Ned Hall

In the metaphysics of laws of nature, one fundamental philosophical question is whether we should give a metaphysical or rather an epistemic account of what they are; that is the core issue that divides ‘Humeans’ from ‘anti-Humeans’. In much the same way, a key question we face with essences is whether to give a metaphysical or rather an epistemic account of what they are. (So note well: in choosing to deploy the term ‘essence’ this chapter is not taking sides on the ‘Go metaphysical, or go epistemic?’ question. Just as we can be anti-metaphysical and still freely use the expression ‘law of nature’, so too we can be anti-metaphysical and freely use ‘essence’.) And the advantage of connecting these two topics is that we have made enough progress on the former for the lessons learned to provide valuable guidance for investigating the latter. Despite the author’s agnosticism about which approach is correct, the chapter mostly investigates the prospects for the ‘go epistemic’ option—what it calls ‘Humean reductionism about essence’.

Causation is at once familiar and mysterious. Neither common sense nor extensive philosophical debate has led us to anything like agreement on the correct analysis of the concept of causation, or an account of the metaphysical nature of the causal relation. Causation: A User's Guide cuts a clear path through this confusing but vital landscape. L. A. Paul and Ned Hall guide the reader through the most important philosophical treatments of causation, negotiating the terrain by taking a set of examples as landmarks. They clarify the central themes of the debate about causation, and cover questions about causation involving omissions or absences, preemption and other species of redundant causation, and the possibility that causation is not transitive. Along the way, Paul and Hall examine several contemporary proposals for analyzing the nature of causation and assess their merits and overall methodological cogency.The book is designed to be of value both to trained specialists and those coming to the problem of causation for the first time. It provides the reader with a broad and sophisticated view of the metaphysics of the causal relation.

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

Recent enthusiasm for grounding often begins by observing that inquiry in metaphysics (and other areas) features a distinctive species of noncausal explanation. Having labeled this species “grounding explanation,” it’s a short step to the conclusion that we need a philosophical theory of grounding itself: an allegedly fundamental relation of metaphysical dependency between facts, such that a “grounding explanation” of some fact succeeds by providing information about what “grounds” that fact. This short step is hasty. For another live option is to accept that grounding explanation is a legitimate form of explanation, but to give it a thoroughly epistemic treatment, one that does not see it as involving any sort of special metaphysical relationship or structure at all. This paper sketches such a treatment, drawing inspiration from reflections on explanatory structure in mathematics.

This chapter investigates the prospects for an important position that falls under the "mere patterns" approach: what, for reasons that will emerge, the author calls"Humean reductionism" about laws of nature, a view championed perhaps most prominently by David Lewis. He reviews some of the most interesting arguments against this position from the literature, and adds some of his own that, he thinks, are more effective. The chapter considers how the best system account (BSA) would apply to the Newtonian particle world. The BSA has been challenged in a wide variety of ways: it violates certain intuitions; It makes a hash out of the connection between laws on the one hand, and counterfactuals, explanation, and induction on the other. The author thinks that the problem he has raised‐challenging though he hopes it is, is really an occasion for the Humean reductionist to sharpen his position still further.

There are, by now, many rival, sophisticated philosophical accounts of causation that qualify as ‘metaphysically reductive’. This is a good thing: these collective efforts have vastly improved our understanding of causation over the last 30 years or so. They also put us in an excellent position to reflect on some central methodological questions: What exactly is the point of offering a metaphysical reduction of causation? What philosophical scruples ought to guide the pursuit of such a reduction? Finally, how should answers to these latter questions affect one’s assessment of the main contemporary approaches? That’s what we investigate in this essay. Section 1 lays out our presuppositions. Section 2 reviews a sample of philosophical accounts. Then comes the main event: Section 3 looks in detail at the foregoing methodological questions, closing with a reconsideration of our sample accounts, in light of what we’ve found.

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.

Causation is a deeply intuitive and familiar relation, gripped powerfully by common sense. Or so it seems. As is typical in philosophy, however, that deep intuitive familiarity has not led to any philosophical account of causation that is at once clean, precise, and widely agreed upon. Not for lack of trying: the last thirty years or so have seen dozens of attempts to provide such an account, and the pace of development is, if anything, accelerating. (See Collins et al. [2003a] for a comprehensive sampling of the latest work.)

What is the compositional structure of reality? That question divides naturally into these two: What is the compositional structure of the particulars that populate reality? And what is the structure of the properties and relations that fix what these entities are like? David Lewis‘s work in ontology and mereology provides the materials for an extraordinarily clean answer to the first question. First, among the particulars1 that populate reality are mereological simples: entities that have no proper parts. Second, every collection of such entities has a unique mereological fusion. And third, every particular is either a simple, or a fusion of simples.2 That‘s it. I propose to take this answer on board.3 What, then, about our second question? Here it looks as though we can draw on an additional Lewisian thesis: Joints: There is a distinction — at the level of metaphysics — between more and less natural properties. Some properties are perfectly natural; others are less-but-still-quite natural; still others are not very natural at all. This distinction earns its philosophical keep because of the number and centrality of the philosophical projects that must presuppose it. And to say that this distinction resides at the level of metaphysics is, at least in part, to say that it is not grounded in facts about human psychology.

Jonardon Ganeri, Paul Noordhof, and Murali Ramachandran (1996) have proposed a new counterfactual analysis of causation. We argue that this – the PCA-analysis – is incorrect. In section 1, we explain David Lewis’s first counterfactual analysis of causation, and a problem that led him to propose a second. In section 2 we explain the PCA-analysis, advertised as an improvement on Lewis’s later account. We then give counterexamples to the necessity (section 3) and sufficiency (section 4) of the PCA-analysis.

David Lewis's influential work on the epistemology and metaphysics of objective chance has convinced many philosophers of the central importance of the following two claims: First, it is a serious cost of reductionist positions about chance (such as that occupied by Lewis) that they are, apparently, forced to modify the Principal Principle--the central principle relating objective chance to rational subjective probability--in order to avoid contradiction. Second, it is a perhaps more serious cost of the rival non-reductionist position that, unlike reductionism, it can give no coherent explanation for why the Principal Principle should hold. I argue that both of these claims are fundamentally mistaken.

The professor announces a surprise exam for the upcoming week; her clever student purports to demonstrate by reductio that she cannot possibly give such an exam. Diagnosing his puzzling argument reveals a deeper puzzle: Is the student justified in believing the announcement? It would seem so, particularly if the upcoming 'week' is long enough. On the other hand, a plausible principle states that if, at the outset, the student is justified in believing some proposition, then he is also justified in believing that he will continue to be justified in believing that proposition. It follows from this 'confidence' principle that the student is not justified in believing the announcement, regardless of the number of days in the week. I argue that the key to resolving this dilemma is to distinguish the confidence principle from a slightly weaker principle governing the student's justified degrees of belief. Representing these degrees of belief as probabilities, and taking 'justified belief' to mean 'justified degree of belief above a certain threshold', I show that we can uphold the weaker, probabilistic analog to the confidence principle, and maintain that, provided the 'week' is long enough, the student can justifiably believe the announcement. The resulting probabilistic analysis of the story leads to a new diagnosis of the logical flaw in the student's reasoning, and suggests, finally, that even those early stages of it which are logically impeccable exhibit another kind of flaw: circularity.