Thinking about space is thinking about spatial things. The table is on the carpet; hence the carpet is under the table. The vase is in the box; hence the box is not in the vase. But what does it mean for an object to be somewhere? How are objects tied to the space they occupy? This book is concerned with these and other fundamental issues in the philosophy of spatial representation. Our starting point is an analysis of the interplay between (...) mereology (the study of part/whole relations), topology (the study of spatial continuity and compactness), and the theory of spatial location proper. This leads to a unified framework for spatial representation understood quite broadly as a theory of the representation of spatial entities. The framework is then tested against some classical metaphysical questions such as: Are parts essential to their wholes? Is spatial colocation a sufficient criterion of identity? What (if anything) distinguishes material objects from events and other spatial entities? The concluding chapters deal with applications to topics as diverse as the logical analysis of movement and the semantics of maps. (shrink)

The history of the idea of predicate is the history of its emancipation. The lesson of this paper is that there are two more steps to take. The first is to recognize that predicates need not have a fixed degree, the second that they can combine with plural terms. We begin by articulating the notion of a multigrade predicate: one that takes variably many arguments. We counter objections to the very idea posed by Peirce, Dummett's Frege, and Strawson. We show (...) that the arguments of a multigrade predicate must be grouped into places, with perhaps several arguments occupying positions at a place. Variability may relate to places or positions. Russell's multiple judgement predicate turns out to be just one example of a family-'is necessarily true of', 'is said of', 'is instantiated by' and so on-of predicates with variably many places. Our main concern, however, is lists. Any adequate account of lists must include plural as well as singular terms. On one account, lists are mere strings of separate arguments, which occupy variably many positions within a place of a multigrade predicate. A quite different account takes the list itself to be a compound plural term. We compare these rival conceptions, and reach some surprising conclusions. As a coda, we deploy the conceptual apparatus developed in the paper to assess Morton's pioneer system of multigrade logic. (shrink)

The surviving sources on the Stoic theory of division reveal that the Stoics, particularly Chrysippus, believed that bodies, places and times were such that all of their parts themselves had proper parts. That is, bodies, places and times were composed of gunk. This realisation helps solve some long-standing puzzles about the Stoic theory of mixture and the Stoic attitude to the present.

In its simplest form, a Spritz is an aperitif made with (sparkling) water and (white) wine. A ‘gunky Spritz’, as I will call it, is a Spritz in which the water and the wine are mixed through and through, so that every proper part of the Spritz has a proper part containing both water and wine. In the literature on the notion of location the possibility of mixtures like a gunky Spritz has been thought of as either threatening seemingly intuitive (...) locative principles, or as requiring the position of multiple primitive locative relations. In this paper I present a new theory of location which assumes as primitive only the notion of pervasive location and show that it can account for the possibility of gunky Spritz in an intuitive and adequate way. (shrink)

Can material objects be weakly located at regions of spacetime and yet fail to be exactly located anywhere? In this paper, I discuss a case which, at least according to one interpretation, answers affirmatively: the case of blending gunky water and wine, in gunky space. Perhaps after such a blend, the water and wine aren't exactly located anywhere while being weakly located at the location of the blend and any region which overlaps it. I show that the case is interesting (...) and complicated, and has consequences for some ideas found in papers by Daniel Nolan and Josh Parsons. (shrink)

According to one of the more popular endurantist packages on the market, a package I will call multilocational endurantism, enduring objects are exactly located at multiple instantaneous regions of spacetime. However, for all we know, the world might turn out to be spatiotemporally gunky and spatiotemporal gunk entails that this package is false. The goal of this paper is to sketch a view which retains the spirit of multilocational endurantism while also recognizing the possibility of certain types of objects which (...) endure through gunk. (shrink)

All of the current leading theories of location are parsimonious: they have at most one locative primitive, and the definitions of all of the other locative relations appeal to nothing beyond that primitive, mereological properties and relations, and basic logic. I argue that if we believe there can be extended, mereologically simple regions, we can construct cases that are incompatible with every possible parsimonious theory of location. In these cases, an object is contained within a simple region that is larger (...) than the object; that is, there is some region, r, and some object, x, are such that every subregion of r fails to be completely free of x, yet x fails to fill r. I argue that we ought to respond to this incompatibility by rejecting the analytic possibility of extended, simple regions. (shrink)

The notion of an extended simple region (henceforth ESR) has recently been marshalled in the service of arguments for a variety of conclusions. Exactly how to understand the idea of extendedness as it applies to simple regions, however, has been largely ignored, or, perhaps better, assumed. In this paper we first (§1) outline what we take to be the standard way that philosophers are thinking about extendedness, namely as an intrinsic property of regions. We then introduce an alternative picture (§2), (...) according to which extendedness is extrinsic. In §3 we argue that it matters which way of thinking about extendedness is the right one, since how ESRs behave is sensitive to what extendedness consists in, and various arguments that appeal to ESRs turn out to be unsound if extendedness is extrinsic rather than intrinsic. (shrink)

Recently, many philosophers have been interested in using locative relations to clarify and pursue debates in the metaphysics of material objects. Most begin with the relation of exact location. But what if we begin instead with the relation known as weak location – the relation an object x bears to any region not completely bereft of x? I explore some of the consequences of pursuing this route for issues including coincidence, extended simples, and endurance, with an eye to evaluating the (...) prospects for taking weak location as our fundamental locative relation. (shrink)

The notion of multiple location plays an important role in the characterization of endurantism. Several authors have recently offered cases intended to demonstrate the incoherence of multiple location. I argue that these cases do not succeed in making multiple location problematic. Along the way, several crucial issues about multiple location and its use by endurantists are clarified.

Hud Hudson offers a fascinating examination of philosophical reasons to believe in hyperspace. He explores non-theistic reasons in the first chapter and theistic ones towards the end; in the intervening sections he inquires into a variety of puzzles in the metaphysics of material objects that are either generated by the hypothesis of hyperspace or else informed by it, with discussions of receptacles, boundaries, contact, occupation, and superluminal motion. Anyone engaged with contemporary metaphysics, and many philosophers of religion, will find much (...) to stimulate them here. (shrink)

Thomas Sattig develops a comprehensive framework for doing philosophy of time, and offers an original three-dimensionalist picture of the material world. He brings together a variety of different perspectives, linking our ordinary conception of time with the physicist's conception, and linking metaphysical questions about time with questions in the philosophy of language.