for extensive and challenging comments (which, I fear, I have not fully addressed). Thanks also to Oxford University Press and to Blackwell Publishing for permission to include bits of Sider (), Sider (), and Sider (a). I'd also like to thank Kit Fine, John Hawthorne, and Phillip Bricker. I've learned much from talking to Kit about fundamentality in the past few years, and from thinking through his writings on the subject. John read large portions of the manuscript and gave me many insightful comments, as well as pushing me, years ago, to go beyond the predicate. Phil directed my dissertation, which was on Lewisian naturalness. He taught me the power of this idea, how to apply it to the philosophy of space and time, and much, much more. My intellectual debt to Phil is massive. Finally, it should be obvious how much this book owes to David Lewis. His ideas on natural properties and relations have always seemed to me among his best: powerful, correct, revolutionary yet deeply intuitive.

According to ‘four‐dimensionalism’, temporally extended things are composed of temporal parts. Most four‐dimensionalists identify ordinary continuants—the persisting objects ordinary language quantifies over and names—with aggregates of temporal parts (‘space‐time worms’), but an attractive alternate version of four‐dimensionalism identifies ordinary continuants with instantaneous temporal slices and accounts for temporal predication using temporal counterpart theory. Arguments for four‐dimensionalism include the following: (1) Either substantivalism or relationalism about space‐time is true, but given substantivalism one might as well identify continuants with regions of space‐time, which have temporal parts, or with instantaneous slices of space‐time, whereas relationalism about space‐time cannot be made to work without temporal parts. (2) It can never be vague how many objects exist; if temporal parts do not exist, then a restrictive account of which filled regions of space‐time contain objects must be given, but no such account can be given that is plausible and non‐vague. (3) Four‐dimensionalism—especially the alternate, counterpart‐theoretic version—provides the most satisfying overall account of the ‘paradoxes of material constitution’, in which numerically distinct material objects (e.g. statues and lumps of clay) apparently share exactly the same parts. Objections to four‐dimensionalism (involving, e.g., motion in homogeneous substances and de re modal properties) may be answered. While logically independent of the question of four‐dimensionalism, the book also defends related theses, including (1) a robust meta‐ontology according to which unrestricted existence‐statements are non‐vague, non‐analytic, and uninfected by human convention; (2) the B‐theory of time (the opposite of presentism); (3) unrestricted composition; and (4) counterpart theory (both modal and temporal).

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First, a Digression: Expansion and ContractionThere will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located, 1 we may ask: i) must there exist expansions of o : objects in fi lled superregions 2 of R?ii) must there exist contractions of o : objects in fi lled subregions of R?Despite the apparent symmetry, entirely different considerations bear on each question. and Wisconsin. 1. Defi nitions: an object is exactly located in a region if and only if the region contains all and only the points in which the object is located (assume for simplicity that spacetime is atomic). A region is fi lled if and only if it has no empty points-no points in which no objects are located.2. = regions of which R is a subregion.