notion of levels means in these approaches, its role in our scientific outlook of the world, and why it is important.

This paper describes a version of type identity physicalism, which we call Flat Physicalism, and shows how it meets several objections often raised against identity theories. This identity theory is informed by recent results in the conceptual foundations of physics, and in particular clar- ifies the notion of ‘physical kinds’ in light of a conceptual analysis of the paradigmatic case of reducing thermody- namics to statistical mechanics. We show how Flat Physi- calism is compatible with the appearance of multiple realisation (...) in the special sciences, and how and in what sense the special sciences laws are autonomous from the laws of physics, despite the full reductive picture of Flat Physicalism. We compare our view with a recent proposal by William Bechtel that accounts for the appearance of levels in mechanistic explanations. (shrink)

For computer simulation models to usefully inform climate risk management, uncertainties in model projections must be explored and characterized. Because doing so requires running the model many ti...

I argue that there are two distinct approaches to understanding reduction: the ontology-first approach and the theory-first approach. They concern the relation between ontological reduction and inter-theoretic reduction. Further, I argue for the significance of this distinction by demonstrating that either one or the other approach has been taken as an implicit assumption in, and has in fact shaped, our understanding of what statistical mechanics is. More specifically, I argue that the Boltzmannian framework of statistical mechanics assumes and relies on (...) the ontology-first approach, whereas the Gibbsian framework should assume the theory-first approach. -/- . (shrink)

Does the brain behave indeterministically? I argue that accounting for ion channels, key functional units in the brain, requires indeterministic models. These models are probabilistic, so the brain does behave indeterministically in a weak sense. I explore the implications of this point for a stronger sense of indeterminism. Ultimately I argue that it is not possible, either empirically or through philosophical argument, to show that the brain is indeterministic in that stronger sense.

Special science generalizations admit of exceptions. Among the class of non-exceptionless special science generalizations, I distinguish minutis rectis generalizations from the more familiar category of ceteris paribus generalizations. I argue that the challenges involved in showing that mr generalizations can play the law role are underappreciated, and quite different from those involved in showing that cp generalizations can do so. I outline a strategy for meeting the challenges posed by mr generalizations.

In their article 'Causes and Explanations: A Structural-Model Approach. Part I: Causes', Joseph Halpern and Judea Pearl draw upon structural equation models to develop an attractive analysis of 'actual cause'. Their analysis is designed for the case of deterministic causation. I show that their account can be naturally extended to provide an elegant treatment of probabilistic causation.

ABSTRACT Joseph Halpern and Judea Pearl draw upon structural equation models to develop an attractive analysis of ‘actual cause’. Their analysis is designed for the case of deterministic causation. I show that their account can be naturally extended to provide an elegant treatment of probabilistic causation. 1Introduction 2Preemption 3Structural Equation Models 4The Halpern and Pearl Definition of ‘Actual Cause’ 5Preemption Again 6The Probabilistic Case 7Probabilistic Causal Models 8A Proposed Probabilistic Extension of Halpern and Pearl’s Definition 9Twardy and Korb’s Account 10Probabilistic (...) Fizzling 11Conclusion. (shrink)

This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a Ψ-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement problem and simultaneously allow us to think sensibly about probability and evolution in quantum cosmology. Our analysis draws upon recent work on the problem of time in quantum gravity and causally symmet- ric local hidden variable theories. Our conclusion weighs the strengths and weaknesses of the approach (...) and points towards paths for future development. (shrink)

A series of recent arguments purport to show that most counterfactuals of the form if A had happened then C would have happened are not true. These arguments pose a challenge to those of us who think that counterfactual discourse is a useful part of ordinary conversation, of philosophical reasoning, and of scientific inquiry. Either we find a way to revise the semantics for counterfactuals in order to avoid these arguments, or we find a way to ensure that the relevant (...) counterfactuals, while not true, are still assertible. I argue that regardless of which of these two strategies we choose, the natural ways of implementing these strategies all share a surprising consequence: they commit us to a particular metaphysical view about chance. (shrink)

This paper shows how a particular resiliency-centered approach to chance lends support for two conditions characterizing chance. The first condition says that the present chance of some proposition A conditional on the proposition about some later chance of A should be set equal to that later chance of A. The second condition requires the present chance of some proposition A to be equal to the weighted average of possible later chances of A. I first introduce, motivate, and make precise a (...) resiliency-centered approach to chance whose basic idea is that any chance distribution should be maximally invariant under variation of experimental factors. Second, I show that any present chance distribution that violates the two conditions can be replaced by another present chance distribution that satisfies them and is more resilient under variation of experimental factors. This shows that the two conditions are an essential feature of chances that maximize resiliency. Finally, I explore the relationship between the idea of resilient chances so understood and so-called Humean accounts of chance—one of the most promising recent philosophical accounts of chance. (shrink)

In this contribution, I comment on Raffaella Campaner’s defense of explanatory pluralism in psychiatry (in this volume). In her paper, Campaner focuses primarily on explanatory pluralism in contrast to explanatory reductionism. Furthermore, she distinguishes between pluralists who consider pluralism to be a temporary state on the one hand and pluralists who consider it to be a persisting state on the other hand. I suggest that it would be helpful to distinguish more than those two versions of pluralism – different understandings (...) of explanatory pluralism both within philosophy of science and psychiatry – namely moderate/temporary pluralism, anything goes pluralism, isolationist pluralism, integrative pluralism and interactive pluralism. Next, I discuss the pros and cons of these different understandings of explanatory pluralism. Finally, I raise the question of how to implement or operationalize explanatory pluralism in scientific practice; how to structure the “genuine dialogue” or shape “the pluralistic attitude” Campaner is referring to. As tentative answers, I explore a question-based framework for explanatory pluralism as well as social-epistemological procedures for interaction among competing approaches and explanations. (shrink)

Laws of nature take center stage in philosophy of science. Laws are usually believed to stand in a tight conceptual relation to many important key concepts such as causation, explanation, confirmation, determinism, counterfactuals etc. Traditionally, philosophers of science have focused on physical laws, which were taken to be at least true, universal statements that support counterfactual claims. But, although this claim about laws might be true with respect to physics, laws in the special sciences (such as biology, psychology, economics etc.) (...) appear to have—maybe not surprisingly—different features than the laws of physics. Special science laws—for instance, the economic law “Under the condition of perfect competition, an increase of demand of a commodity leads to an increase of price, given that the quantity of the supplied commodity remains constant” and, in biology, Mendel's Laws—are usually taken to “have exceptions”, to be “non-universal” or “to be ceteris paribus laws”. How and whether the laws of physics and the laws of the special sciences differ is one of the crucial questions motivating the debate on ceteris paribus laws. Another major, controversial question concerns the determination of the precise meaning of “ceteris paribus”. Philosophers have attempted to explicate the meaning of ceteris paribus clauses in different ways. The question of meaning is connected to the problem of empirical content, i.e., the question whether ceteris paribus laws have non-trivial and empirically testable content. Since many philosophers have argued that ceteris paribus laws lack empirically testable content, this problem constitutes a major challenge to a theory of ceteris paribus laws. (shrink)

The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.

You and I lead different lives. While we share a society and a world, our existence is separate from one another. You and I matter individually, by ourselves. My dissertation is about this simple thought. I argue that this simple insight, the separateness of persons, tells us something fundamental about morality. My dissertation seeks to answer how the separateness of persons matters. I develop a precise view of the demands of the separateness of persons. The separateness of persons imposes both (...) a requirement on the justification of first-order moral principles as well as a requirement on the content of first-order moral principles. In specifying these demands, I argue that respecting the separateness of persons requires taking into consideration each person’s point of view separately. This requires taking into account the moral relations in which individuals stand to one another. I make use of this relational understanding of the separateness of persons to advance various debates in moral and political philosophy. I argue for a framework to assess to which extent the veil of ignorance can be reconciled with the separateness of persons. I also argue for a new view on the ethics of risk which is a form of contractualism that discounts risks only by their objective risk. Furthermore, I argue for a new solution to the problem of aggregation that is skeptical of aggregation and can set plausible limits to aggregation. Lastly, I provide a new relational agent-based justification for deontological constraints. In addition to answering how the separateness of persons matters, I defend the separateness of persons against challenges. Most importantly, I argue that the importance of the separateness of persons is not undermined even if we believe that our personal identity, i.e. whether we persist as the same person, is unimportant. (shrink)

The main objective of this dissertation is to philosophically assess how the use of informational concepts in the field of classical thermostatistical physics has historically evolved from the late 1940s to the present day. I will first analyze in depth the main notions that form the conceptual basis on which 'informational physics' historically unfolded, encompassing (i) different entropy, probability and information notions, (ii) their multiple interpretative variations, and (iii) the formal, numerical and semantic-interpretative relationships among them. In the following, I (...) will assess the history of informational thermophysics during the second half of the twentieth century. Firstly, I analyse the intellectual factors that gave rise to this current in the late forties (i.e., popularization of Shannon's theory, interest in a naturalized epistemology of science, etc.), then study its consolidation in the Brillouinian and Jaynesian programs, and finally claim how Carnap (1977) and his disciples tried to criticize this tendency within the scientific community. Then, I evaluate how informational physics became a predominant intellectual current in the scientific community in the nineties, made possible by the convergence of Jaynesianism and Brillouinism in proposals such as that of Tribus and McIrvine (1971) or Bekenstein (1973) and the application of algorithmic information theory into the thermophysical domain. As a sign of its radicality at this historical stage, I explore the main proposals to include information as part of our physical reality, such as Wheeler’s (1990), Stonier’s (1990) or Landauer’s (1991), detailing the main philosophical arguments (e.g., Timpson, 2013; Lombardi et al. 2016a) against those inflationary attitudes towards information. Following this historical assessment, I systematically analyze whether the descriptive exploitation of informational concepts has historically contributed to providing us with knowledge of thermophysical reality via (i) explaining thermal processes such as equilibrium approximation, (ii) advantageously predicting thermal phenomena, or (iii) enabling understanding of thermal property such as thermodynamic entropy. I argue that these epistemic shortcomings would make it impossible to draw ontological conclusions in a justified way about the physical nature of information. In conclusion, I will argue that the historical exploitation of informational concepts has not contributed significantly to the epistemic progress of thermophysics. This would lead to characterize informational proposals as 'degenerate science' (à la Lakatos 1978a) regarding classical thermostatistical physics or as theoretically underdeveloped regarding the study of the cognitive dynamics of scientists in this physical domain. (shrink)

Much recent philosophical attention has been devoted to variants on the Best System Analysis of laws and chance. In particular, philosophers have been interested in the prospects of such Best System Analyses for yielding *high-level* laws and chances. Nevertheless, a foundational worry about BSAs lurks: there do not appear to be uniquely appropriate measures of the degree to which a system exhibits theoretical virtues, such as simplicity and strength. Nor does there appear to be a uniquely correct exchange rate at (...) which the theoretical virtues of simplicity, strength, and likelihood trade off against one another in the determination of a best system. Moreover, it may be that there is no *robustly* best system: no system that comes out best under *any* reasonable measures of the theoretical virtues and exchange rate between them. This worry has been noted by several philosophers, with some arguing that there is indeed plausibly a set of tied-for-best systems for our world. Some have even argued that this entails that there are no Best System laws or chances in our world. I argue that, while it *is* plausible that there is a set of tied-for-best systems for our world, it doesn't follow from this that there are no Best System chances. Rather, it follows that the Best System chances for our world are *unsharp*. (shrink)

Pettit (2006) argues that deferring to majority testimony is not generally rational: it may lead to inconsistent beliefs. He suggests that “another ... approach will do better”: deferring to supermajority testimony. But this approach may also lead to inconsistencies. In this paper, I describe conditions under which deference to supermajority testimony ensures consistency, and conditions under which it does not. I also introduce the concept of “consistency of degree k”, which is weaker than full consistency by ruling out only “blatant” (...) inconsistencies in an agent’s beliefs while permitting less blatant ones, and show that, while super-majoritarian deference often fails to ensure full consistency, it is a route to consistency in this weaker sense. (shrink)

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two Boltzmannian accounts of the Second Law, viz. a globalist and a localist one. In both cases, the probabilities fail to be chances because they have rivals that are roughly equally good. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character (...) of explanations in statistical physics. (shrink)