Objective interpretations of probability are usually discussed in two varieties: frequency and propensity accounts. But there is a third, neglected possibility, namely, probabilities as deriving from ranges in suitably structured initial state spaces. Roughly, the probability of an event is the proportion of initial states that lead to this event in the space of all possible initial states, provided that this proportion is approximately the same in any not too small interval of the initial state space. This idea can also (...) be expressed by saying that in the types of situations that give rise to probabilistic phenomena we may expect to find an initial state space such that any "reasonable" density function over this space leads to the same probabilities for the possible outcomes. This "method of arbitrary functions" was introduced by Poincaré, studied and extended by Hopf and more recently by Eduardo Engel, Jan von Plato and Michael Strevens. The natural-range, or method-of-arbitrary-functions approach to probabilities is usually treated as an explanation for the occurrence of probabilistic patterns, whereas I examine its prospects for an objective interpretation of probability, in the sense of providing truth conditions for probability statements that do not depend on our state of mind or information. The main objection to such a proposal is that it is circular, i.e. presupposes the concept of probability, because a measure on the initial state has to be introduced, and density functions over the space are considered. I try to argue that this objection can be successfully met. (shrink)

In this paper I will present a puzzle about epistemic akrasia, and I will use that puzzle to motivate accepting some non-standard views about the nature of epistemological judgment. The puzzle is that while it seems obvious that epistemic akrasia must be irrational, the claim that epistemic akrasia is always irrational amounts to the claim that a certain sort of justified false belief—a justified false belief about what one ought to believe—is impossible. But justified false beliefs seem to be possible (...) in any domain, and it’s hard to see why beliefs about what one ought to believe should be an exception. I will argue that when we get clearer about what sort of psychological state epistemic akrasia is, we can resolve the puzzle in favor of the intuitive view that epistemic akrasia is always irrational. (shrink)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can happen can (...) just as naturally happen backwards. Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem. The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students. Table of Contents: Preface 1. Time-Reversal Invariance 2. Thermodynamics 3. Statistical Mechanics 4. The Reversibility Objections and the Past-Hypothesis 5. The Scope of Thermodynamics 6. The Asymmetries of Knowledge and Intervention 7. Quantum Mechanics Appendix: Gedankenexperiments with Heat Engines Index Reviews of this book: The foundations of statistical mechanisms are often presented in physics textbooks in a rather obscure and confused way. By challenging common ways of thinking about this subject, Time and Chance can do quite a lot to improve this situation. --Jean Bricmont, Science Albert is perfecting a style of foundational analysis that is uniquely his own...It has a surgical precision...and it is ruthless with pretensions. The foundations of thermodynamics is a topic that has accumulated a good deal of dead wood; this is a fire that will burn and burn. --Simon W. Saunders, Oxford University As usual with Albert's work, the exposition is brisk and to the point, and exceptionally clear...The book will be an extremely valuable contribution to the literature on the subject of philosophical issues in thermodynamics and statistical mechanics, a literature which has been thin on the ground but is now growing as it deserves to. --Lawrence Sklar, University of Michigan. (shrink)

This paper has the aim of making Johannes von Kries’s masterpiece, Die Principien der Wahrscheinlichkeitsrechnung of 1886, a little more accessible to the modern reader in three modest ways: first, it discusses the historical background to the book ; next, it summarizes the basic elements of von Kries’s approach ; and finally, it examines the so-called “principle of cogent reason” with which von Kries’s name is often identified in the English literature.

We defend Uniqueness, the claim that given a body of total evidence, there is a uniquely rational doxastic state that it is rational for one to be in. Epistemic rationality doesn't give you any leeway in forming your beliefs. To this end, we bring in two metaepistemological pictures about the roles played by rational evaluations. Rational evaluative terms serve to guide our practices of deference to the opinions of others, and also to help us formulate contingency plans about what to (...) believe in various situations. We argue that Uniqueness vindicates these two roles for rational evaluations, while Permissivism clashes with them. (shrink)

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps, and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may (...) freely copy and distribute this work, as no entity has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

A rational person doesn’t believe just anything. There are limits on what it is rational to believe. How wide are these limits? That’s the main question that interests me here. But a secondary question immediately arises: What factors impose these limits? A first stab is to say that one’s evidence determines what it is epistemically permissible for one to believe. Many will claim that there are further, non-evidentiary factors relevant to the epistemic rationality of belief. I will be ignoring the (...) details of alternative answers in order to focus on the question of what kind of rational constraints one’s evidence puts on belief. Our main question concerns how far epistemic permission and obligation can come apart.1 Suppose I am epistemically permitted to believe P, i.e., it would not be irrational for me to believe it. Am I thereby obliged to believe P, or are other options rationally available to me?2 Might I be equally rational in remaining agnostic about P, or even believing not-P? Or could even a slightly stronger or weaker degree of confidence be just as reasonable? (shrink)

Maxwell's deduction of the probability distribution over the velocity of gas molecules—one of the most important passages in physics (Truesdell)—presents a riddle: a physical discovery of the first importance was made in a single inferential leap without any apparent recourse to empirical evidence. -/- Tychomancy proposes that Maxwell's derivation was not made a priori; rather, he inferred his distribution from non-probabilistic facts about the dynamics of intermolecular collisions. Further, the inference is of the same sort as everyday reasoning about the (...) physical probabilities attached to such canonical chance setups as tossed coins or rolled dice. The structure of this reasoning is investigated and some simple rules for inferring physical probabilities from symmetries and other causally relevant properties of physical systems are proposed. -/- Not only physics but evolutionary biology and population ecology, the science of measurement error, and climate modeling have benefited enormously from the same kind of reasoning, the book goes on to argue. Inferences from dynamics to probability are so obvious to us, however, that their methodological importance has been largely overlooked. (shrink)

This paper explores some issues about the choice of variables for causal representation and explanation. Depending on which variables a researcher employs, many causal inference procedures and many treatments of causation will reach different conclusions about which causal relationships are present in some system of interest. The assumption of this paper is that some choices of variables are superior to other choices for the purpose of causal analysis. A number of possible criteria for variable choice are described and defended within (...) a broadly interventionist approach to causation. (shrink)

Improbable knowing is knowing something even though it is almost certain on one’s evidence at the time that one does not know that thing. Once probabilities on the agent’s evidence are introduced into epistemic logic in a very natural way, it is easy to construct models of improbable knowing, some of which have realistic interpretations, for instance concerning agents like us with limited powers of perceptual discrimination. Improbable knowing is an extreme case of failure of the KK principle, that is, (...) of a case of knowing something even though one does not know at the time that one knows that thing. A generalization of the argument yields cases of improbable rationality, in which it is rational for one to do something even though it is almost certain on one’s evidence at the time that it is not rational for one to do that thing. When the models are elaborated to represent appearances and beliefs as well as knowledge, they turn out to contain Gettier cases. Neglect of the possibility of improbable knowing may cause some sceptical claims and claims of the non-closure of knowledge under competent deduction to look more plausible than they deserve to. A formal appendix explores the closely related question of the conditions under which a reflection principle is violated. The principle says that the evidential probability of a proposition conditional on the evidential probability of that proposition’s being c is itself c. (shrink)

Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...) of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is. (shrink)

This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics (ergodic theory) is of independent interest, but also adds weight to the claim that it is possible to justify an (...) objective interpretation of probabilities in a theory having as a basis the paradigmatically deterministic theory of classical mechanics. (shrink)

This article defends the Fixed Point Thesis: that it is always a rational mistake to have false beliefs about the requirements of rationality. The Fixed Point Thesis is inspired by logical omniscience requirements in formal epistemology. It argues to the Fixed Point Thesis from the Akratic Principle: that rationality forbids having an attitude while believing that attitude is rationally forbidden. It then draws out surprising consequences of the Fixed Point Thesis, for instance that certain kinds of a priori justification are (...) indefeasible and that misleading all-things-considered evidence about rational requirements is impossible. Finally, the Fixed Point Thesis is applied to defend the Right Reasons position on peer disagreement, according to which an agent who has drawn the correct conclusion from her evidence should retain belief in that conclusion even in the face of disagreeing peers. (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.

Can there be deterministic chance? That is, can there be objective chance values other than 0 or 1, in a deterministic world? I will argue that the answer is no. In a deterministic world, the only function that can play the role of chance is one that outputs just Os and 1s. The role of chance involves connections from chance to credence, possibility, time, intrinsicness, lawhood, and causation. These connections do not allow for deterministic chance.

Epistemologists have recently noted a tension between (i) denying access internalism, and (ii) maintaining that rational agents cannot be epistemically akratic, believing claims akin to ‘p, but I shouldn’t believe p’. I bring out the tension, and develop a new way to resolve it. The basic strategy is to say that access internalism is false, but that counterexamples to it are ‘elusive’ in a way that prevents rational agents from suspecting that they themselves are counterexamples to the internalist principles. I (...) argue that this allows us to do justice to the motivations behind both (i) and (ii). And I explain in some detail what a view of evidence that implements this strategy, and makes it independently plausible, might look like. (shrink)

A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to (...) call the “natural-range conception” of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called “method of arbitrary functions”. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed. (shrink)

A conception of probability that can be traced back to Johannes von Kries is introduced: the “Spielraum” or range conception. Its close connection to the so-called method of arbitrary functions is highlighted. Possible interpretations of it are discussed, and likewise its scope and its relation to certain current interpretations of probability. Taken together, these approaches form a class of interpretations of probability in its own right, but also with its own problems. These, too, are introduced, discussed, and proposals in response (...) to them are surveyed, some of which also go back to von Kries. (shrink)

Abrams, Rosenthal, and Strevens have recently presented interpretations of the objective probabilities posited by some scientific theories that build on von Kries’s idea of identifying probabilities with ranges of values in a space of possible states. These interpretations face a problem, forcefully pointed out by Rosenthal, about how to determine ‘input probabilities.’ I argue here that Abrams’s and Strevens’s attempts to solve this problem do not succeed. I also argue that the problem can be solved by recognizing the possibility of (...) laws of nature that manifest themselves not as universal regularities, but instead as constraints on relative frequencies. (shrink)

This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics is of independent interest, but also adds weight to the claim that it is possible to justify an objective interpretation (...) of probabilities in a theory having as a basis the paradigmatically deterministic theory of classical mechanics. (shrink)

The most important theories in fundamental physics, quantum mechanics and statistical mechanics, posit objective probabilities or chances. As important as chance is there is little agreement about what it is. The usual “interpretations of probability” give very different accounts of chance and there is disagreement concerning which, if any, is capable of accounting for its role in physics. David Lewis has contributed enormously to improving this situation. In his classic paper “A Subjectivist's Guide to Objective Chance” he described a framework (...) for representing single case objective chances, showed how they are connected to subjective credences, and sketched a novel account what they are within his Humean account of scientific laws. Here I will describe these contributions and add a little to them. (shrink)

It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as 'ignorance' probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role (...) of probability in explanation and laws. This is the 'paradox of deterministic probabilities'. After surveying the usual list of accounts of objective chance and finding them inadequate I argue that an account of chance sketched by David Lewis can be modified to solve the paradox of deterministic probabilities and provide an adequate account of the probabilities in deterministic theories like statistical mechanics. (shrink)

Tn this paper I explore and to an extent defend HS. The main philosophical challenges to HS come from philosophical views that say that nomic concepts-laws, chance, and causation-denote features of the world that fail to supervene on non-nomic features. Lewis rejects these views and has labored mightily to construct HS accounts of nomic concepts. His account of laws is fundamental to his program, since his accounts of the other nomic notions rely on it. Recently, a number of philosophers have (...) criticized Lewis's account, and Humean accounts of laws generally, for delivering, at best, a pale imitation ofthe genuine item. These philosophers think that the notion of law needed by science requires laws-if there are any-to be fundamental features of our world that are completely distinct from and not supervenient on the particular facts that they explain. I side with Lewis against these philosophers. Here I will argue that although Lewis-laws don't fulfill all our philosophical expectations, they do play the roles that science needs laws to play. The metaphysics and epistemology of Humean laws, and more specifically, Lewis-laws, are in much better shape than the metaphysics and epistemology of the main anti-Humean alternatives. However, I do have inisgivings about Lewis's account. Both he and his critics assume that the basic properties are so individuated so that the laws are not metaphysically necessary. If this assumption is rejected, then the question of Humean supervenience lapses. I conclude with a brief discussion of this position. (shrink)

Numerous authors have defended the rough idea that it is irrational to fail to conform to one’s judgments about what it would be rational to do, or what doxastic states it would be rational to be in. This chapter examines rational reflection principles as an attempt to implement this idea in contexts of uncertainty about what credence distributions are rational. After outlining some problems with Old Rational Reflection, the chapter discusses what seems like a well-motivated fix, New Rational Reflection. It (...) is argued that an intuitive way of trying to motivate the principle fails, and that it faces counterexamples. To say the least, the principle imposes substantial and controversial constraints on the kinds of epistemic situations it is possible to be in. A more general problem is that rational reflection principles seem doomed to take seriously certain kinds of uncertainty about what is rational, but not others. (shrink)

Recent authors have drawn attention to a new kind of defeating evidence commonly referred to as higher-order evidence. Such evidence works by inducing doubts that one’s doxastic state is the result of a flawed process – for instance, a process brought about by a reason-distorting drug. I argue that accommodating defeat by higher-order evidence requires a two-tiered theory of justification, and that the phenomenon gives rise to a puzzle. The puzzle is that at least in some situations involving higher-order defeaters (...) the correct epistemic rules issue conflicting recommendations. For instance, a subject ought to believe p, but she ought also to suspend judgment in p. I discuss three responses. The first resists the puzzle by arguing that there is only one correct epistemic rule, an Über-rule. The second accepts that there are genuine epistemic dilemmas. The third appeals to a hierarchy or ordering of correct epistemic rules. I spell out problems for all of these responses. I conclude that the right lesson to draw from the puzzle is that a state can be epistemically rational or justified even if one has what looks to be strong evidence to think that it is not. As such, the considerations put forth constitute a non question-begging argument for a kind of externalism. (shrink)

The role of probability is one of the most contested issues in the interpretation of contemporary physics. In this paper, I’ll be reevaluating some widely held assumptions about where and how probabilities arise. Larry Sklar voices the conventional wisdom about probability in classical physics in a piece in the Stanford Online Encyclopedia of Philosophy, when he writes that “Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role.” And the conventional wisdom (...) about quantum probabilities is that they are basic, not reducible to the types of probabilities we see in statistical mechanics. In the first section of this paper, I’ll argue that in fact classical physics was steeped in probability long before statistical mechanics came on the scene, specifically, that an objective measure over phase space is an indispensable component of any informative physical theory. In the next section, I’ll argue that this objective measure is the fundamental form of physical probability and that quantum probabilities can be defined in terms of it. In the last, I’ll raise some questions about the metaphysical status of the fundamental measure. (shrink)

Many views rely on the idea that it can never be rational to have high confidence in something like, “P, but my evidence doesn’t support P.” Call this idea the “Non-Akrasia Constraint”. Just as an akratic agent acts in a way she believes she ought not act, an epistemically akratic agent believes something that she believes is unsupported by her evidence. The Non-Akrasia Constraint says that ideally rational agents will never be epistemically akratic. In a number of recent papers, the (...) Non-Akrasia Constraint has been called into question. The goal of this paper is to defend it... for the most part. (shrink)

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (shrink)

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances might seem to (...) land us in contradiction. The fundamental laws of deterministic worlds project trivial probabilities for the very same events that are assigned non-trivial probabilities by the special scientific laws. I argue that any appearance of tension is dissolved by recognition of the level-relativity of chances. There is therefore no obstacle to accepting non-trivial chance-role-playing deterministic probabilities as genuine chances. (shrink)

Several philosophers have embraced the view that high-level events—events like Zimbabwe's monetary policy and its hyper-inflation—are causally related if their corresponding low-level, fundamental physical events are causally related. I dub the view which denies this without denying that high-level events are ever causally related causal emergentism. Several extant philosophical theories of causality entail causal emergentism, while others are inconsistent with the thesis. I illustrate this with David Lewis's two theories of causation, one of which entails causal emergentism, the other of (...) which entails its negation. I then argue for causal emergentism on the grounds that it provides the only adequate means of squaring the apparent plenitude of causal relations between low-level events with the apparent scarcity of causal relations between high-level events. This tension between the apparent abundance of low-level causation and the apparent scarcity of high-level causation has been noted before. However, it has been thought that various theses about the semantics or the pragmatics of causal claims could be used to ameliorate the tension without going in for causal emergentism. I argue that none of the suggested semantic or pragmatic strategies meet with success, and recommend emergentist theories of causality in their stead. As Lewis's 1973 account illustrates, causal emergentism is consistent with the thesis that all facts reduce to microphysical facts. (shrink)

Vague subjective probability may be modeled by means of a set of probability functions, so that the represented opinion has only a lower and upper bound. The standard rule of conditionalization can be straightforwardly adapted to this. But this combination has difficulties which, though well known in the technical literature, have not been given sufficient attention in probabilist or Bayesian epistemology. Specifically, updating on apparently irrelevant bits of news can be destructive of one’s explicitly prior expectations. Stability of vague subjective (...) opinion appears to need a more complex model. (shrink)