Stephan Leuenberger

How can we construct a concise and ideologically parsimonious scrutability base—a summary that a priori implies everything that is true in a given scenario? A natural approach is to proceed in stages: first, summarise what is true about the world of the scenario; second, what is true about the individual at the centre of the scenario; and third what is true about the time at the centre of the scenario (David J. Chalmers, Constructing the World). I use a fiction involving an a priori intelligence agency to show that this approach fails for certain types of scenarios: those that display glide reflection symmetries, and those that contain coincident entities. I present a solution to the problem raised by glide reflection symmetries. However, I argue that the problem of coincident entities may have wider ramifications for the question of how we can construct an optimally concise and ideologically parsimonious scrutability base.

What can the notion of ground do for the metaphysics of consciousness that modal notions such as supervenience cannot? At least three things, I suggest. First, it gives us a relation with the right formal features to articulate interlevel relations. I rebut recent claims to the effect that we can just define up suitably asymmetric or non-monotonic relations of supervenience: the defined notions lack some desired features along with the undesired ones. Second, it gives us a relation that is usefully linked to conceivability. For better or worse, it is no longer generally accepted that conceivability has modal import, and positing brute necessities is no longer considered a theoretical cost. Third, it allows us to articulate at least one interesting version of emergentism, a view that is notoriously tricky to capture in modal terms. Along the way, the paper features zombies, ghosts, and attacks by FIST (failure of implied supervenience thesis) and by FIGHT (failure of implied grounding hypothesis).

Much philosophy presupposes a picture of reality as stratified into levels or layers. Yet a precise articulation of such a picture has been missing. It is tempting to think that we now have the tools to remedy this, notably due to ground-theoretic accounts of relative fundamentality. One might expect levels of facts, and their hierarchical arrangement, to be definable from relative fundamentality among facts. I show that such a project can at best partially succeed, by establishing certain limitative results. Moreover, I argue that the limitations should not be surprising, in light of an analogy between levels of reality and instants of time. Facts may exist at more than one level, just like persisting objects exist at more than one time. Finally, I develop a new positive proposal, on which levels are not made up of facts, but of what I call “fact realisations”—roughly, facts together with a complete genealogy of their grounds.

Modality played a central role in Christian Wolff’s philosophy. In his extensive writings on the topic, he was unusually explicit about the definitions of modal notions and what sort of principles they satisfy. His alleged endorsement of fatalism prompted his expulsion from Prussia in 1723, an event that caused a major stir among Europe’s intellectual circles. This chapter examines whether Wolff was indeed committed to fatalism, despite his protestations to the contrary. It is argued that Wolff’s theory of propositions allows him to avoid the letter of view: there are truths that are not necessary. However, Wolff fails to make room for the kind of contingency in which his opponents were interested. On the interpretation proposed, Wolff’s view is in the spirit of fatalism.

The contributions to this special issue offer different perspectives on the question whether reality has foundation—whether metaphysical foundationalism is true. The purpose of this introduction is to provide some background. It starts by discussing how metaphysical foundationalism might be characterised—specifically, whether it is committed to the asymmetry, transitivity, or well-foundedness of reality-structuring relations such as parthood, causation, or ground. It then summarises how the articles in the special issue relate anti-foundationalism to the following topics: the history of analytic philosophy, modal epistemology, the relationship between ground and explanation, and between grounds and metagrounds.

This book celebrates and explores some philosophical issues raised by the work of Alan Weir, who is Professor Emeritus at the University of Glasgow, having previously held positions at the Universities of Oxford, Edinburgh and Queen’s, Belfast. In a number of areas, Weir has elaborated strikingly original views which involve a radical departure from the mainstream. These include formalism in the philosophy of mathematics, and as well as naïve set theory, with a universal set, and a naïve theory of truth. In contrast to other contemporary defenders of the latter two theories, Weir rejects dialetheism and accepts classical rules for the logical connectives. He avoids contradictions by restricting certain structural inference rules, specifically some generalized versions of transitivity. In addition, Weir has developed radical versions of naturalism and physicalism (partly informed by his work on Quine) and perceptual realism. This collection includes contributions by a distinguished group of philosophers on Weir’s philosophy, as well as a memoir and a new essay on the philosophy of mathematics by Weir himself.

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.

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.

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.

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.

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.

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.

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.

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.

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.