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)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The second of these articles discusses the regularity approach to statistical mechanical probabilities, and describes some areas (...) where further research is needed. (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)

Laws form counterfactually stable sets -- Natural necessity -- Three payoffs of my account -- A world of subjunctives.

A modest proposal concerning laws, counterfactuals, and explanations - - Why be Humean? -- Suggestions from physics for deep metaphysics -- On the passing of time -- Causation, counterfactuals, and the third factor -- The whole ball of wax -- Epilogue : a remark on the method of metaphysics.

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 ...

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

This is a study of a crucial and controversial topic in metaphysics and the philosophy of science: the status of the laws of nature. D. M. Armstrong works out clearly and in comprehensive detail a largely original view that laws are relations between properties or universals. The theory is continuous with the views on universals and more generally with the scientific realism that Professor Armstrong has advanced in earlier publications. He begins here by mounting an attack on the orthodox and (...) sceptical view deriving from Hume that laws assert no more than a regularity of coincidence between instances of properties. In doing so he presents what may become the definitive statement of the case against this position. Professor Armstrong then goes on to establish his own theory in a systematic manner defending it against the most likely objections, and extending both it and the related theory of universals to cover functional and statistical laws. This treatment of the subject is refreshingly concise and vivid: it will both stimulate vigorous professional debate and make an excellent student text. (shrink)

John Carroll undertakes a careful philosophical examination of laws of nature, causation, and other related topics. He argues that laws of nature are not susceptible to the sort of philosophical treatment preferred by empiricists. Indeed he shows that emperically pure matters of fact need not even determine what the laws are. Similar, even stronger, conclusions are drawn about causation. Replacing the traditional view of laws and causation requiring some kind of foundational legitimacy, the author argues that these phenomena are inextricably (...) intertwined with everything else. This distinctively clear and detailed discussion of what it is to be a law will be valuable to a broad swathe of philosophers in metaphysics, the philosophy of mind, and the philosophy of science. (shrink)

In a recent article, Adam Elga outlines a strategy for “Defeating Dr Evil with Self-Locating Belief”. The strategy relies on an indifference principle that is not up to the task. In general, there are two things to dislike about indifference principles: adopting one normally means confusing risk for uncertainty, and they tend to lead to incoherent views in some ‘paradoxical’ situations. I argue that both kinds of objection can be levelled against Elga’s indifference principle. There are also some difficulties with (...) the concept of evidence that Elga uses, and these create further difficulties for the principle. (shrink)

Newton’s equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move. It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics, or it is “unphysical,” or it employs illicit idealizations. I analyze and reject each of these reasons. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA (...) 15260; e‐mail: [email protected]. (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)

I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...) proposing a third modification of Lewis's theory, one which explains many of the common features shared by the chance theories of physics. (shrink)

David Lewis (1941-2001) was Class of 1943 University Professor of Philosophy at Princeton University. His contributions spanned philosophical logic, philosophy of language, philosophy of mind, philosophy of science, metaphysics, and epistemology. In On the Plurality of Worlds, he defended his challenging metaphysical position, "modal realism." He was also the author of the books Convention, Counterfactuals, Parts of Classes, and several volumes of collected papers.

I hear the patter of little feet around the house, I expect Bruce. What I expect is a cat, a particular cat. If I heard such a patter in another house, I might expect a cat but no particular cat. What I expect then seems to be a Meinongian incomplete cat. I expect winter, expect stormy weather, expect to shovel snow, expect fatigue---a season, a phenomenon, an activity, a state. I expect that someday mankind will inhabit at least five planets. (...) This time what I expect is a state of affairs. If we let surface grammar be our guide, the objects of expectation seem quite a miscellany. The same goes for belief, since expectation is one kind of belief. The same goes for desire: I could want Bruce, want a cat but no particular cat, want winter, want stormy weather, want to shovel snow, want fatigue, or want that someday mankind will inhabit at least five planets. The same goes for other attitudes to the extent that they consist partly of beliefs or desires or lacks thereof. But the seeming diversity of objects might be an illusion. Perhaps the objects of attitudes are uniform in category, and it is our ways of speaking elliptically about these uniform objects that are diverse. That indeed is our consensus. We mostly think that the attitudes uniformly have propositions as their objects. That is why we speak habitually of "propositional attitudes.". (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 the best scientific package is anti-Humean in its ontology, but Humean in its laws. This is because potencies and the best system account of laws complement each other surprisingly well. If there are potencies, then the BSA is the most plausible account of the laws of nature. Conversely, if the BSA is the correct theory of laws, then formulating the laws in terms of potencies rather than categorical properties avoids three serious objections: the mismatch objection, the impoverished (...) worlds objection, and the metaphysical 'oomph' objection. I argue that combining anti-Humean properties with Humean laws into a Potency-Best System Account of Laws is a powerful and science-friendly account---something that people on both sides should be able to appreciate. (shrink)

This paper examines the debate between permissive and impermissive forms of Bayesianism. It briefly discusses some considerations that might be offered by both sides of the debate, and then replies to some new arguments in favor of impermissivism offered by Roger White. First, it argues that White’s (Oxford studies in epistemology, vol 3. Oxford University Press, Oxford, pp 161–186, 2010) defense of Indifference Principles is unsuccessful. Second, it contends that White’s (Philos Perspect 19:445–459, 2005) arguments against permissive views do not (...) succeed. (shrink)

Conditionalization is a widely endorsed rule for updating one’s beliefs. But a sea of complaints have been raised about it, including worries regarding how the rule handles error correction, changing desiderata of theory choice, evidence loss, self-locating beliefs, learning about new theories, and confirmation. In light of such worries, a number of authors have suggested replacing Conditionalization with a different rule — one that appeals to what I’ll call “ur-priors”. But different authors have understood the rule in different ways, and (...) these different understandings solve different problems. In this paper, I aim to map out the terrain regarding these issues. I survey the different problems that might motivate the adoption of such a rule, flesh out the different understandings of the rule that have been proposed, and assess their pros and cons. I conclude by suggesting that one particular batch of proposals, proposals that appeal to what I’ll call “loaded evidential standards”, are especially promising. (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)

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.

We develop a Bayesian framework for thinking about the way evidence about the here and now can bear on hypotheses about the qualitative character of the world as a whole, including hypotheses according to which the total population of the world is infinite. We show how this framework makes sense of the practice cosmologists have recently adopted in their reasoning about such hypotheses.

Since the publication of David Lewis's ''New Work for a Theory of Universals,'' the distinction between properties that are fundamental – or perfectly natural – and those that are not has become a staple of mainstream metaphysics. Plausible candidates for perfect naturalness include the quantitative properties posited by fundamental physics. This paper argues for two claims: (1) the most satisfying account of quantitative properties employs higher-order relations, and (2) these relations must be perfectly natural, for otherwise the perfectly natural properties (...) cannot play the roles in metaphysical theorizing as envisaged by Lewis. (shrink)

Several variants of Lewis's Best System Account of Lawhood have been proposed that avoid its commitment to perfectly natural properties. There has been little discussion of the relative merits of these proposals, and little discussion of how one might extend this strategy to provide natural property-free variants of Lewis's other accounts, such as his accounts of duplication, intrinsicality, causation, counterfactuals, and reference. We undertake these projects in this paper. We begin by providing a framework for classifying and assessing the variants (...) of the Best System Account. We then evaluate these proposals, and identify the most promising candidates. We go on to develop a proposal for systematically modifying Lewis's other accounts so that they, too, avoid commitment to perfectly natural properties. We conclude by briefly considering a different route one might take to developing natural property-free versions of Lewis's other accounts, drawing on recent work by Williams. (shrink)

One popular approach to statistical mechanics understands statistical mechanical probabilities as measures of rational indifference. Naive formulations of this ``indifference approach'' face reversibility worries - while they yield the right prescriptions regarding future events, they yield the wrong prescriptions regarding past events. This paper begins by showing how the indifference approach can overcome the standard reversibility worries by appealing to the Past Hypothesis. But, the paper argues, positing a Past Hypothesis doesn't free the indifference approach from all reversibility worries. For (...) while appealing to the Past Hypothesis allows it to escape one kind of reversibility worry, it makes it susceptible to another - the Meta-Reversibility Objection. And there is no easy way for the indifference approach to escape the Meta-Reversibility Objection. As a result, reversibility worries pose a steep challenge to the viability of the indifference approach. (shrink)

The law of gravitation, an example of physical law The relation of mathematics to physics The great conservation principles Symmetry in physical law The distinction of past and future Probability and uncertainty: the quantum mechanical view of nature Seeking new laws.

Michael G. Titelbaum presents a new Bayesian framework for modeling rational degrees of belief—the first of its kind to represent rational requirements on agents who undergo certainty loss.

A gas prepared in a non-equilibrium state will approach equilibrium and stay there. An influential contemporary approach to Statistical Mechanics explains this behaviour in terms of typicality. However, this explanation has been criticised as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases which are epsilon-ergodic are typical with respect to the Whitney topology. Because equilibrium states are typical, (...) we argue that there follows the desired conclusion that typical initial conditions approach equilibrium and stay there. (shrink)

Determinism is a perennial topic of philosophical discussion. Very little acquaintance with the philosophical literature is needed to reveal the Tower of ...

Dr. Evil learns that a duplicate of Dr. Evil has been created. Upon learning this, how seriously should he take the hypothesis that he himself is that duplicate? I answer: very seriously. I defend a principle of indifference for self-locating belief which entails that after Dr. Evil learns that a duplicate has been created, he ought to have exactly the same degree of belief that he is Dr. Evil as that he is the duplicate. More generally, the principle shows that (...) there is a sharp distinction between ordinary skeptical hypotheses, and self-locating skeptical hypotheses. (shrink)

The 'best-system' analysis of lawhood [Lewis 1994] faces the 'zero-fit problem': that many systems of laws say that the chance of history going actually as it goes--the degree to which the theory 'fits' the actual course of history--is zero. Neither an appeal to infinitesimal probabilities nor a patch using standard measure theory avoids the difficulty. But there is a way to avoid it: replace the notion of 'fit' with the notion of a world being typical with respect to a theory.

Statistical mechanics involves probabilities. At the same time, most approaches to the foundations of statistical mechanics--programs whose goal is to understand the macroscopic laws of thermal physics from the point of view of microphysics--are classical; they begin with the assumption that the underlying dynamical laws that govern the microscopic furniture of the world are deterministic. This raises some potential puzzles about the proper interpretation of these probabilities.

This chapter explores some issues having to do with the structure of the evidential reasoning we use to infer causal and lawful claims. It is argued that such reasoning always makes use of prior, causally, or nomologically committed information, thus undercutting various views that attempt to reduce causal and lawful claims to claims about regularities. A non-reductive account of laws and causes built around the notion of invariance is advanced as an alternative.