Fabrice Correia

This chapter responds to criticismsmade in Volume 8 of this series, in reply to another chapter of that volume. The initial chapter resurrected the Growing Block Theory (GBT) from its grave, devising a coherent formulation of it and arguing that its burial was premature. It aimed to show that GBT has the wherewithal to explain how we might easily come to know that we are living on the edge of reality posited by GBT. Braddon-Mitchell, in the reply, remained unconvinced. His objections are addressed here.

This paper clarifies what proponents of the Growing Block Theory (GBT) should and what they should not say, and what they consistently can say. Once all the central tenets of the view are on the table, discussion turns to David Braddon-Mitchell’s and Trenton Merricks’ recent eulogies for GBT, based on what is representative of a certain type of argument meant to show that GBT is internally incoherent. It is argued that this type of argument proceeds from a mistaken assumption about GBT’s core – i.e. that GBT works with an untensed notion of what, in the metaphysically most fundamental sense, there is. The upshot is that this type of argument misfires and that, for all that is presently known, we might be living on the brink of reality.

We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical views that its predecessors rule out by fiat.

Starting with Kit Fine’s article “Some Puzzles of Ground” (2010), grounding has been argued to give rise to serious puzzles. The way the puzzles should be handled, I contend, depends on whether the concepts of grounding involved in the puzzles are worldly or representational. Here I focus on worldly grounding, and I argue that the formally best understood worldly concepts of worldly grounding, which I dub “weak-first”, escape all the currently known puzzles, including new puzzles that I introduce in due course.

In this chapter we introduce the system of propositional tense logic that we will use throughout the book, clarify what it means to take tense seriously for the purposes of metaphysical enquiry, and clarify the contrast between dynamic and static conceptions of reality. In Sect. 1.1 we set out Arthur Prior’s operator approach to tense and distinguish between the grammatical and the logical notions of tense, which latter calls for a systematic regimentation of ordinary language. In Sect. 1.2 we present axioms governing non-metric temporal operators, including non-standard operators of the form ‘At t’. In Sect. 1.3 we use the notion of truth simpliciter to discern two broad types of metaphysical views that disagree on whether a complete description of reality requires the use of tense.

In this chapter we critically discuss the so-called epistemic objection against the Growing Block Theory of time and argue that it rests on flawed conceptions of tense and of the import of the theory’s main tenets. We show how the theory enables knowledge of the location of the edge of reality that it posits. After introducing the epistemic objection as it figures in the extant literature, we argue in Sect. 6.1 and Sect. 6.2 that this objection either rests on a gross misunderstanding of the theory’s conception of the past, or else on a gross misunderstanding of the way in which utterances, or judgements, with tensed contents are evaluated for truth and falsity. In Sect. 6.3 we provide a constructive response to the remaining challenge, viz. to show how we might know that we are not in the past of the growing block’s edge of becoming.

In this chapter we introduce the relations of temporal location and precedence, critically review McTaggart’s conception of the existential import of these relations, and devise axioms governing them that are acceptable to permanentists and temporaryists alike. In Sect 3.1 we critically review McTaggart’s characterisation of the B-series according to which B-series relations are permanent, distinguish between two relevant senses of ‘permanent’ as applied to relations, and show that depending on whether such relations are taken as existence-entailing, on either reading, temporaryists can consistently avail themselves of such relations. In Sect. 3.2 we clarify the relation of temporal location by laying down axioms for it, taking into account things in time of various kinds. In Sect. 3.3 we first provide axioms for the relation of precedence amongst times, and then use it to define a relation of precedence for things in time quite generally.

In this chapter we critically discuss the objection that since truths require grounds, the Growing Block Theory must take bivalence to fail for future contingents, while it proves at odds with the best account of such a failure. We challenge the version of the grounding requirement driving this objection, devise a better formulation, and show that the theory can retain bivalence and accommodate an interesting form of indeterminism. After rehearsing the objection in Sect. 7.1, in Sect. 7.2 we review different ways to articulate the grounding requirement, conclude that it should suffice that, for any tensed truth, sometimes there be grounds for it, and show how this requirement can be met by contingent truths about the future. In Sect. 7.3 we explicate a conception of the asymmetry between the open future and the fixed past, consistent with bivalence and available to the Growing Block Theory but none of its rivals.

The concept of location—of something being located at, or occupying, a region or a place—has been an important topic of philosophical investigation over the past fifteen years or so. Yet all the theories of location that have been put forward so far are unsatisfactory, because they fail to have the conceptual resources to describe certain basic locational phenomena. I introduce and partly develop a novel theory of location that does better in this respect than its predecessors. Its most distinctive feature is the way in which it handles so-called cases of multilocation: according to the theory, objects capable of being multilocated occupy regions via proxies, and—in a slogan, and very roughly—to be multilocated is to have several proxies located at different regions.

The concept of grounding - of a fact obtaining in virtue of other facts - has been a topic of intensive philosophical and logical investigation over roughly the past two decades. Many philosophers take grounding to deserve a central place in metaphysical theorizing, in great part because it is thought to do a better job than other concepts - for example, reduction and supervenience - at capturing certain phenomena. Studies on the logic of grounding have largely been conducted with this philosophical background in mind. In this Element, the author tries to give a faithful picture of the contemporary development of the logic of grounding in a way that is both reasonably comprehensive and reasonably systematic.

In this chapter we reconstruct the original version of the Growing Block Theory of time first advanced by C. D. Broad, highlight its shortcomings, and propose an improved version of the theory. We show that this improved version of the theory is superior to two more recent attempts to capture the idea of the growing block. In Sect. 4.1 we critically review central passages from Broad’s Scientific Thought, identify core principles that give substance to the image of a growing block, delimited by an edge of becoming beyond which nothing exists, and diagnose a number of problems with Broad’s account. In Sect. 4.2 we then present a neater version of the theory that still incorporates central ideas of Broad’s, yet avoids those problems. In Sect 4.3 we critically review the accounts respectively advanced by M. Tooley and T. Button and conclude that our version of the theory fares much better.

In this chapter we offer novel characterisations of presentism and permanentism which, or so we argue, significantly improve upon extant accounts. In particular, we show that, given the availability of these characterisations, neither presentism nor dynamic permanentism needs to invoke any substantial notion of presentness. In Sect. 5.1 we rehearse T. Williamson’s misgivings about the use of the notion of presentness in attempts to articulate presentism. While Williamson takes these misgivings to be sufficient to discard presentism, in Sect. 5.2 we show that the view allows for its systematic reformulation solely in terms of tensed quantification, temporal operators and a predicate for times. In Sect. 5.3, after giving a characterisation of static permanentism and critically discussing R. Cameron’s recent account of the Moving Spotlight Theory, we offer an equally lean formulation of dynamic permanentism solely in terms of temporal operators and a tensed proposition true at one time only.

In this chapter we explicate the challenge posed to classical theories of time by relativistic physics, and show that two recent attempts to reconcile such theories with Special and General Relativity founder. We conclude that a systematic revision of the classical theories is called for. In Sect. 8.1 we argue that the challenge is best conceived as threatening the intelligibility of the postulate, common to all classical theories, that there is an absolute and total temporal order. We show that C. Bourne’s appeal to primitive tenses is insufficient to avert the challenge. In Sect. 8.2 we scrutinize D. Zimmerman’s recent attempt to construe the postulated temporal order as being imposed by the contents of spacetime rather than its structure. We argue that this attempt fails to answer the challenge, and conclude in Sect. 8.3 that metaphysicians should move on and devise successor theories that no longer postulate such an order.

In this chapter we introduce the distinction between permanentist and temporaryist ontologies and present a non-classical theory of unrestricted quantification and identity that is compatible with either type of view. We discuss and defuse a recent objection that temporaryism cannot accommodate unrestricted quantification. In Sect. 2.1 we use temporal operators and quantification in order to articulate the core tenets of permanentism and temporaryism, and show that static conceptions of reality are committed to permanentism. In Sect. 2.2 we observe that classical quantification theory favours permanentism, and for reasons of neutrality, replace it by a quantification theory that, jointly with corresponding axioms for identity, yields a positive free logic. In Sect. 2.3 we reject T. Williamson’s argument meant to show that temporaryists should endorse the so-called temporal being constraint, lest they be accused of using restricted quantification when articulating their view.

In this chapter we devise a spacetime logic and argue that temporaryism must give way to spatiotemporaryism, which latter construes variation in what exists as variation across spacetime. In Sect. 9.1 we argue that much of the rationale for thinking, in a prerelativistic setting, that what exists varies across time, should survive the finding that there is no absolute and total temporal order and rationalise the corresponding thought that what exists varies across spacetime. In Sect. 9.2 we introduce a spacetime-sensitive language and a spacetime logic with operators and relations defined over the fourfold causal structure of spacetime. In Sect. 9.3 and Sect 9.4 we use these tools to articulate and compare competing spatiotemporaryist ontologies and contrast them with spatiopermanentism according to which what exists does not vary across spacetime. In Sect. 9.5 we show which relativistic views can naturally be taken to correspond to which classical theories of time.

In this chapter, I discuss the distinction between essential and accidental properties from a contemporary perspective. I first distinguish between the modal notion and the Aristotelian notion of essence. I present various ways of cashing out the modal notion, and then I turn to the Aristotelian notion, which has been at the centre of metaphysical enquiry over the past thirty years or so. I present and discuss simple modal accounts of that notion, then sophisticated accounts and finally non-modal accounts. In the very last part of the chapter, I briefly go through various topics: individual essences; the question of what is essential to what; the use of essence in the characterisation of other notions; so-called generic essence and other generalizations of the standard, objectual notion of essence; and finally, scepticism and anti-realism about essence.

Grounding is a hyperintensional notion: necessarily equivalent sentences need not be equivalent from a ground-theoretic perspective. How fine-grained, exactly, is grounding? There is a striking lack of consensus on this question. In this chapter, I try to systematize and review the main options that have been put forward in the literature. For reasons that have to do with both naturalness and convenience, I for the most part take the question to be about what is sometimes called, following Kit Fine’s (2012a) terminology, strict full grounding, and I take for granted a conception of grounding as a relation that is many-to-one and non-factive. I discuss the consequences of making alternative assumptions only in the very last section.

Many philosophers have recently been impressed by an argument to the effect that all grounding facts about “derivative entities”—e.g. the facts expressed by the (let us suppose) true sentences ‘the fact that Beijing is a concrete entity is grounded in the fact that its parts are concrete’ and ‘the fact that there are cities is grounded in the fact that p’, where ‘p’ is a suitable sentence couched in the language of particle physics—must themselves be grounded. This argument relies on a principle, _Purity_, which states that facts about derivative entities are non-fundamental. Purity is questionable. In this paper, I introduce a new argument—the argument from _Settledness_—for a similar conclusion but which does not rely on Purity. The conclusion of the new argument is that every “thick” grounding fact is grounded, where a grounding fact [F is grounded in G, H, …] is said to be thick when at least one of F, G, H, … is a fact—a condition that is automatically satisfied if grounding is factive. After introducing the argument, I compare it with the argument from Purity, and I assess its cogency relative to the relevant accounts of the connections between grounding and fundamentality that are available in the literature.

In what follows, we will reply to the critical comments one by one in the order that seemed most natural to us, given the topics covered. Apart from the references section towards the end, our replies are conceived as pieces each of which can be read independently from any of the others (but not, of course, independently from the comments it responds to). We hope to have done justice to the critical points made by our commentators and to have come up with viable answers to the various challenges they raise.

As Time Goes By offers an overview of different versions of tense realism, or A-theories of time, critically assesses those that have found supporters in the extant literature, and finally explicates and defends a hitherto neglected A-theory of time that combines many of the virtues that the B-theory claims for itself, while avoiding many of the vices that afflict more standard A-theories. Proceeding from certain general assumptions about time and its structure, the authors first provide an exhaustive classification of mutually exclusive realist views of tense in terms of precise criteria. They then critically review the more familiar of these views, such as presentism and relativism, in the light of desiderata any A-theory should satisfy, before showing how their favourite A-theory can satisfy all of these desiderata and how it escapes the McTaggartian trilemma recently expounded by Kit Fine. In the last part, the authors devise a systematic metaphysics for that view, give a reduction of times, and of the temporal order, in its terms, and provide a full semantics, statable exclusively in tensed terms, for both tensed and untensed language. The book closes by addressing and defusing the challenge that the authors' favourite A-theory is a B-theory in disguise.

Cross-temporal grounding is a type of grounding whereby present facts about the past (for example that Caesar was alive) are explained in terms of past facts (for example that Caesar is alive) rather than in terms of other present facts. This paper lays the foundations for a theory of cross-temporal grounding. After introducing the general idea of a type of grounding connecting facts to past facts, we offer two arguments that past-directed facts require cross-temporal grounds—the ‘argument from intimacy’ and the ‘argument from past explanation’. We then go on to show that cross-temporal grounding statements can be understood as instances of a type of explanation which is perfectly legitimate and intelligible, even if somewhat unusual. Finally, we explain how the logic of grounding can be extended to accommodate cross-temporal grounding statements.

Ontological dependence and grounding are two important items in the metaphysician’s toolbox: both notions can be used to formulate important philosophical claims and to define other notions that play a central role in philosophical theorising. Philosophical inquiry about ontological dependence and (especially) grounding has been very lively over the past few years, making it difficult to write a short review article on any of them, let alone a short review article on both. I try to reach a good compromise between a discussion of each notion taken separately and a discussion of how they relate to one another. I begin by introducing the notions and discussing a number of their connections with modality (Sections 9.1 and 9.2), starting with grounding for systematic reasons (some important concepts of ontological dependence are defined in terms of grounding). I then further the discussion of how the notions are connected to each other, by arguing against the view that (partial) grounding is equivalent to (the converse of) ontological dependence between facts (Section 9.3). Finally, I discuss their respective roles in the theory of fundamentality (Section 9.4).