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)

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.

The Principal Principle (PP) says that, for any proposition A, given any admissible evidence and the proposition that the chance of A is x%, one's conditional credence in A should be x%. Humean Supervenience (HS) claims that, among possible worlds like ours, no two differ without differing in the spacetime-point-by-spacetime-point arrangement of local properties. David Lewis (1986b, 1994a) has argued that PP contradicts HS, and the validity of his argument has been endorsed by Bigelow et al. (1993), Thau (1994), Hall (...) (1994), Strevens (1995), Ismael (1996), Hoefer (1997), and Black (1998). Against this consensus, I argue that PP might not contradict HS: Lewis's argument is invalid, and every attempt – within a broad class of attempts – to amend the argument fails. (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)

David Lewis, Michael Thau, and Ned Hall have recently argued that the Principal Principle—an inferential rule underlying much of our reasoning about probability—is inadequate in certain respects, and that something called the ‘New Principle’ ought to take its place. This paper argues that the Principle Principal need not be discarded. On the contrary, Lewis et al. can get everything they need—including the New Principle—from the intuitions and inferential habits that inspire the Principal Principle itself, while avoiding the problems that originally (...) caused them to abandon that principle. (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.

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)

I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple (...) chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues. (shrink)

The sample space of the chance distribution at a given time is a class of possible worlds. Thanks to this connection between chance and modality, one’s views about modal space can have significant consequences in the theory of chance and can be evaluated in part by how plausible these implications are. I apply this methodology to evaluate certain forms of modal contingentism, the thesis that some facts about what is possible are contingent. Any modal contingentist view that meets certain conditions (...) that I specify generates difficulties in the philosophy of chance, including a problem usually associated with Humeanism that is known as ‘the problem of undermining futures’. I consider two well-known versions of modal contingentism that face this difficulty. The first version, proposed by Hugh Chandler and Nathan Salmon, rests on an argument for the claim that many individuals have their modal features contingently. The second version is motivated by the thesis that the existence of a possible world depends on the existence of the contingent individuals inhabiting it, and that many worlds are therefore contingent existents. (shrink)

I argue that an unHumean ontology of irreducibly dispositional properties might be fruitfully combined with what has typically been thought of as a Humean account of laws, namely, the best-system account, made popular by David Lewis (e.g., 1983, 1986, 1994). In this paper I provide the details of what I argue is the most defensible account of Humean laws in an unHumean world. This package of views has the benefits of upholding scientific realism while doing without any suspect metaphysical entities (...) to account for natural law. I conclude by arguing that the Humean laws-unHumean ontology package is well placed to provide an account of objective, nontrivial chances, a famous stumbling block for the Humean laws-Humean ontology package developed by Lewis. (shrink)

Larry Wright and others have advanced causal accounts of functional explanation, designed to alleviate fears about the legitimacy of such explanations. These analyses take functional explanations to describe second order causal relations. These second order relations are conceptually puzzling. I present an account of second order causation from within the framework of Eells' probabilistic theory of causation; the account makes use of the population-relativity of causation that is built into this theory.

Marc Lange objects to scientific essentialists that they can give no better account of the counterfactual invariance of laws than Humeans. While conceding this point succeeds ad hominem against some essentialists, I show that it does not undermine essentialism in general. Moreover, Lange's alternative account of the relation between laws and counterfactuals is - with minor modification - compatible with essentialism.

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)

A common type of argument against the existence of God is to argue that certain essential features associated with the existence of God are inconsistent with certain other features to be found in the actual world. for an analysis of the different ways to deploy the term “God” in philosophical and theological discourse and for an analysis of the logical form of arguments for and against the existence of God.) A recent example of this type of argument against the existence (...) of God is based on the assumption that there are random processes or chancy states of affairs in the actual world that contradict God being absolute sovereign over his creation: Chancy states of affairs are said to entail a denial of divine providence or omniscience. argues that “classical Big Bang cosmology is inconsistent with theism due to the unpredictable nature of the Big Bang singularity.”) More often than not, however, this apparent conflict is formulated only intuitively and lacks sufficient conceptual clarification of the crucial terms involved. As a consequence, it is seldom clear where the conflict really lies. In what follows, I first provide a brief analysis of chance and randomness before I turn to cosmological and evolutionary arguments against the existence of God that in some way or other are based on chance and randomness. I end by way of comparing three popular conceptions of God as regards their ability to deal with God’s relation to a world of chance and randomness. Neither classical theism, nor open theism, nor indeed process panentheism has difficulties in accounting for God’s relation to a world of chance and randomness. (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)

I argue against the common and influential view that non-trivial chances arise only when the fundamental laws are indeterministic. The problem with this view, I claim, is not that it conflicts with some antecedently plausible metaphysics of chance or that it fails to capture our everyday use of ‘chance’ and related terms, but rather that it is unstable. Any reason for adopting the position that non-trivial chances arise only when the fundamental laws are indeterministic is also a reason for adopting (...) a much stronger, and far less attractive, position. I suggest an alternative account, according to which chances are probabilities that play a certain explanatory role: they are probabilities that explain associated frequencies. 1 Introduction2 A Paradigm Case3 The Incompatibilist’s Criterion4 Against the Incompatibilist’s Criterion5 The Explanatory Criterion6 Conclusion. (shrink)

I argue against the common and influential view that non-trivial chances arise only when the fundamental laws are indeterministic. The problem with this view, I claim, is not that it conflicts with some antecedently plausible metaphysics of chance or that it fails to capture our everyday use of ‘chance’ and related terms, but rather that it is unstable. Any reason for adopting the position that non-trivial chances arise only when the fundamental laws are indeterministic is also a reason for adopting (...) a much stronger, and far less attractive, position. I suggest an alternative account, according to which chances are probabilities that play a certain explanatory role: they are probabilities that explain associated frequencies. (shrink)

This is the first part of a two-part article in which we defend the thesis of Humean Supervenience about Laws of Nature (HS). According to this thesis, two possible worlds cannot differ on what is a law of nature unless they also differ on the Humean base. The Humean base is easy to characterize intuitively, but there is no consensus on how, precisely, it should be defined. Here in Part I, we present and motivate a characterization of the Humean base (...) that, we argue, enables HS to capture what is really stake in the debate, without taking on extraneous commitments. (shrink)

This the first part of a two‐part article in which we defend the thesis of Humean Supervenience about Laws of Nature (HS). According to this thesis, two possible worlds cannot differ on what is a law of nature unless they also differ on the Humean base. the Humean base is easy to characterize intuitively, but there is no consensus on how, precisely, it should be defined. Here in Part I, we present and motivate a characterization of the Humean base that, (...) we argue, enables HS to capture what is really stake in the debate, without taking on extraneous commitments. “I tend to picture the [facts of the form “it is a law that s” and “is is not a lw that s”] as having been sprinkled been sprinkled like powdered sugar over the doughy surface of the non‐nomic facts.”—Marc Lange2 “Avoid empty carbohydrates.”—Runner's World3. (shrink)

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)

A previously unrecognised argument against deterministic chance is introduced. The argument rests on the twin ideas that determined outcomes are settled, while chancy outcomes are unsettled, thus making cases of determined but chancy outcomes impossible. Closer attention to tacit assumptions about settledness makes available some principled lines of resistance to the argument for compatibilists about chance and determinism. Yet the costs of maintaining compatibilism may be higher with respect to this argument than with respect to existing incompatibilist arguments.

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 his ‘A Subjectivist’s Guide to Objective Chance’, Lewis argued that a particular kinematical model for chances follows from his principal principle. According to this model, any later chance function is equal to an earlier chance function conditional on the complete intervening history of non-modal facts. This article first investigates the conditions that any kinematical model for chance needs to satisfy to count as Lewis’s kinematics of chance. Second, it presents Lewis’s justification for his kinematics of chance and explains why (...) it is bound to be problematic. Third, it gives an alternative justification for Lewis’s kinematics of chance that does not appeal to the principal principle. Instead, this justification appeals to a well-supported requirement for chance, according to which any prior chance function must be a convex combination of the possible posterior chance functions. It is shown that under a plausible assumption, Lewis’s kinematics of chance is equivalent to this requirement. Finally, by focusing on this requirement, it is explained why the so-called self-undermining chances fail to obey Lewis’s kinematics of chance. (shrink)

Drawing on Earman’s definition of determinism and Lewis’ best systems account of laws, in What Makes Time Special? Craig Callender develops an account of time as ‘the strongest thing’. The characterisation of this account apparently assumes no action at a temporal distance, an assumption that also underlies Earman’s account of determinism. In this paper I show that there is a way to define determinism that allows worlds with action at a temporal distance to count as deterministic, that action at a (...) temporal distance is possible on a best systems account of laws, and hence that Callender need not make this assumption. (shrink)

Drawing on Earman’s definition of determinism and Lewis’ best systems account of laws, in What Makes Time Special? Craig Callender develops an account of time as ‘the strongest thing’. The characterisation of this account apparently assumes no action at a temporal distance, an assumption that also underlies Earman’s account of determinism. In this paper I show that there is a way to define determinism that allows worlds with action at a temporal distance to count as deterministic, that action at a (...) temporal distance is possible on a best systems account of laws, and hence that Callender need not make this assumption. (shrink)

I argue that the past can be objectively chancy in cases of backwards causation, and defend a view of chance that allows for this. Using a case, I argue against the popular temporal view of chance, according to which chances are defined relative to times, and all chancy events must lie in the future. I then state and defend the causal view of chance, according to which chances are defined relative to causal histories, and all chancy events must lie causally (...) downstream. The causal view replicates the intuitively correct results of the temporal view in cases of ordinary forwards causation, while correctly handling cases of backwards causation. I conclude that objective chance is more closely related to the direction of causation than it is to the direction of time. (shrink)

David Lewis’s ‘Humean Supervenience’ (henceforth ‘HS’) combines realism about laws, chances, and dispositions with a sparse ontology according to which everything supervenes on the overall spatiotemporal distribution of non-dispositional properties (Lewis 1986a, Philosophical papers: Volume II, pp. ix–xvii, New York: Oxford Univesity Press, 1994, Mind 103:473–490). HS faces a serious problem—a “big bad bug” (Lewis 1986a, p. xiv): it contradicts the Principal Principle, a seemingly obvious norm of rational credence. Two authors have tried to rescue Lewis’s ontology from the ‘big (...) bad bug’ (henceforth ‘the Bug’) by rejecting realism about laws, chances, and dispositions (Halpin 1994, Aust J Phil 72:317–338, 1998, Phil Sci 65:349–360; Ward 2005, Phil Sci 71:241–261). I will argue that this strategy cannot possibly work: it is the ontology, not the realist thesis, that lies at the root of the problem. (shrink)

We review the question of whether objective chances are compatible with determinism. We first outline what we mean by chance and what we mean by determinism. We then look at the alleged incompatibility between those concepts. Finally, we look at some ways that one might attempt to overcome the incompatibility.

Why do we value higher-level scientific explanations if, ultimately, the world is physical? An attractive answer is that physical explanations often cite facts that don’t make a difference to the event in question. I claim that to properly develop this view we need to commit to a type of deterministic chance. And in doing so, we see the theoretical utility of deterministic chance, giving us reason to accept a package of views including 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)

David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense in which the Principal Principle is (...) a theorem of quantum probability theory for any credence function satisfying a suitable additivity requirement. No additional principle of rationality is needed to bring credence into line with objective chance. (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)

Humeanism about laws of nature — the view that the laws reduce to the Humean mosaic — is a popular view, but currently existing versions face powerful objections. The non-supervenience objection, the non-fundamentality objection and the explanatory circularity objection have all been thought to cause problems for the Humean. However, these objections share a guiding thought — they are all based on the idea that there is a certain kind of divergence between the practice of science and the metaphysical picture (...) suggested by Humeanism. -/- I suggest that the Humean can respond to these objections not by rejecting this divergence, but by arguing that is appropriate. In particular the Humean can, in the spirit of Loewer (2012), distinguish between scientific and metaphysical explanation — this is motivated by differing aims of explanation in science and metaphysics. And they can further leverage this into distinctions between scientific and metaphysical fundamentality and scientific and metaphysical possibility. We can use these distinctions to respond to the objections that the Humean faces. (shrink)

There are at least three core principles that define the chance role: ill the Principal Principle, l21 the Basic Chance Principle, and l31 the Humean Principle. These principles seem mutually incompatible. At least, no extant account of chance meets more than one of them. I ofier an account of chance which meets all three: L~-chance. So the good news is that L~-chance meets ill — l31. The bad news is that L~-chance turns out unlawful and unstable. But perhaps this is (...) not such bad news: L~-chance turns out to at least approximate plausible additional core principles concerning lawfulness and stability. And perhaps there is better news: one may treat 'chance' as vague, in a way that allows every core principle of chance to be met. (shrink)

The discussion of different principles of additivity for probability functions has been largely focused on the personalist interpretation of probability. Very little attention has been given to additivity principles for physical probabilities. The form of additivity for quantum probabilities is determined by the algebra of observables that characterize a physical system and the type of quantum state that is realizable and preparable for that system. We assess arguments designed to show that only normal quantum states are realizable and preparable and, (...) therefore, quantum probabilities satisfy the principle of complete additivity. We underscore the little remarked fact that unless the dimension of the Hilbert space is incredibly large, complete additivity in ordinary non-relativistic quantum mechanics reduces to countable additivity. We then turn to ways in which knowledge of quantum probabilities may constrain rational credence about quantum events and, thereby, constrain the additivity principle satisfied by rational credence functions. (shrink)