There are actually two somewhat different conceptions of coincidence. One involves the sharing of a time-slice or instantaneous temporal part. This is Temporal Coincidence. A second kind of coincidence involves having exactly the same parts (whether spatially or temporally extended or both) at the same time:
Def D25.1 Temporary Mereological Coincidence. x and y are coincident entities at time t if and only if x ≠ y and x and y have exactly the same proper parts at t (at some sufficiently small scale of decomposition).
25.2T Possibility of Temporary Mereological Coincidence. It is possible for there to be two coincident entities.
25.2A Impossibility of Temporary Mereological Coincidence. It is impossible for there to be two coincident entities.
On some views, Temporal Coincidence and Temporary Mereological Coincidence are exactly the same things. In particular, Replacementists will see little or no difference between the two, since for Replacementists all of the fundamental things are instantaneous. The time-slice of a thing includes all of the instantaneous parts of the thing that co-exist in the same instant, and so, for Replacementists, the time-slice includes everything that is both fundamental and a part of the thing at that time. However, Endurantists (24.1T.1T.1T.1T) see an important difference between the two. Endurantists reject the very idea of instantaneous parts, and so the idea of a time-slice. If there are no time-slices, then there is no such thing as Temporal Coincidence (for Time-Slice Substratists 24.1T.1T.1T.1A, matters complicated in ways that would not be helpful to inventory here). However, Temporary Mereological Coincidence makes sense for all Substratists and Replacementists. Consequently, we will focus on the issue of whether temporary mereological coincidence is possible.
Besides the cases of temporally coincident objects that we considered in the last section, the most compelling case of temporary mereological coincidence is that of composite things and their matter. We, therefore, turn to that case.
25.2.1 Composite things and their matter
Consider Statue, which is a statue. Statue is made of Lump, which is a mass of clay. Are Statue and Lump one and the same thing? It seems that they cannot be. For example, Lump may have existed for millions of years, while Statue was just made today. Similarly, Statue could be destroyed without destroying Lump. Even if both Statue and Lump have existed forever and will exist forever, they can still differ in many of their properties. Statue is the sort of thing that would not survive being smashed into a ball, while Lump is the sort of thing that would survive such smashing. Statue might have the property of being classical in style, while Lump has no style, at least not essentially. By Leibniz's Law, Statue and Lump cannot be identical because they have different properties. They must be distinct.
So, it seems that we have two things that perfectly coincide with one another during some stretch of time (perhaps only for an instant if Statue is very short-lived). Not only do they coincide in space; they have exactly the same atomic parts or if they consist of gunk, the very same gunky parts (at some sufficiently small scale). How can two things made of the same parts be different? How can they have different powers, whether active, passive, or immanent?
What is the problem with distinct, coincident entities? Not the overcrowding of the physical space involved. There is no general rule that distinct physical entities cannot occupy the same space. It is a particular law of physics, the Pauli exclusion principle, that gives ordinary matter (composed of fermions) its power of mutual exclusivity. The Pauli principle forbids two bosons (including protons, neutrons, and electrons, which make up the bulk of ordinary matter) from occupying the same quantum state at the same place. However, non-fermions, like photons and neutrinos, are under no such prohibition, despite the fact that they are no less physical.
Coincidence is somewhat more problematic when living organisms or conscious agents are involved. Suppose there are two distinct but coincident people before fission (or after fusion). Each has two hands and a heart and each weighs 150 pounds. Ordinarily, that would mean that we would have four hands, two hearts, and at least 300 pounds of weight altogether, and yet these inferences clearly fail in this case.
The defenders of coincidence could respond that these cases are just extreme versions of Siamese twins. Just as two Siamese twins can share a certain amount of skin and flesh, and even an entire limb, so two coincident human beings can share all of their material parts and all of their mass.
But what about mental acts and passions? Suppose the coincident people experience a red sensation, form a mathematical thought or freely choose between two options. Do we have two sensations, two thoughts, and two acts of choice or just one of each? Sensations, thoughts, and choices do not seem to be the sorts of thing that could be shared by distinct persons.
An even greater metaphysical problem with coincidence is that of shared composition. If two entities are composites and the two have exactly the same basic parts, in what could their distinct existences consist? If we answer that the distinct existences consist in their distinct persistence conditions or in their belonging to distinct sorts, then we merely push the problem back a step. If two entities are composites with exactly the same basic parts, how can the two have different persistence conditions or belong to different sorts?
25.2.2 The grounding objection to coincidence
The most important objection to the Possibility of Temporary Mereological Coincidence is the grounding objection: if coincident objects differ in their modal properties (including their persistence conditions), what grounds this difference? By definition, two coincident objects are composed of exactly the same proper parts during some period of time. Those parts are related to each other in a certain way during that period. Obviously, this arrangement of the parts is also shared by the two coincident objects—same parts, in the same arrangement. How can the two differ? If the two composite objects are wholly grounded in the parts and their arrangement, and if grounding involves entailment (as asserted by 3.8T), then it must follow that both composite objects have exactly the same properties, including their modal properties, the properties that determine their persistence.
We can put the objection another way. The standard view of coincidence is one developed by David Wiggins (originally 1980, updated in Wiggins 2001). In Wiggins's account, two coincident objects belong to different kinds called ‘sortals’. For example, Statue belongs to the sortal statue or art work, while Lump belongs to the sortal piece of clay or piece of matter. There are persistence conditions associated with sortals. Typically, different sortals will have different persistence conditions. A piece of matter can survive being smashed or ground into dust; a statue cannot. These persistence conditions, in turn, correspond to modal properties of the objects that belong to them. Thus, statues and pieces of clay have different modal properties. The piece of clay has the modal property of being possibly in a condition of being perfectly flattened; the statue lacks such a property. Now we can ask what makes the clay have this property and prevents the statue from doing so. What facts about the piece of clay are these modal properties grounded in?
The defender of the Possibility of Temporary Mereological Coincidence must say that the material parts of the clay and the statue have certain properties, like the property of possibly composing something with the modal properties of a piece of clay and the property of possibly composing something with the modal properties of a statue. When the material pieces are in the right condition, both of these potentialities are realized, resulting in the existence of two new objects. For the moment, let's call the objects “Tweedledee” and “Tweedledum”. Now, we know that one of these objects must be a statue and the other must be a piece of clay. What is responsible for making Tweedledee the statue and Tweedledum the piece of clay or vice versa? Both Tweedledee and Tweedledum stand in exactly the same causal relation to the same material bits. The defenders of Coincidence cannot explain how they end with such different properties.
Probably the best answer for the defender of Coinc
idence is to claim that the two resultant objects stand in different causal relations to the underlying parts, since the parts have two distinct joint powers: one power of producing a piece of clay and another power of producing a statue. These powers are instances of what Aristotle called ‘material causation’. However, this Aristotelian solution is one that involves a significant cost. If defenders of the Possibility of Temporary Mereological Coincidence want to claim that there are billions and trillions of coincident objects at each time and place, they will have to attribute a myriad of primitive material powers to the atoms.
The other approach to defending the Possibility of Temporary Mereological Coincidence relies instead on a deflationary understanding of the coincident objects. Priority Atomists (22.7T), who believe that no composite object is metaphysically fundamental, can countenance a large number of composite and coincident objects, since they do not believe that such objects make up any part of the fundamental structure of reality. This is especially so if the Priority Atomists take composite things to be conceptually grounded in their parts (as per Chapter 3.4), since this implies that the composite objects do not really exist. If we believe we can give a complete and adequate description of reality without mentioning composite and coincident objects, then we can treat our beliefs in coincident objects as Ontological Free Lunches. The large number of such objects is no longer of much concern, and we wouldn't need to resort to any special kind of causal explanation to account for their existence.
However, this ontological deflation comes at a high cost, since we (or at least our bodies) are among the entities whose pretensions to reality are being deflated. Can one reasonably believe that a perfectly complete description of reality could utterly omit to mention oneself?
25.2.3 Avoiding coincident entities: Nihilism and Near-Nihilism
The arguments for coincident entities depend on some principle of mereological composition. Obviously, Mereological Nihilists will be under no pressure to posit temporally coincident entities. The world would consist only of simple things, metaphysical atoms. If there are no composite things, then there are no mereologically inconstant things and so no coincidence.
Peter van Inwagen (1990a) has argued that it is obvious that there are mereologically inconstant things, namely, living organisms. He uses the existence of mereologically inconstant organisms as part of an argument against Mereological Universalism and in favor of a position that could be described as ‘Near-Nihilism’. Van Inwagen denies the existence of all composite entities except for living organisms. Van Inwagen argues that if we were to accept Mereological Universalism, it would be impossible for any mereologically inconstant thing to exist. Consider again the Tib and Tibbles paradox. If we are Mereological Universalists, we should deny that any persisting thing has lost any part in this scenario. All that has happened is that one persisting thing, Tib, has become isolated from another, Tibbles, and that Tibbles has gone from a state of being connected to being scattered.
Van Inwagen claims that in order to believe in an inconstant object, we must give up Mereological Universalism. Then we can say that, both before and after the removal of the leg, there are only two kinds of things in existence: simple atoms and the rabbit. Both persist, but the rabbit loses some of the atoms as parts. There is no such thing as Tib before the leg is removed, nor such a thing as Tibbles after the leg is removed. The three-legged rabbit and the separated foreleg do not together compose anything, and the set of parts that compose Tibbles after the loss of the leg do not compose anything before the leg is removed. The only parts the rabbit has are atoms: it has no composite parts at all.
Van Inwagen's solution eliminates coincident entities. There is only the rabbit and the atomic parts. The atomic parts do not compose any entity other than the rabbit: there are no incomplete rabbits and no wholes composed of scattered rabbit-parts.
25.2.4 Avoiding coincidence through dominant sortals
Michael Burke (1994) proposed a position that is somewhat more liberal than van Inwagen's. In effect, van Inwagen proposed that there is only one sortal that picks out composite entities, namely organism. Burke proposed instead that there might be many such sortals, so long as they can be linearly ordered. Take any two sortals: one will always dominate the other. The object belonging to the less dominant sortal fails to exist whenever the more dominant sortal is instantiated. Lump ceases to exist when Statue is created. Tib ceases to exist when the Tibbles's leg is detached. Thus, Burke's account is, like van Inwagen's, able to avoid temporary coincidence entirely.
However, Burke's account is no panacea. Like Wiggins's account, Burke's account doesn't apply to puzzles of coincidence involving things of the same sort. Thus, it won't help with cases of fission or fusion or vague identity. In addition, Burke has to make some implausible claims about things' ceasing to exist. Why doesn't Tib persist? Burke replies that before amputation, it was only a part of a cat (and so not a living thing); in order to exist before the amputation, it would have to have been a cat (and so a living thing). However, as Sider (2001: 163–164) points out, Tib was close to being a living thing before amputation. How can something as minor and extrinsic as removing the tail bring Tib into being?
Burke also owes us an account of dominance that will guarantee that in every case we can find a maximally dominant sort. Burke suggests, “The dominant sortal is the one whose satisfaction entails the possession of the widest range of properties” (Burke 1994: 610). The “range” of properties must be measured by the number and importance of the categories to which the properties belong: physical, chemical, biological, ethical, and so on. How can Burke guarantee that one of each pair of sortals will always be maximal in the range of properties it entails? Michael Rea (1996) has offered a number of counterexamples of temporarily coincident objects whose sortals cannot be ranked. For example, there might be a statue that is also a pillar, an axe that is also a hammer, or a human being that is also a chess piece.
25.2.5 An Aristotelian solution to apparent coincidence
Aristotelians reject the Possibility of Temporary Mereological Coincidence. Aristotle seems to occupy a position between van Inwagen and Burke. He affirmed, in effect, two sortals, namely, homogeneous blobs of matter and organisms. Consequently, there are only three problem cases for Aristotelians to consider: (i) cases in which there are two homogeneous blobs that are temporarily coincident, (ii) cases in which two organisms are temporarily coincident, and (iii) cases in which an organism is temporarily coincident with a homogeneous blob. Aristotelians can plausibly claim that all three are metaphysically impossible.
Case (i): two homogeneous blobs. If two blobs have all the same proper parts at some time, then they are simply identical.
Case (ii): two organisms. The proper parts of an organism are all metaphysically dependent on the organism. They have the powers they do and they persist through time by virtue of the persisting nature of the organism as a whole. Thus, it is impossible for any material body to be a proper part of two different organisms at a time. In other words, for Aristotelians, it is impossible for two organisms even to overlap, much less to coincide.
Case (iii): an organism and a homogeneous blob. First of all, it is far from obvious that it is possible for any organisms to consist of a single, homogeneous blob. Second, even if this is possible, the Aristotelians could argue a blob is destroyed whenever an organism is engendered from it and that a new blob is generated whenever the organism is destroyed. The material parts of an organism have their identities, powers, and natures tied essentially to the organism, while apparently similar material blobs that are not parts of any organism have autonomous identities, powers, and natures. This profound difference provides Aristotelians with grounds for denying the persistence of the underlying blobs.
25.2.6 Replacementist solutions: temporal counterparts
Since the van Inwagenian and Aristotelian solutions require some heavy metaphysical commitments to the fundamental existence of organisms and the non-existence of
the material parts of organisms (as fundamental entities), those solutions are not available to metaphysicians who wish to maintain the universal fundamentality of merely physical things. Such physicalists must again look to Replacementism, in one of two forms: Worm Theory or Stage Theory. Both views are committed to Ramsey-Lewis-Sider Perdurantism (24.3T.3, which we will re-label as ‘25.3T’) and agree that there is an important connection between persistence and spacetime worms (Def 24.6). The difference concerns the identity of what we think of as persisting objects. According to Worm Theory, persisting objects are identical to spacetime worms. According to Stage Theory, persisting objects are identical to temporal parts of spacetime worms.
25.3T Ramsey-Lewis-Sider Perdurantism. A spacetime worm S over interval T corresponds to the existence of a derived thing persisting through T if and only if the simplest and most powerful scientific theory of the actual world assigns a persisting entity to S. [=24.3T.3]
25.3T.1 Worm Theory. Ramsey-Lewis-Sider Perdurantism is true, and persisting objects are identical to spacetime worms.
25.3A.2 Stage Theory. Ramsey-Lewis-Sider Perdurantism is true, and objects that can rightly be said to ‘persist’ are identical to temporal parts of spacetime worms.
The Atlas of Reality Page 92
