The 3D/4D Controversy and Non-present Objects

Humana Mente Journal of Philosophical Studies, 2010

20 This section is not supposed to be an exhaustive treatment of such issues. It should give the reader a flavor, so to say, of how a fruitful interaction between Physics and Metaphysics might work. For a careful analysis see Calosi (unpublished). 21 I am taking for granted that these debates are genuine metaphysical debates and not just semantic debates in disguise. Those who are inclined to endorse such a semantical skepticism should read my claims counterfactually. 22 The justification for this conjunction is based upon some implicit technical assumptions about reducibility of objects to spacetime regions. It should be noted that the presentism eternalism debate is not to be confused with another classical debate in philosophy of time, namely the debate between A-theory of time and B-theory of time. 23 I am personally inclined to read this claim within the framework of a formal theory of location. Such a theory is a formal theory in the logic sense. It is a set of definitions, axioms and theorems in the language of the first order calculus. See again Calosi (unpublished). 24 In what follows I focus on Presentism. Most of the arguments will apply to Possibilism too so there is no need to distinguish here. 25 As I maintain it is. 26 See the excellent Barons, Evans and Miller (this volume). 27 Most notably Barbour, Pooley and Stein. 32 This claim is allegedly based upon the causal structure of Minkowski Spacetime. 33 Though I know that this might be, again, a controversial claim. 34 For a detailed presentation see Calosi (unpublished). 35 This is due to facts about signature and facts about causal isomorphisms of Minkowski spacetime, i.e., maps of the form : A  A where A is the underlying affine space that preserves the causal structure. Formally if pKq stands for p is causally connectible with q then invariance under causal isomorphism can be written as pKq   (p)K(q). Then the distinction between a 3D and a 4D object can be make precise in locational terms, along those lines. A three-dimensional object is an object that 38 I cannot enter into the details of different formal theories of location. I will therefore stick to the theory that is almost invariably used, as it is found in Gilmore 2007 or Balashov (forthcoming). I have personally some reservations about those theories of location. 39 Notation and definitions are taken from Calosi (unpublished). 40 << stands for the mereological notion of proper parthood. The mereological system presupposed in what follows is Minimal mereology. For those and other mereological details see Varzi (2009). 41 If there is just one such a region than it follows that ExL(x, Path (x)). 42 Index i ranges over spacetime regions. 43 The relativistic counterpart of this notion is achronality. See later on. 44 Where pq is spacelike iff <pq, pq> < 0. 45 Note that Pers (x) is redundant here. This definition of a 3D object can indeed be improved upon, but I cannot refine it here. 46 I cannot enter here into the subtleties about the relationships between Mereological Persistence and Locational Perisistence. * I would like to thank the Japan Society for the Promotion of Science (www.jsps.go.jp) for giving me the means to attend this conference.

The paper presents a thorough exploration of the problem of persistence in a relativistic context. Using formal methods such as mereology, formal theories of location and the so called intrinsic formulation of special relativity we provide a new, more rigorous and more comprehensive taxonomy of persisting entities. This new taxonomy differs significantly from the ones that are present in the recent literature. 1 We are being deliberately vague here. By things we simply mean whatever entities someone is committed to in their ontology. 2 We will use endurantism and perdurantism interchangeably for three and four-dimensionalism respectively. Those familiar with the debate will probably see that we will not talk about what is sometimes referred as exdurantism or stage-view. This is because we do believe, although we cannot argue for it here, that exdurantism has the same ontological commitments as four-dimensionalism, i.e. exdurantism commits to a four-dimensionalist ontology. 3 It is indebted to the pioneering works of Gilmore , Gilmore (

I argue that four-dimensionalism is inconsistent with phenomenal experience as we know it to be. There currently exist good arguments to show why perdurantism must be false on phenomenological grounds. Such arguments are often used to motivate stage theory. I defend these arguments but argue against the motivation for stage theory. Phenomenology is incompatible with instantaneous person-stages and non- instantaneous person-stages are implausible. Given that the views discussed exhaust four-dimensionalist treatments of persons, the framework must be false.

2000

I examine the issue of persistence over time in the context of the special theory of relativity (SR). The four-dimensional ontology of perduring objects is clearly favored by SR. But it is a different question if and to what extent this ontology is required, and the rival endurantist ontology ruled out, by this theory. In addressing this question, I take the essential idea of endurantism, that objects are wholly present at single moments of time, and argue that it commits one to unacceptable conclusions regarding coexistence, in the context of SR. I then propose and discuss a plausible account of coexistence for perduring objects, which is free of these defects. This leaves the endurantist room for some maneuvers. I consider them and show that they do not really help the endurantist out. She can accommodate the notion of coexistence in the relativistic framework only at the cost of renouncing central endurantist intuitions.

2021

This thesis is composed of three essays on the perdurantist approach to persistence and identity over time. In Chapter 1, I discuss how the following papers are to be understood as parts of a unified perdurantist account of persistence over time. This chapter also outlines some of my philosophical assumptions and provides some background information about the metaphysics of persistence. In Chapter 2, I respond to the objection that the worm theory is unable to account for our intuitions about ordinary counting sentences. I do this by invoking the standard linguistic phenomenon of covert quantifier domain restriction and supplementing the worm theory with situation semantics. My version of the worm theory makes our intuitive judgements come out true, and it does so well enough that there is no need to adopt the stage theory or revisionary theories of counting. Furthermore, my version of the worm theory offers a unified account of event- and object-related counting. Chapter 3 focuses ...