Humean supervenience is the doctrine that there are no necessary connections in the world. David Lewis identifies one big bad bug to the programme of providing Humean analyses for apparently non-Humean features of the world. The bug is chance. We put the bug under the microscope, and conclude that chance is no special problem for the Humean.

CHAPTER ONE Causality and Chance in Natural Law. INTRODUCTION IN nature nothing remains constant. Everything is in a perpetual state of transformation, ...

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.

The chance objection to incompatibilist accounts of free action maintains that undetermined actions are not under the agent’s control. Some attempts to circumvent this objection locate chance in events posterior to the action. Indeterministic-causation theories locate chance in events prior to the action. However, neither type of response gives an account of free action which avoids the chance objection. Chance must be located at the act of will if actions are to be both undetermined and under the agent’s control. This (...) dissolves the apparent paradox of Frankfurt-type cases as well as the chance objection to incompatibilist free will. (shrink)

John Earman and John T. Roberts advocate a challenging and radical claim regarding the semantics of laws in the special sciences: the statistical account. According to this account, a typical special science law “asserts a certain precisely defined statistical relation among well-defined variables” (Earman and Roberts 1999) and this statistical relation does not require being hedged by ceteris paribus conditions. In this paper, we raise two objections against the attempt to cash out the content of special science generalizations in statistical (...) terms. (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.

Suppose that unobtanium-346 is a rare radioactive isotope. Consider: (1) Every Un346 atom, at its creation, decays within 7 microseconds (µs). (50%) Every Un346 atom, at its creation, has a 50% chance of decaying within 7µs. (1) and (50%) can be true together, but (1) and (50%) cannot together be laws of nature. Indeed, (50%)'s mere (non-vacuous) truth logically precludes (1)'s lawhood. A satisfactory analysis of chance and lawhood should nicely account for this relation. I shall argue first that David (...) Lewis's Humean picture accounts for this relation only by inserting this relation ‘by hand’. Next, I shall argue that this relation between law and chance also threatens a radically non-Humean picture of laws and chances. Finally, I shall offer an account of natural law that nicely explains the relation between chancy facts and deterministic laws. This explanation is not ad hoc because it derives the relation from the very same features of lawhood that account for the laws' special relation to counterfactuals and explain how the laws (unlike the accidents) possess a variety of necessity. The reason that a chancy fact such as (50%) keeps (1) from being a law, without keeping (1) from being true, is ultimately that a chancy fact constrains the subjunctive facts and (1)'s lawhood, unlike (1)'s truth, depends upon the subjunctive facts. (shrink)

In What is a Law of Nature? (1983) David Armstrong promotes a theory of laws according to which laws of nature are contingent relations of necessitation between universals. The metaphysics Armstrong develops uses deterministic causal laws as paradigmatic cases of laws, but he thinks his metaphysics explicates other sorts of laws too, including probabilistic laws, like that of the half-life of radium being 1602 years. Bas van Fraassen (1987) gives seven arguments for why Armstrong’s theory of laws is incapable of (...) explicating probabilistic laws. The main thrust of the arguments is that Armstrong’s metaphysical apparatus serves to drive up the initial probability values stated by probabilistic laws. Armstrong replies .. (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 first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...) to statistical mechanical probabilities. (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)

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)

This article sketches a theory of objective probability focusing on "nomic probability", which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the "statistical syllogism". It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...) is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...) is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)

A law about frequencies would be a law of nature that imposes a constraint on one or more (actual, global) frequencies. On any of the leading philosophical approaches to laws of nature, there could be laws about frequencies. Hypotheses that posit laws about frequencies turn out to behave very similarly to hypotheses that posit corresponding laws about probabilities or chances -- they make the same predictions, provide similar explanations, and are confirmed or disconfirmed by empirical evidence in the same ways. (...) This makes it interesting to consider the possibility of interpreting probabilistic laws from scientific theories as laws about frequencies. This is surprising proposal, but I argue that the resulting view (which I call 'nomic frequentism') is able to overcome all of the standard objections to frequentist interpretation of objective probabilities. (shrink)