Currently Persisting Paradoxes: Getting Clear about Endurantism

Res Cogitans Volume 5 | Issue 1 Article 10 6-4-2014 Currently Persisting Paradoxes: Getting Clear about Endurantism Joshua Jarrott University of Iowa Follow this and additional works at: http://commons.pacificu.edu/rescogitans Part of the Philosophy Commons Recommended Citation Jarrott, Joshua (2014) "Currently Persisting Paradoxes: Getting Clear about Endurantism," Res Cogitans: Vol. 5: Iss. 1, Article 10. http://dx.doi.org/10.7710/2155-4838.1102 This Article is brought to you for free and open access by CommonKnowledge. It has been accepted for inclusion in Res Cogitans by an authorized administrator of CommonKnowledge. For more information, please contact . Res Cogitans (2014) 5:69-76 2155-4838 | commons.pacificu.edu/rescogitans Currently Persisting Paradoxes: Getting Clear about Endurantism Joshua Jarrott University of Iowa Published online: 4 June 2014 © Joshua Jarrott 2014 Abstract This paper addresses a mereological paradox which faces proponents of endurantism, the theory of persistence according to which objects may be wholly located at several times. The paradox is intended to demonstrate that endurantism is false because it entails that enduring objects are both 3D and 4D. I offer three ways for the endurantist to avoid the paradoxical conclusion by demonstrating that the fusion principle required to generate the paradox is untenable. One central thesis championed by many endurantists 1 is what has been called multilocation. An object is multi-located if it exists at two or more distinct space-times. Very roughly, endurantists believe that a persisting object is multi-located at each of the times during which it exists. Just as we can imagine an object existing at more than one place at one time, so we can conceive of an object existing "wholly" at multiple times. If this thesis were undermined, it would be a significant and possibly fatal blow to the endurantist's theory. Stephen Barker and Phil Dowe 2 present a series of related paradoxes which, based largely on mereological notions, supposedly cause a lot of problems for the endurantist thesis of multi-location. I will show that these paradoxes fail to be troubling for the endurantist because it is open to the endurantist to question the legitimacy of the mereological fusion required to generate them. Although Barker and Dowe present several paradoxes, they are all very similar and, as far as I can tell, rely upon the same mistaken fusion principle. I will, therefore, only address the central mereological paradox. The paradox is formulated in a way which assumes eternalism about space-time, but this is no serious concern since many 1 2 See for example (McCall & Lowe, 2006) (Barker & Dowe, Paradoxes of Multi-Location, 2003), (Barker & Dowe, Endurance Is Paradoxical, 2005) Res Cogitans (2014) 5 Jarrott | 70 (perhaps most) endurantists assume eternalism anyway. According to Barker and Dowe, if one accepts multi-location, then one is forced to conclude that enduring entities are both three- and four-dimensional in nature. Let's first look at a summary of the paradoxical argument. The Paradox Consider and object, O, which persists from time t until t*. For simplicity, imagine that O is a small spherical object. Suppose further that O is multi-located throughout the space-time region, R, bounded by t and t*. R can be divided into sub-regions ri, and O is located at each sub-region ri within R. Call the particular manifestation of O at a given sub-region an Or. Intuitively, each Or is identical to O, since O is multi-located, and O is a three-dimensional persisting sphere; so each of the Ors is a threedimensional thing. Now suppose that we take the mereological sum or fusion of all of the Ors within R. Call this the F(Or). F(Or) is such that it is temporally extended by having temporal parts, the Ors of which it is a fusion, and so F(Or) must be a fourdimensional entity. However, F(Or) is just the fusion of identical entities Or, so F(Or) must just be identical to every Or. But each Or is identical to O, and O is threedimensional. Therefore, F(Or) is three-dimensional. So F(Or) is both three- and fourdimensional, and since F(Or) is identical to Or is identical to O, it follows that O is also both three- and four-dimensional. This is our paradox. There have been a couple responses to this paradox 3, and at least one of them 4 points out what I believe to be essentially wrong with the paradox. Namely, it is not at all clear that O could be a genuine fusion of itself. More fundamentally, one might worry that the fusion principle is being taken with too much metaphysical seriousness and that a proper investigation into its nature should be made before we accept the paradoxical conclusion. Below I will address this concern and try to do the requisite investigation. Before we go into this, however, let's look at one solution which has generally been ignored in the literature: mereological nihilism. Nihilism Mereological nihilism 5 is the thesis that there are no instances of composition. That is, however many mereological objects there are, each is a partless simple, and fusions or sums are strictly impossible. There are no objects of ordinary discourse such as tables and chairs. There are lumps of mereological simples arranged chair-wise and table3 (McDaniel, 2003), (Beebee & Rush, 2003) 4 (Beebee & Rush, 2003) 5 The pluralistic version: see (Sider, Against Parthood, 2013), and (Schaffer, 2007) 2155-4838 | commons.pacificu.edu/rescogitans Res Cogitans (2014) 5 Jarrott | 71 wise, and these lumps have all of the causal powers necessary to be considered ordinary everyday objects. 6 If nihilism is true, then Barker and Dowe's paradox is not formulable, since there can be no F(Or) in the first place because there cannot be a fusion of anything. Fusions are simply not possible. But the ability of the Ors to be fused into F(Or) is necessary for the conclusion that O is both three- and four-dimensional. What we can learn from this is that in order to subvert the paradox, the endurantist only needs to show that a fusion of the Ors is not possible. Below I will show how this can be done without recourse to mereological nihilism. Even if I am not successful, it is still open to the endurantist to endorse nihilism—an acceptable conclusion for those with a very strong aversion to four-dimensionalism. 7 Fusion The problem then lies in a mistaken understanding of the fusion principle. The paradox is given in somewhat a rough fashion in that it glosses over the importance of certain hidden premises. For example, how strongly are we to be committed to the fusion principle in the first place? It is assumed that the fusion of the Ors is just plain old fusion and that the fusion principle applies equally to multi-located objects as it would to anything else. The paradox is supposed to show that endurantism is false because multi-location is impossible, but why should we not think instead that certain kinds of (...truncated)