By “physical probability” I mean the empirical concept of probability in ordinary language. It can be represented as a function of an experiment type and an outcome type, which explains how non-extreme physical probabilities are compatible with determinism. Two principles, called specification and independence, put restrictions on the existence of physical probabilities, while a principle of direct inference connects physical probability with inductive probability. This account avoids a variety of weaknesses in the theories of Levi and Lewis.

I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with 'CAN'-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is to draw attention to the (...) connection between the truth conditions of sentences involving 'CAN' and 'CHANCE', and argue for the context sensitivity of each term. Awareness of this context sensitivity has consequences for the evaluation of particular philosophical arguments for (in) compatibilism when they are presented in particular contexts. (shrink)

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.

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.

A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born’s rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging (...) the pros and cons of various positions, it defends particular answers to how the probabilities emerge from Bohmian mechanics and how they ought to be interpreted. (shrink)

In October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...) to read it. That is what you have in front of you. The account of Laplace’s theory of probability in Chapter 4 is very different to what I said in my seminar lectures, and also very different to any other account I have seen; it is based on a reading of important texts by Laplace that appear not to have been read by other commentators. The discussion of von Mises’ theory in Chapter 7 is also new, though perhaps less revolutionary. And the final chapter is a new attempt to come to grips with the popular, but amorphous, subjective theory of probability. The material in the other chapters has mostly appeared in previous articles of mine but things are sometimes expressed differently here. I would like to say again that this is an incomplete draft of a book, not the book I would have written if I had decided to finish it. It no doubt contains poor expressions, it may contain some errors or inconsistencies, and it doesn’t cover all the theories that I originally intended to discuss. Apart from this preface, I have done no work on the book since October 2009. (shrink)

An essay review of Richard Johns "A Theory of Physical Probability" (University of Toronto Press, 2002). Forthcoming in Studies in History and Philosophy of Science.

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)

Book reviewed in this article: D.H. MELLOR, The Facts of Causation JOHN W. CARROLL: Laws of nature.

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are (...) not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability. (shrink)

This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous (...) omelet example of a rational choice problem. An example motivating causal decision theory illustrates the need for representing subjunctive dependencies to do justice to intuitive examples where epistemic and causal independence come apart. We argue to extend Lewis’s account of chance as a guide to epistemic probability to include De Finetti’s convergence results. We explore Diachronic Dutch book arguments as illustrating commitments for treating transitions as learning experiences. Finally, we explore implications for Martingale convergence results for motivating commitment to objective chances. (shrink)

There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewhere. To see why, observe (...) that there are many things in the world that have the mathematical structure of probabilities---the set of measurable regions on the surface of a table, for example---but that one would never mistake for being probabilities. So probability is distinguished by more than just its formal characteristics. The bulk of this essay will be taken up with the central question of what this “more” might be. (shrink)

Fundamental physics makes no clear use of causal notions; it uses laws that operate in relevant respects in both temporal directions and that relate whole systems across times. But by relating causation to evidence, we can explain how causation fits in to a physical picture of the world and explain its temporal asymmetry. This paper takes up a deliberative approach to causation, according to which causal relations correspond to the evidential relations we need when we decide on one thing in (...) order to achieve another. Tamsin's taking her umbrella is a cause of her staying dry, for example, if and only if her deciding to take her umbrella for the sake of staying dry is adequate grounds for believing she'll stay dry. This correspondence explains why causation matters: knowledge of causal structure helps us make decisions that are evidence of outcomes we seek. The account also explains why we can control the future and not the past, and why causes come before their effects. When agents properly deliberate, their decisions can never count as evidence for any outcomes they may seek in the past. From this it follows that causal relations don't run backwards. This deliberative asymmetry is itself traced back to asymmetries of evidence and entropy, providing a new way of deriving causal asymmetry from temporally symmetric laws. (shrink)