The ‘Principal Principle’ states, roughly, that one's subjective probability for a proposition should conform to one's beliefs about that proposition's objective chance of coming true. David Lewis has argued (i) that this principle provides the defining role for chance; (ii) that it conflicts with his reductionist thesis of Humean supervenience, and so must be replaced by an amended version that avoids the conflict; hence (iii) that nothing perfectly deserves the name ‘chance’, although something can come close enough by playing the (...) role picked out by the amended principle. We show that in fact there must be ‘chances’ that perfectly play what Lewis takes to be the defining role. But this is not the happy conclusion it might seem, since these ‘chances’ behave too strangely to deserve the name. The lesson is simple: much more than the Principal Principle—more to the point, much more than the connection between chance and credence—informs our understanding of objective chance. 1 Introduction 2 Preliminaries 3 Undermining futures and the New Principle 4 The Old Principle rescued? 5 The New Bug 6 Conclusion. (shrink)

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)

David Lewis's approach to objective chance is doubly distinctive. On the one hand, Lewis uses an epistemic principle to disclose the nature of chance. One the other, Lewis conjoins realism about chance with a reductive Humean metaphysics. I aim to undermine both aspects of his view. Specifically, I argue that reductive Humeanism fails across the board, and I use my discussion of chance to explain why. I also argue Lewis's "best-systems" approach to chance fails his own criteria for a metaphysics (...) of chance. (edited). (shrink)

According to principles of probability coordination, such as Miller's Principle or Lewis's Principal Principle, you ought to set your subjective probability for an event equal to what you take to be the objective probability of the event. For example, you should expect events with a very high probability to occur and those with a very low probability not to occur. This paper examines the grounds of such principles. It is argued that any attempt to justify a principle of probability coordination (...) encounters the same difficulties as attempts to justify induction. As a result, no justification can be found. (shrink)

The existence of "undermining futures" appears to show that a contradiction can be deduced from the conjunction of Humean supervenience (HS) about chance and the Principal Principle. A number of strategies for rescuing HS from this problem have been proposed recently. In this paper, a novel way of defending HS from the threat is presented, and it is argued that this defense has advantages not shared by others. In particular, it requires no revisionism about chance, and it is equally available (...) to defenders of HS who hold HS to be necessary and those who hold it to be contingent. (shrink)

The existence of “undermining futures” appears to show that a contradiction can be deduced from the conjunction of Humean supervenience about chance and the Principal Principle. A number of strategies for rescuing HS from this problem have been proposed recently. In this paper, a novel way of defending HS from the threat is presented, and it is argued that this defense has advantages not shared by others. In particular, it requires no revisionism about chance, and it is equally available to (...) defenders of HS who hold HS to be necessary and those who hold it to be contingent. (shrink)

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)

The chance of a physical event is the objective, single-case probability that it will occur. In probabilistic physical theories like quantum mechanics, the chances of physical events play the formal role that the values of physical quantities play in classical (deterministic) physics, and there is a temptation to regard them on the model of the latter as describing intrinsic properties of the systems to which they are assigned. I argue that this understanding of chances in quantum mechanics, despite being a (...) part of the orthodox interpretation of the theory and the most prevalent view in the physical community, is incompatible with a very wide range of metaphysical views about the nature of chance. The options that remain are unlikely to be attractive to scientists and scientifically minded philosophers. (shrink)

August 16, 1997 David Lewis2 has long defended an account of scientific law acceptable even to an empiricist with significant metaphysical scruples. On this account, the laws are defined to be the consequences of the best system for axiomitizing all occurrent fact. Here "best system" means the set of sentences which yields the best combination of strength of descriptive content 3 with simplicity of exposition. And occurrent facts, the facts to be systematized, are roughly the particular facts about a localized (...) space-time region that are non-modal, non-dispositional, and non-causal. Scientists providing or attempting to provide laws are plausibly seen as giving general principles that unify a body of data. Thus they organize or systematize the arrangement of occurrences. For this reason, Lewis's account has the important merits of providing contact with actual scientific practice while making sense of the standard philosophical conception that laws should be general but more than mere accidental generalizations. However, Lewis has long known about a potential problem with this account, a problem involving chance and credence.4 In a recent series of articles he, Michael Thau, and Ned Hall have developed a new formulation of the relationship between chance and credence which solves the problem. However, I will argue that these articles leave untouched and even exacerbate a closely related and more fundamental problem with the best system account, the problem of nomic necessity. Laws are supposed to be more than true; in some sense they must be true. Yet a principle's membership in the best systematization for one world seems to say nothing about its necessity, i.e., its truth at other worlds. I close by briefly describing how an alternative empiricist account may remove both problems. (shrink)