Mind the Gap

Journal of Philosophical Logic https://doi.org/10.1007/s10992-021-09609-5 Mind the Gap The Space between Coincidence and Colocation Jeroen Smid1,2 Received: 22 December 2020 / Accepted: 31 May 2021 / © The Author(s) 2021 Abstract In debates about the metaphysics of material objects examples of colocated objects are commonly taken to be examples of coincidence too. But the argument that colocation is best understood as involving coincidence is never spelled out. This paper shows under what conditions colocation entails coincidence and argues that the entailment depends on a principle that actually rules out certain forms of colocation. This undermines the argument from colocation to coincidence. Keywords Mereology · Parthood · Colocation · Coincidence 1 Introduction Many philosophers are attracted to The Standard View according to which an artefact is distinct from its matter [1, 10, 12, 23, 26–28, 32, 39, 43, 46]. Since the artefact and its matter have the same location at exactly the same moment in time, this view implies that some objects are colocated. Those who accept colocation will be called ‘colocationists’. Colocationists commonly also hold that distinct objects can be made of the same parts. This amounts to a denial of the extensionality of proper parthood, the principle which states that sameness of proper parts is sufficient for identity. I will use ‘coincidentalists’ as a name for those who accept that objects can coincide. Most coincidentalists are colocationists. This is not too surprising. If distinct objects can be made of the same parts, it seems plausible these objects are also colocated. However, one could be a coincidentalist while denying colocation; for Thanks to Vetenskapsrådet for funding my research (international postdoc grant 2017-06160 3).  Jeroen Smid 1 Department of Philosophy, Lund University, Lund, Sweden 2 Department of Philosophy, University of Manchester, Manchester, UK J. Smid example, by holding that in all cases where two objects coincide they have multilocated parts that compose distinct objects, one fusion of those parts is located at one region, whilst the other fusion is located at another region. For example, Michael Burke [4] and Michael Rea [36] deny colocation but allow for distinct objects made of the same parts, although not the same parts at the same time. If we take different times to be different spacetime regions, their view is an example of coincidence without colocation. Another possible example of coincidence without colocation, as suggested by Kit Fine [12, p. 198], is a loaf of bread and the bread of which it is made: the loaf is also (weakly) located at the air pockets in the bread, but the bread is not. (Thanks to a reviewer for this journal for drawing my attention to this example.) Conversely, most colocationists are coincidentalists. Notable exceptions are bundle theorists who hold that an object is a fusion of colocated properties, be they tropes or universals; and certain Neo-Aristotelians who defend hylomorphic theories according to which an object like a statue has a formal part that its matter lacks (more about this below). But by far the majority of colocationists are coincidentalists. So much so that colocation and coincidence are often conflated or that colocation is taken to entail coincidence. For example, Karen Bennett writes that ‘the puzzle of colocation can be framed in mereological terms. The question is whether a mereological principle called uniqueness or extensionality is true—can the same parts compose more than one thing?’ [3, p. 45]. Similarly, we find remarks such as ‘they deny that two numerically distinct physical objects could be “wholly co-located”. That is, they deny that two distinct physical objects could be composed of exactly the same parts at some level of decomposition’ [31, p. 38]; and ‘cases of collocated objects are cases of part sharing’ [45, p. 625]. (See also [9, p. 310], [40, pp. 498–99], [39, p. 399], and [43, pp. 117 and 248]). So although colocation and coincidence are different things—as has been explicitly stated before by Fine [12, p. 198] and Achille Varzi [48, pp. 118–119]— colocation is commonly taken to entail coincidence. But the argument for this is never given. My aim is to map the exact terrain in logical space by showing under what conditions colocation and coincidence are equivalent. I will also ask whether there are reasonable exit points on the road from colocation to coincidence. In particular I will show that the argument from colocation to coincidence uses, unsurprisingly, a principle that Neo-Aristotelians could object to. But it also uses another principle that, quite surprisingly, is objectionable from the perspective of a colocationalist. It turns out that examples of colocation are examples of coincidence only if one accepts a principle that bans certain forms of colocation. Here’s the plan. Section 2 introduces some definitions and principles concerning coincidence, colocation, and related notions. I then present two arguments from coincidence to colocation in Section 3; and, more significantly, an argument from colocation to coincidence in Section 4. Since examples of colocation are commonly taken as examples of coincidence too, the rest of the paper discusses the effectiveness of this argument from colocation to coincidence. In particular, Section 5 discusses a key principle in the argument and explains why it is not colocation-friendly. I conclude that whatever reasons one has for accepting colocation, they do not transfer to reasons for accepting coincidence, too. To the contrary, a friend of colocation would deny a crucial principle needed in the derivation from colocation to coincidence. Mind the Gap 2 Locations and Extensional Mereology We start with purely mereological definitions and principles, i.e. those concerning the part–whole relation. The mereological theory presented here is extensional because it identifies entities with the same overlappers or the same parts. Coincident objects are thus ruled out. This set-up is deliberate since, first, for the arguments from coincidence to colocation we will have to suppose that regions of space form a model of extensional mereology (but in those cases we suppose very little about the mereology of objects) and, second, the argument from colocation to coincidence below will be a reductio ad absurdum, making it easier to see under which conditions colocation is compatible with extensionality. Since we care about the mereological structure of both objects and regions of space the following definitions and principles are meant to apply to both. Later we distinguish between variables ranging over objects and variables ranging over regions. From the primitive ‘is part of’, formalised as P xy, we define the following notions (Proper Parthood) P P xy =df P xy ∧ ¬P yx Oxy =df ∃z(P zx ∧ P zy) (Overlap) (Atom) Ax =df ¬∃yP P yx F u(z, ϕx) =df ∀x(ϕx → P xz) ∧ ∀y(P yz → ∃w(Owy ∧ ϕw)) ( (...truncated)