The elucidations and regimentations of grounding offered in the literature standardly take it to be a necessary connection. In particular, authors often assert, or at least assume, that if some facts ground another fact, then the obtaining of the former necessitates the latter; and moreover, that grounding is an internal relation, in the sense of being necessitated by the existence of the relata. In this article, I challenge the necessitarian orthodoxy about grounding by offering two prima facie counterexamples. First, some (...) physical facts may ground a certain phenomenal fact without necessitating it; and they may co-exist with the latter without grounding it. Second, some instantiations of categorical properties may ground the instantiation of a dispositional one without necessitating it; and they may co-exist without grounding it. After arguing that these may be genuine counterexamples, I ask whether there are modal constraints on grounding that are not threatened by them. I propose two: that grounding supervenes on what facts there are, and that every grounded fact supervenes on what grounds there are. Finally, I attempt to provide a rigorous formulation of the latter supervenience claim and discuss some technical questions that arise if we allow descending grounding chains of transfinite length. (shrink)

Fundamentality plays a pivotal role in discussions of ontology, supervenience, and possibility, and other key topics in metaphysics. However, there are two different ways of characterising the fundamental: as that which is not grounded, and as that which is the ground of everything else. I show that whether these two characterisations pick out the same property turns on a principle—which I call “Dichotomy”—that is of independent interest in the theory of ground: that everything is either fully grounded or not even (...) partially grounded. I then argue that Dichotomy fails: some facts have partial grounds that cannot be complemented to a full ground. Rejecting Dichotomy opens the door to recognising a bifurcation in our notion of fundamentality. I sketch some of the far-reaching metaphysical consequences this might have, with reference to big-picture views such as Humeanism. Since Dichotomy is entailed by the standard account of partial ground, according to which partial grounds are subpluralities of full grounds, a non-standard account is needed. In a technical “Appendix”, I show that truthmaker semantics furnishes such an account, and identify a semantic condition that corresponds to Dichotomy. (shrink)

The concept of supervenience and a regimented concept of grounding are often taken to provide rival explications of pre-theoretical concepts of dependence and determination. Friends of grounding typically point out that supervenience claims do not entail corresponding grounding claims. Every fact supervenes on itself, but is not grounded in itself, and the fact that a thing exists supervenes on the fact that its singleton exists, but is not grounded in it. Common lore has it, though, that grounding claims do entail (...) corresponding supervenience claims. In this article, I show that this assumption is problematic. On one way of understanding it, the corresponding supervenience claim is just an entailment claim under a different name. On another way of understanding it, the corresponding claim is a distinctive supervenience claim, but its specification gives rise to what I call the "reference type problem": to associate the classes of facts that are the relata of grounding with the types of facts that are the relata of supervenience. However it is understood, supervenience rules out prima facie possibilities: alien realizers, blockers, heterogeneous realizers, floaters, and heterogeneous blockers. Instead of being rival explications of one and the same pre-theoretical concept, grounding and supervenience may be complementary concepts capturing different aspects of determination and dependence. (shrink)

Supervenience is a topic-neutral, broadly logical relation between classes of properties or facts. In a slogan, A supervenes on B if and only if there cannot be an A-difference without a B-difference. The first part of this paper considers different ways in which that slogan has been cashed out. The second part discusses applications of concepts of supervenience, focussing on the question whether they may provide an explication of determination theses such as physicalism.

The relation of global supervenience is widely appealed to in philosophy. In slogan form, it is explained as follows: a class of properties A supervenes on a class of properties B if no two worlds differ in the distribution of A-properties without differing in the distribution of B-properties. It turns out, though, that there are several ways to cash out that slogan. Three different proposals have been discussed in the literature. In this paper, I argue that none of them is (...) adequate. Furthermore, I present a puzzle that reveals a tension in our concept of global supervenience. (shrink)

In "Ramseyan Humility," David Lewis argues that we cannot know what the fundamental properties in our world are. His arguments invoke the possibility of permutations and replacements of fundamental properties. Most responses focus on Lewis’s view on the relationship between properties and roles, and on the assumptions about knowledge that he makes. I argue that no matter how the debates about knowledge and about the metaphysics of properties turn out, Lewis’s arguments are unconvincing since they rely on a highly implausible (...) assumption about the expressive power of our language. (shrink)

Does the global supervenience of one class on another entail reductionism, in the sense that any property in the former class is definable from properties in the latter class? This question appears to be at the same time formally tractable and philosophically significant. It seems formally tractable because the concepts involved are susceptible to rigorous definition. It is philosophically significant because in a number of debates about inter-level relationships, there are prima facie plausible positions that presuppose that there is no (...) such entailment: standard versions of non-reductive physicalism and of normative non-naturalism accept global supervenience while rejecting reductionism. I identify a gap in an influential argument for the entailment, due to Frank Jackson and Robert Stalnaker, and draw on the model theory of infinitary languages to argue that some globally supervening properties are not reducible. (shrink)

All standard epistemic logics legitimate something akin to the principle of closure, according to which knowledge is closed under competent deductive inference. And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. One might think that serious concerns about closure point us away from epistemic logic altogether—away from the very idea that the knowledge relation could be fruitfully treated as a kind of modal operator. This, however, need not be so. The (...) abandonment of closure may yet leave in place plenty of formal structure amenable to systematic logical treatment. In this paper we describe a family of weak epistemic logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled. One of these—which we term plurality semantics—is relatively unfamiliar. We explore under what conditions plurality frames validate certain much-discussed principles of epistemic logic. It turns out that plurality frames can be interpreted in a very natural way in light of one motivation for rejecting closure, adding to the significance of our technical work. The second framework that we employ—neighbourhood semantics—is much better known. But we show that it too can be interpreted in a way that comports with a certain motivation for rejecting closure. (shrink)

Where does the line between the possible and the impossible fall? One influential answer to this question is succinctly expressed by the thesis that there are no brute necessities. Typically, that thesis is taken to be non-contingent by its proponents. In this paper, I shall argue that if it is necessary, it is so brutely. From this, it follows that there could be brute necessities. But this has no tendency to show that there are any. On the resulting view, the (...) world is full of contingency—but only contingently so. (shrink)

What formulas are tense-logically valid depends on the structure of time, for example on whether it has a beginning. Logicians have investigated what formulas correspond to what physical hypotheses about time. Analogously, we can investigate what formulas of modal logic correspond to what metaphysical hypotheses about necessity. It is widely held that physical hypotheses about time may be contingent. If so, tense-logical validity may be contingent. In contrast, validity in modal logic is typically taken to be non-contingent, as reflected by (...) the general acceptance of the so-called “rule of necessitation.” But as has been argued by various authors in recent years, metaphysical hypotheses may likewise be contingent. If, in particular, hypotheses about the extent of possibility are contingent, we should expect modal-logical validity to be contingent too. Let “contingentism” be the view that everything that is not ruled out by logic is possible. I shall investigate what the right system of modal logic is, if contingentism is true. Given plausible assumptions, the system contains the McKinsey principle, and is thus not even contained in S5. It also contains simple and elegant iteration principles for the contingency operator: something is contingent if and only if it is contingently contingent. (shrink)

This paper extends the definition of strong supervenience to cover classes of relations of any adicity, including transworld relations. It motivates that project by showing that not all interesting supervenience claims involving relations are global supervenience claims. The proposed definition has five welcome features: it reduces to the familiar definition in the special case where the classes contain only monadic properties; it equips supervenience with the expected formal properties, such as transitivity and monotonicity; it entails that a relation supervenes on (...) its converse; it classifies certain paradigms correctly; it makes distinctions even in the realm of the non-contingent, as witnessed by the fact that identity does not supervene on any class of relations. Finally, the paper applies the defined concept, and the related concept of orthogonality, to the study of internal and external relations. (shrink)

Karen Bennett’s Making Things Up starts with the claim that despite all the differences between them, analytic philosophers share an interest in ‘claims about what builds – or fails to build – what’. Be that as it may, there is another candidate for a shared interest: in generalizing, and identifying common patterns in ostensibly different domains. It is that interest that Bennett pursues in the book, by developing a general theory of building relations.

Examining the depiction of Jerusalem in German-Jewish literature between 1848 and 1948, this essay explores the occupation of real places by the imagination. The work with the old myths as well as the invention of new ones about Jerusalem expressed the negotiation of cultural identity and the German-Jewish situation in an era that saw the far-reaching modernization of Judaism. In the tension between the force of descent and the horizon of self-invention, some authors created the space for the,,invention of a (...) tradition" in modernity. (shrink)

This chapter explores how LEGO compare to the metaphysics of the real, actual world—our universe. LEGO worlds and real worlds at least differ in how many there are: there are many LEGO worlds, but only one real world. According to David Lewis, there are worlds in which people were saved from entering the dark ages. There are worlds where they have a billion bricks at their disposal. But there are also worlds where LEGO has never been invented. On Lewis's view, (...) other worlds are just as real as the actual world. Lewis's plausible thesis of Humean supervenience need not be combined with his extravagant claim that there is a real world for any possible arrangement of the fundamental building blocks. A pervasive and obvious phenomenon of our world, is absent in a LEGO world. Things change—cars move, babies grow, coffee goes cold, leaves turn brown. (shrink)

Universal reductionism—the sort of project pursued by Carnap in the Aufbau, Lewis in his campaign on behalf of Humean supervenience, Jackson in From Metaphysics to Ethics, and Chalmers in Constructing the World—aims to reduce everything to some specified base, more or less austere as it may be. In this paper, I identify two constraints that a promising strategy to argue for universal reductionism needs to satisfy: the exhaustion constraint and the chaining constraint. As a case study, I then consider Chalmers’ (...) Constructing the World, in which a priori implication, or “scrutability”, plays the role of reduction. Chalmers first divides up the total vocabulary of our language into different families, and then argues, for each family separately, that truths involving expressions in that family are scrutable from the putative base. He does not systematically address the question whether “cross-family sentences”—sentences involving expressions from more than one family—are scrutable. I shall argue that this lacuna cannot be filled, since scrutability does not allow for the exhaustion constraint and the chaining constraint to be jointly satisfied. I further suggest that Carnap’s account, in which definability plays the role of reduction, has better prospects of meeting these constraints. (shrink)