Consider two epistemic experts—for concreteness, let them be two weather forecasters. Suppose that you aren’t certain that they will issue identical forecasts, and you would like to proportion your degrees of belief to theirs in the following way: first, conditional on either’s forecast of rain being x, you’d like your own degree of belief in rain to be x. Secondly, conditional on them issuing different forecasts of rain, you’d like your own degree of belief in rain to be some weighted (...) average of the forecast of each. Finally, you’d like your degrees of belief to be given by an orthodox probability measure. Moderate ambitions, all. But you can’t always get what you want. (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.

The most familiar philosophical conception of objective chance renders determinism incompatible with non-trivial chances. This conception – associated in particular with the work of David Lewis – is not a good fit with our use of the word ‘chance’ and its cognates in ordinary discourse. In this paper we show how a generalized framework for chance can reconcile determinism with non-trivial chances, and provide for a more charitable interpretation of ordinary chance-talk. According to our proposal, variation in an admissible ‘evidence (...) base’ generates a spectrum of different chance functions. Successive coarse-grainings of the evidence base generates a partial ordering of chance functions, with finer trumping coarser if known. We suggest that chance-attributions in ordinary discourse express different chance functions in different contexts, and we sketch a potential contextual mechanism for making particular chance functions salient. The mechanism involves the idea that admissible evidence is available evidence: propositions that could be known. A consequence is that attributions of objective chances inherit the relatively familiar context-sensitivity associated with the modal ‘could’. We show how this context-dependency undermines certain arguments for the incompatibility of chance with determinism. (shrink)

It is a standard view that the concept of chance is inextricably related to the technical concept of credence . One influential version of this view is that the chance role is specified by (something in the neighborhood of) David Lewis's Principal Principle, which asserts a certain definite relation between chance and credence. If this view is right, then one cannot coherently affirm that there are chance processes in the physical world while rejecting the theoretical framework in which credence is (...) defined, namely the Bayesian framework. This is surprising; why should adopting a theory that says there are chances at work in nature put any particular constraints on our theorizing about epistemology and rational choice? It is quite plausible that in order for anything to count as the referent of our concept chance , it would have to be related to epistemic rationality in a certain way—roughly, it is rational to have more confidence that something will happen the greater you think its chance is. But this commonsensical idea does not seem to be inherently committed to any particular theoretical approach to rationality, so why should we think that adopting the Bayesian approach is a prerequisite for thinking coherently about chance? I propose and defend a replacement for the Principal Principle which makes no use of the concept of credence. I also argue that this replacement is advantageous for the project of theorizing about the nature of chance. (shrink)

This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic relatively unfamiliar to philosophers.

The beauty of electricity, or of any other force, is not that the power is mysterious and unexpected, touching every sense at unawares in turn, but that it is under law... Michael Faraday, Wheatstone's Electric Telegraph's Relation to Science (being an argument in favour of the full recognition of Science as a branch of Education), 1854.

I offer an argument regarding chances that appears to yield a dilemma: either the chances at time t must be determined by the natural laws and the history through t of instantiations of categorical properties, or the function ch(•) assigning chances need not satisfy the axioms of probability. The dilemma's first horn might seem like a remnant of determinism. On the other hand, this horn might be inspired by our best scientific theories. In addition, it is entailed by the familiar (...) view that facts about chances at t are ontologically reducible to facts about the laws and the categorical history through t. However, that laws are ontologically prior to chances stands in some tension with the view that chances are governed by laws just as categorical-property instantiations are. The dilemma's second horn entails that if chances are in fact probabilities, then this is a matter of natural law rather than logical or conceptual necessity. I conclude with a suggestion for going between the horns of the dilemma. This suggestion involves a generalization of the notion that chances evolve by conditionalization. Introduction "Chances evolve by conditionalization" How might the lawful magnitude principle be defended? A historical interlude What if chances failed to be determined by the laws and categorical facts? (shrink)

In this paper we motivate the ‘principles of trust’, chance-credence principles that are strictly stronger than the New Principle yet strictly weaker than the Principal Principle, and argue, by proving some limitative results, that the principles of trust conflict with Humean Supervenience.

According to an infinite frequency principle, it is rational, under certain conditions, to set your credence in an outcome to the limiting frequency of that outcome if the experiment were repeated indefinitely. I argue that most infinite frequency principles are undesirable in at least one of the following ways: accepting the principle would lead you to accept bets with sure losses, the principle gives no guidance in the case of deterministic experiments like coin tosses and the principle relies on a (...) metaphysical property, ‘chanciness’, whose necessary and sufficient conditions are unknown. I show that a frequency principle that is based on the principal principle suffers from problems related to the definition of ‘chance’ or ‘chanciness’, which could lead to all three of the above problems. I introduce a version of the infinite frequency principle that does not rely on a notion of chance or chanciness and does not suffer from any of these problems. (shrink)

A probability distribution is regular if it does not assign probability zero to any possible event. Williamson argued that we should not require probabilities to be regular, for if we do, certain “isomorphic” physical events must have different probabilities, which is implausible. His remarks suggest an assumption that chances are determined by intrinsic, qualitative circumstances. Weintraub responds that Williamson’s coin flip events differ in their inclusion relations to each other, or the inclusion relations between their times, and this can account (...) for their differences in probability. Haverkamp and Schulz rebut Weintraub, but their rebuttal fails because the events in their example are even less symmetric than Williamson’s. However, Weintraub’s argument also fails, for it ignores the distinction between intrinsic, qualitative differences and relations of time and bare identity. Weintraub could rescue her argument by claiming that the events differ in duration, under a non-standard and problematic conception of duration. However, we can modify Williamson’s example with Special Relativity so that there is no absolute inclusion relation between the times, and neither event has longer duration except relative to certain reference frames. Hence, Weintraub’s responses do not apply unless chance is observer-relative, which is also problematic. Finally, another symmetry argument defeats even the appeal to frame-dependent durations, for there the events have the same finite duration and are entirely disjoint, as are their respective times and places. (shrink)

The view that chances are relative frequencies of occurrence within actual, finite reference classes has long been written off. I argue that it ought to be reconsidered. Focusing on non-deterministic chance, I defend a version of finite frequentism in which reference classmates are required to have qualitatively identical pasts. While my analysis can evade or resist several standard objections, it has a counterintuitive consequence: non-trivial chances entail the existence of past light cones that are perfect intrinsic duplicates. In mitigation, I (...) argue that our scientific knowledge is consistent with the hypothesis that there are many such duplicates in the actual world. Moreover, my analysis has some striking advantages: it is simple, it is metaphysically undemanding, and it makes possible a satisfying explanation of the chance–credence connection. 1 Introduction2 Target3 Sketch and Skirmish4 Articulation5 Standard Worries5.1 Frequency tolerance5.2 Leibniz’s dictum5.3 Single case chance5.4 Missing values5.5 Explanation5.6 Counterfactual chances6 Chance and Credence6.1 An indefeasible indifference intuition6.2 Articulating the credence principle6.3 Appraising the credence principle7 Confirmation8 Laws9 Summing Up. (shrink)

Ever since David Lewis argued for the indispensibility of natural properties, they have become a staple of mainstream metaphysics. This dissertation is a critical examination of natural properties. What roles can natural properties play in metaphysics, and what structure do natural properties have? In the first half of the dissertation, I argue that natural properties cannot do all the work they are advertised to do. In the second half of the dissertation, I look at questions relating to the structure of (...) natural properties. I argue that the metric structure of fundamental quantitative properties cannot be reduced to mereological structure, and I argue that the simplistic picture of natural properties as monadic must be abandoned in light of theories of fundamental physics. (shrink)

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

Risk is inherent to many, if not all, transformative decisions. The risk of regret, of turning into a person you presently consider to be morally objectionable, or of value change are all risks of choosing to transform. This aspect of transformative decision-making has thus far been ignored, but carries important consequences to those wishing to defend decision theory from the challenge posed by transformative decision-making. I contend that a problem lies in a common method used to cardinalise utilities – the (...) von Neumann and Morgenstern (vNM) method – which measures an agent's utility function over sure outcomes. I argue that the risks involved in transformative experiences are constitutively valuable, and hence their value cannot be accurately measured by the vNM method. In Section 1, I outline what transformative experiences are and the problem they pose to decision theory. In Section 2, I outline Pettigrew's (2019, Choosing for Changing Selves) decision-theoretic response, and in Section 3, I present the case for thinking that risks can carry value. In Section 4, I argue for the claim that at least some transformative experiences involve constitutive risk. I argue that this causes a problem for decision-theoretic responses within the vNM framework in Section 5. (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)

This paper examines the stability of objective chance. I defend the stable chance thesis : that in any given possible world, any pair of intrinsic duplicate physical setups with the same chances of being subject to the same external influences must yield the same chances. I argue that SCT compares favourably to rivals in the literature. I then consider a challenge to SCT involving time travel and causal loops. I argue that SCT survives this challenge, but that such cases expose (...) chance as less stable than we might unreflectively have thought. In particular, the chances associated with a physical setup are sensitive to the way that this setup is embedded in a wider causal structure. (shrink)

Non-Humean accounts of lawhood are said to founder on the Inference Problem, which is the problem of saying how laws that go beyond the regularities can entail the regularities. I argue that the Inference Problem has a simple solution – the Axiomatic Solution – on which the non-Humean only needs to outfit her laws with a law-to-regularity axiom. There is a remaining Epistemic Bulge, as to why one should believe that the posit-so-axiomatized is to be found in nature, but the (...) non-Humean can flatten the bulge. Lawhood serves as a case study of how fundamental posits can do their business. (shrink)

Chance both guides our credences and is an objective feature of the world. How and why we should conform our credences to chance depends on the underlying metaphysical account of what chance is. I use considerations of accuracy (how close your credences come to truth-values) to propose a new way of deferring to chance. The principle I endorse, called the Trust Principle, requires chance to be a good guide to the world, permits modest chances, tells us how to listen to (...) chance even when the chances are modest, and entails but is not entailed by the New Principle. As I show, a rational agent will obey this principle if and only if she expects chance to be at least as accurate as she is on every good way of measuring accuracy. Much of the discussion, and the technical results, extend beyond chance to deference to any kind of expert. Indeed, you will trust someone about a particular question just in case you expect that person to be more accurate than you are about that question. (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)

In ‘A Non-Pragmatic Vindication of Probabilism’, Jim Joyce attempts to ‘depragmatize’ de Finetti’s prevision argument for the claim that our partial beliefs ought to satisfy the axioms of probability calculus. In this paper, I adapt Joyce’s argument to give a non-pragmatic vindication of various versions of David Lewis’ Principal Principle, such as the version based on Isaac Levi's account of admissibility, Michael Thau and Ned Hall's New Principle, and Jenann Ismael's Generalized Principal Principle. Joyce enumerates properties that must be had (...) by any measure of the distance from a set of partial beliefs to the set of truth values; he shows that, on any such measure, and for any set of partial beliefs that violates the probability axioms, there is a set that satisfies those axioms that is closer to every possible set of truth values. I replace truth values by objective chances in his argument; I show that for any set of partial beliefs that violates the probability axioms or a version of the Principal Principle, there is a set that satisfies them that is closer to every possible set of objective chances. (shrink)

The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the second of two reviews of the Everett interpretation, and focuses on probability. Branching processes are identified as chance processes, and the squares of branch amplitudes are chances. Since branching is emergent, physical probability is emergent as well.

Philosophical accounts of causation have traditionally been framed as attempts to analyze the concept of a cause. In recent years, however, a number of philosophers have proposed instead that causation be empirically reduced to some relation uncovered by the natural sciences: e.g., a relation of energy transfer. This paper argues that the project of empirical analysis lacks a clearly defined methodology, leaving it uncertain how such views are to be evaluated. It proposes several possible accounts of empirical analysis and argues (...) that the most promising approach would treat it as a contingent identity discovered by identifying the relation (or relations) that most nearly approximate the inferential role of causal concepts in a psychological theory of causal judgment. (shrink)

considers what I call free-floating chances—objective chances that obtain at a given time despite the fact that their values are not determined by the laws of nature together with the full history of non-chancy facts up to that time. I offer an intuitive example of this phenomenon, and use it to argue that free-floating chances are indeed possible. Their possibility violates three quite widely held principles about chances: the lawful magnitude principle, the principle that chances evolve by conditionalization and a (...) version of David Lewis' principal principle. I argue that we should reject common formulations of each of these principles, though I offer revised understandings of each which retain much of the intuitive attractiveness of the originals and are consistent with the possibility of free-floating chances. I conclude by arguing that, while considerations of free-floating chances are important, they will not sustain the extravagant conclusions Lange attempts to draw from them. Introduction First- and Higher-Order Chances Free-Floating Chances Support for the Intuitive Assessment Three Principles Violated What to do? COND as a Default Hypothesis A More Principled Principal Principle Conclusion. (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)

This article surveys several interrelated issues in the metaphysics of chance. First, what is the relationship between the probabilities associated with types of trials (for instance, the chance that a twenty‐eight‐year old develops diabetes before age thirty) and the probabilities associated with individual token trials (for instance, the chance that I develop diabetes before age thirty)? Second, which features of the the world fix the chances: are there objective chances at all, and if so, are there non‐chancy facts on which (...) they supervene? Third, can chance be reconciled with determinism, and if so, how? (shrink)