In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. (...) The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality. (shrink)

This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. Those assumptions (...) arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (shrink)

I consider two usages of the expression "gauge theory". On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in which one formulation of electromagnetism, the paradigmatic gauge theory on both usages, may be understood to have excess structure, and then argue that gauge theories on the second usage, including Yang-Mills theory and general relativity, do not generally have excess structure (...) in this sense. (shrink)

This paper is concerned with the question of the truth conditions of nomological statements. My fundamental thesis is that it is possible to set out an acceptable, noncircular account of the truth conditions of laws and nomological statements if and only if relations among universals - that is, among properties and relations, construed realistically - are taken as the truth-makers for such statements. My discussion will be restricted to strictly universal, nonstatistical laws. The reason for this limitation is not that (...) I feel there is anything dubious about the concept of a statistical law, nor that I feel that basic laws cannot be statistical. The reason is methodological. The case of strictly universal, nonstatistical laws would seem to be the simplest case. If the problem of the truth conditions of laws can be solved for this simple subcase, one can then investigate whether the solution can be extended to the more complex cases. I believe that the solution I propose here does have that property, though I shall not pursue that question here.1. (shrink)

Recently, proponents of Humean Supervenience have challenged the plausibility of the intuition that the laws of nature ‘govern’, or guide, the evolution of events in the universe. Certain influential thought experiments authored by John Carroll, Michael Tooley, and others, rely strongly on such intuitions. These thought experiments are generally regarded as playing a central role in the lawhood debate, suggesting that the Mill-Ramsey-Lewis view of the laws of nature, and the related doctrine of the Humean Supervenience of laws, are false. (...) In this paper, I take on these recent challenges, arguing that the intuition that the laws govern should be taken seriously. Still, I find the recent discussions insightful, in certain ways. Employing some ideas from one of the critics, I draw some non-standard conclusions about the significance of the thought experiments to the lawhood debate. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

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)

On the received view, counterfactuals are analysed using the concept of closeness between possible worlds: the counterfactual 'If it had been the case that p, then it would have been the case that q' is true at a world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity between them. The question I consider in the (...) paper is which weights attach to different respects of similarity. I start by considering Lewis's answer to the question and argue against it by presenting several counterexamples. I use the same examples to motivate a general principle about closeness: if a fact obtains in both of two worlds, then this similarity is relevant to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and some ideas of Lewis's to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present version of the account and therefore necessitate further work on the details. (shrink)

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional - necessarily, if C then p - where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone, that the standard account has several unpalatable consequences. We argue that Humberstone’s alternative account has certain disadvantages, (...) and offer another - considerably simpler - solution. (shrink)

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. (shrink)

In this paper I shall present some of the results I have obtained on modal theories which contain quantifiers for propositions. The paper is in two parts: in the first part I consider theories whose non-quantificational part is S5; in the second part I consider theories whose non-quantificational part is weaker than or not contained in S5. Unless otherwise stated, each theory has the same language L. This consists of a countable set V of propositional variables pl, pa, ... , (...) the operators v (or), ~ (not) and □ (necessarily), the universal quantifier (p), p a propositional variable, and brackets ( and ). The formulas of L are then defined in the usual way. (shrink)

I defend a version of Kripke's claim that the metaphysically necessary and the knowable a priori are independent. On my version, there are two independent families of modal notions, metaphysical and epistemic, neither stronger than the other. Metaphysical possibility is constrained by the laws of nature. Logical validity, I suggest, is best understood in terms of epistemic necessity.

I defend a version of Kripke's claim that the metaphysically necessary and the knowable a priori are independent. On my version, there are two independent families of modal notions, metaphysical and epistemic, neither stronger than the other. Metaphysical possibility is constrained by the laws of nature. Logical validity, I suggest, is best understood in terms of epistemic necessity.

It is a traditional empiricist doctrine that natural laws are universal truths. In order to overcome the obvious difficulties with this equation most empiricists qualify it by proposing to equate laws with universal truths that play a certain role, or have a certain function, within the larger scientific enterprise. This view is examined in detail and rejected; it fails to account for a variety of features that laws are acknowledged to have. An alternative view is advanced in which laws are (...) expressed by singular statements of fact describing the relationship between universal properties and magnitudes. (shrink)

This paper is an investigation of the general logic of "identifications", claims such as 'To be a vixen is to be a female fox', 'To be human is to be a rational animal', and 'To be just is to help one's friends and harm one's enemies', many of which are of great importance to philosophers. I advocate understanding such claims as expressing higher-order identity, and discuss a variety of different general laws which they might be thought to obey. [New version: (...) Nov. 4th, 2016]. (shrink)

Some scientists try to discover and report laws of nature. And, they do so with success. There are many principles that were for a long time thought to be laws that turned out to be useful approximations, like Newton’s gravitational principle. There are others that were thought to be laws and still are considered laws, like Einstein’s principle that no signals travel faster than light. Laws of nature are not just important to scientists. They are also of great interest to (...) us philosophers, though primarily in an ancillary way. Qua philosophers, we do not try to discover what the laws are. We care about what it is to be a law, about lawhood, the essential difference between something’s being a law and something’s not being a law. It is one of our jobs to understand lawhood and convey our understanding to others. (shrink)