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Four-Dimensionalism is a thorough, lively and forceful defence of the claim that “necessarily, every spatiotemporal object has a temporal part at every moment at which it exists” (59). The standard four-dimensionalist view is perdurance theory, according to which everyday things like boats are temporally extended. But Sider rejects perdurance theory, nicely disparaging it as the “worm view”, and he argues for the “stage view” version of fourdimensionalism instead. According to the stage view, everyday things like boats are instantaneous, and claims about the history of the Anstruther lifeboat are made true or false by the boat’s past counterparts. Sider reserves the term “four-dimensionalism” for these two views of persistence; he also defends a tenseless B-theory of time. The book develops, extends and systematises work which Sider has published over the last few years, and it makes a compelling and readable whole. I am sympathetic with many of the conclusions, but I will take issue with some of the arguments.

In ‘Location and Perdurance’ (2010), I argued that there are no compelling mereological or sortal grounds requiring the perdurantist to distinguish the molecule Abel from the atom Abel in Gilmore’s original case (2007). The remaining issue Gilmore originally raised concerned the ‘mass history’ of Adam and Abel, the distribution of ‘their’ mass over spacetime. My response to this issue was to admit that mass histories needed to be relativised to a way of partitioning the location of Adam/Abel, but that did not amount to relativising any fundamental natural intrinsic properties—the latter are all had unrelativised, and (so most perdurantists would say).

I offer an argument in defense of four-dimensionalism, the view that objects are temporally, as well as spatially extended. The argument is of the inference-to-the-best-explanation variety and is based on relativistic considerations. It deals with the situation in which one and the same object has different three-dimensional shapes at the same time and proceeds by asking what sort of thing it must be in order to present itself in such different ways in various “perspectives” (associated with moving reference frames) without being different from itself. I argue that the best answer is that the object must be four-dimensional. It will then have differing 3D shapes in different perspectives because such shapes are intrinsic properties of its 3D parts.

Under the eternalist hypothesis that objects or events exist independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in (space-)time, and persisting objects perdure if they are singly located by having numerically different temporal parts. Recently, several authors (Balashov, Hales/Johnson, Gilmore, Gibson/Pooley) have argued that special relativity (SR) favours perdurantism over its endurantist rival. In my talk, I want to show that in fact the purported arguments are only those against endurantism, and that with similar ones we should argue against perdurantism, as well: Enduring and perduring entities are both in conflict with SR which undermines the eternalist hypothesis. For arguing in favour of perdurantism Yuri Balashov (2000b; 2005), on the one hand, considers spatially unextended (persisting) objects in Minkowski space-time and claims that for the endurantists there are unwelcome consequences from an adequate concept of their coexistence. On the other hand, spacelike extended (persisting) objects are under investigation. Concerning point-like objects, Cody Gilmore (2002) has convincingly shown that Balashov’s arguments fail and, therefore, I will confine me to extended object. My paper has two parts following the two different strategies – namely, concerning the problem of the endurantist “explanatory deficiency” according to Balashov (2000a; 2008), and the problem of criss-crossing hyperplanes according to Gilmore (2006).

While there has been considerable recent criticism of perdurance theory in connection with a Humean understanding of causality, perdurance theory conjoined with causal realism has received relatively little attention. One might, then, form the impression that perdurance theory under the auspices of causal realism is a relatively safe view. I shall argue, however, to the contrary. My general strategy is to show that there is no plausible way of spelling out the perdurance position (of the non-Humean, causal realist sort). I implement this strategy by revealing several general problems concerning the causally-connected temporal parts scheme. I begin with a short account of perdurance theory. There follows a description of two general views of causality and the two subsequent accounts of the perduring object; then, the criticism.

We have two aims in this paper. The first is to provide the reader with a critical guide to recent work on relativity and persistence by Balashov, Gilmore and others. Much of this work investigates whether endurantism can be sustained in the context of relativity. Several arguments have been advanced that aim to show that it cannot. We find these unpersuasive, and will add our own criticisms to those we review. Our second aim, which complements the first, is to demarcate the most defensible form of relativistic endurantism (and similarly, of perdurantism). A recurring theme of this paper is that even those philosophers who do worry about relativity have not taken it seriously enough.

I offer an argument in defense of four-dimensionalism, the view that objects are temporally, as well as spatially extended. The argument is of the inference-to-the-best-explanation variety and is based on relativistic considerations. It deals with the situation in which one and the same object has different three-dimensional shapes at the same time and proceeds by asking what sort of thing it must be in order to present itself in such different ways in various "perspectives" (associated with moving reference frames) without being different from itself. I argue that the best answer is that the object must be four-dimensional. It will then have differing 3D shapes in different perspectives because such shapes are intrinsic properties of its 3D parts.

In two earlier works (Balashov, 2000a: Philosophical Studies 99, 129–166; 2000b: Philosophy of Science 67 (Suppl), S549–S562), I have argued that considerations based on special relativity and the notion of coexistence favor the perdurance view of persistence over its endurance rival. Cody Gilmore (2002: Philosophical Studies 109, 241–263) has subjected my argument to an insightful three fold critique. In the first part of this paper I respond briefly to Gilmore’s first two objections. I then grant his observation that anyone who can resist the first objection is liable to succumb to the third one. This, however, opens a way to other closely related relativistic arguments against endurantism that are immune to all three objections and, in addition, throw new light on a number of important issues in the ontology of persistence. I develop two such novel arguments in the second half of the paper.

How is the debate between endurantism and perdurantism affected by the transition from pre-relativistic spacetimes to relativistic ones? After suggesting that the endurance vs. perdurance distinction may run together a pair of cross-cutting distinctions (mereological endurance vs. mereological perdurance and locational endurance vs. locational perdurance), I discuss two recent attempts to show that the transition in question does serious damage to endurantism (at least of the locational variety).

Background and assumptions. Persistence and philosophy of time ; Atomism and composition ; Scope ; Some matters of methodology -- Persistence, location, and multilocation in spacetime. Endurance, perdurance, exdurance : some pictures ; More pictures ; Temporal modification and the "problem of temporary intrinsics" ; Persistence, location and multilocation in generic spacetime ; An alternative classification -- Classical and relativistic spacetime. Newtonian spacetime ; Neo-Newtonian (Galilean) spacetime ; Reference frames and coordinate systems ; Galilean transformations in spacetime ; Special relativistic spacetime ; Length contraction and time dilation ; Invariant properties of special relativistic spacetime -- Persisting objects in classical spacetime. Enduring, perduring, and exduring objects in Galilean spacetime ; The argument from vagueness ; From minimal D-fusions to temporal parts ; Motivating a sharp cutoff ; Some objections and replies ; Implications -- Persisting objects in Minkowski spacetime. Enduring, perduring, and exduring objects in Minkowski spacetime ; Flat and curved achronal regions in Minkowski spacetime ; Early reflections on persisting objects in Minkowski spacetime : Quine and Smart ; "Profligate ontology"? ; Is achronal universalism tenable in Minkowski spacetime? ; "Crisscrossing" and immanent causation -- Coexistence in spacetime. The notion of coexistence ; Desiderata ; Coexistence in Galilean spacetime ; Coexistence in Minkowski spacetime : CASH ; Alexandrov-Stein present and Alexandrov-Stein coexistence ; AS-Coexistence v. CASH : symmetry, multigrade, and objectivity ; As-coexistence v. CASH : relevance ; The mixed past of coexistence ; No need in the extended now -- Strange coexistence? Coexistence and existence@ ; The asymmetry thesis ; The absurdity thesis ; Collective CASH value of coexistence ; Collective existence@ and coexistence in classical spacetime ; Collective existence@ and coexistence in Minkowski spacetime ; Contextuality ; Chronological incoherence ; Some objections -- Shapes and other arrangements in Minkowski spacetime. How rigid is a granite block? ; Perspectives in space ; Perspectives in spacetime ; Are shapes intrinsic to objects? ; The causal objection ; The micro-reductive objection ; Pegs, boards, and shapes ; Perduring objects exist.