Dire Ambiguities in Rea's “In Defense of Mereological Universalism”
Many arguments have been made promoting the idea that the ontology of the universe is much smaller than we might be practically inclined to assume. Whether it is Peter Unger arguing for Mereological Nihilism or Peter van Inwagen making the case that organisms are the only composite entities, these brilliant men have encouraged us to remove every day items such as tables, televisions, and tricycles from our ontology. Few of these arguments have been convincing to me, so it was with interest that I approached Professor Michael Rea's article “In Defense of Mereological Universalism”. Rea takes a vastly different approach, arguing that the number of things that exists in the world is much greater than our instincts would have us believe. Specifically, Rea argues for Mereological Universalism, which, by his definition, is the notion that, “for any set S of disjoint objects, there is an object that the members of S compose” (p. 348). In short, not only does Rea support the existence of tables, televisions, and tricycles, he believes that, if you were to pick one of each at random from all of the tables, television, and tricycles that exist, they would also composite their own distinct object. More generally, Rea is saying that any collection of distinct objects will form another object. As much as this proposition is counterintuitive, I feel that Rea makes a reasonable case for it. Unfortunately, I also feel that Rea's arguments, at least in this article, suffer from a certain vagueness that could easily lead to severe inconsistencies and make it difficult to endorse outright. I will examine some of these problems and suggest alternative approaches that I feel strengthen Rea's argument.
The first problem that I encountered when dealing with this article has nothing to do with the specific arguments that Rea uses so much as the definition of Mereological Universalism as he provides. The fundamental question that I can't help asking is, “How many objects is Rea claiming exist?” My first instinct was that the answer was, “infinitely many.” This would be an absurdity, as there is a mere finite amount of matter in existence. Examination proves this to be a false instinct, though. It is important to note that the objects in S are disjoint – that is, if we were to break them down into their own components, there will be no smaller object that belongs to more than one of the objects in S. Thus, there is no object that is composed of both my body and my kidney, as all of the components of my kidney are also components of my body. This reduces the necessity of the question, but it doesn't eliminate it, and understanding the ways in which the objects in S combine helps us to recognize that certain other complaints are invalid.
Assume, for a moment, that the universe contains only four non-composite objects: a, b, c, and d. Clearly, under Mereological Universalism, the universe also contains the composite objects {a, b}, {c,d}, and {a, b, c, d} among others. Now, what I want to know is this: does the universe also contain the object {{a, b}, {c, d}}, or is that object identical to {a, b, c, d}? That is, are objects distinguished by their most basic components, or by their most complex ones? It is not remotely clear from the definition of Mereological Universalism as Rea states it; but brief examination will show that endorsing the latter is simply absurd. Consider, momentarily, the following ASCII stick figure:
\O/
|
/ \
For simplicity's sake, let's call him Adam. We can see that Adam is composed of a head (h), left arm, (al), right arm (ar), torso (t), left leg (ll), and right leg (lr). Let us assume that in the ASCII art universe, the lines which compose these parts are, themselves, simple. It seems obvious that Adam is composed of {h, al, ar, t, ll, lr}. If we use the first interpretation of our definition of Mereological Universalism, the one that declares that composite objects are defined by their most basic components, then this is the only way in which we can identify Adam. If we take into account the second possible understanding, though, we can also pull out a distinct object composed of {h, {al, ar, t, ll, lr}}. The object {h, {al, ar}, t, {ll, lr}} exists under this interpretation, as well. It strikes me, however, that both of these supposedly distinct objects are exactly Adam, just as the first object we identified was. Truly, there are easily a dozen different ways in which we can pick out an object sharing Adam's composition if we allow ourselves to pick out composites of composite parts; and we would be identifying each of these as a fundamentally unique object in our ontology. This is clearly absurd. So, as a charity, we must assume that Rea, despite a glaring lack of clarity, intends for us to interpret his definition in the first way. As such, we must remember that all objects are composed only of simples and recognize that any talk from here out about an object being a composite of composites is merely an effort to simplify discussion.
With that digression out of the way, we can begin examining Rea's actual arguments for Mereological Universalism. First of all, we need to recognize that the strongest reason for rejecting Mereological Universalism is unsound. van Inwagen and others would have us believe that, if Mereological Universalism is true, for a set of objects to compose something larger, all that is necessary is their existence, and that the particular object that they comprise depends only on the objects comprising it. Rea takes a slightly different view, suggesting that what is most important isn't the specific objects in question, but the way in which these simple objects are arranged (p. 349). This makes sense when we remember that all objects are composed only of simples, which come in only the smallest handful of varieties. If the nature of an object were determined only by the elements composing it, our world would be much less diverse and fascinating than it is. It also makes sense to take arrangement into account when we consider our reasoning for wanting to accept the existence of composite objects.
Effectively, there must be something unique about composites above and beyond the things that compose them. It is this uniqueness by which we identify and count them. Consider a table and a bookcase made out of the same type and quantity of wood. It is the particular arrangement of the wood that causes us to count one as a table and the other as a bookcase. In general, we say that objects whose parts are arranged in such away that they perform a certain function belong to a certain functional kind; and it is by membership in these functional kinds that we identify composites and include them in our ontology. However, these functional kinds cannot be limited to only those arrangements whose functions we have identified and found use for. If we were to limit kinds in this way, then the existence of composite objects would be entirely dependent on the existence of sapient individuals capable of discerning or assigning such functions. That is to say, under such a limitation, existence would be an almost wholly relative matter, which is no small consequence. How, then, are we to determine what arrangements are kind constituting? In not so few words, Rea suggests that all arrangements could hold some function that we have yet to discern, and therefore that all arrangements ought to be held as kind constituting (p. 354).
This is another statement that suffers from a crippling ambiguity. There are two distinct ways in which the phrase “Every way of arranging objects is kind constituting” (p. 353) can be read.
- Every way of arranging objects constitutes some kind or another.
- Every way of arranging objects constitutes some unique kind.
Rea does not, within the body of “In Defense of Mereological Universalism” clarify which of these phrasings he meant; but if correspondences we were read in class are to be believed, Rea endorses the second reading. This seems, to me, to be ridiculous for two reasons, one practical and one, again, mathematical.
Let's look at the practical objection first. It seems to me that we would like to say that the keyboard on which I am typing this and the functionally and aesthetically identical keyboard sitting at the computer next to me embody the same kind. Even if that keyboard may have developed stiffer springs than this on or if mine has a slightly displaced light for its Num Lock indicator. If every arrangement of matter uniquely constitutes its own kind, though, these to keyboards are not the same kind by Rea's definition. In fact, due to the simple motion of particles if nothing else, it would strike me that even if these keyboards did not have these minor, but apparent dissimilarities, the probability of them (or any other two seemingly identical objects) ever having the exact same arrangement of parts at a given time is effectively zero. How, then, can we say that things as obviously dissimilar in arrangement but identical in function as my roommates' cars embody the same kind? In the same correspondence in which Rea put forth his endorsement of the second reading, he seemingly argued, that the arrangements he is talking about are not simply physical arrangements; he is talking about functional arrangements. As surely as there's more than one way to skin a cat, there are multiple ways of arranging things spatially that can bring about the same function. I doubt anybody would disagree with this. But changing the use of the word “arrangement” in this way is counterintuitive and wholly unnecessary; as the second statement, under functional arrangements, is identical to the first statement under spatial arrangements. So, Rea needs to either clarify from the beginning that the arrangements he is talking about are non-spatial or he needs to clarify that any arrangement of objects is kind constituting for some kind K. As the argument stands, it is runs dangerously near absurdity once more.
I say this because, under the natural assumption of spatial arrangements, we once again encounter problems of cardinality if we espouse the second reading of what it means for an all arrangements to be kind-constituting. The problem here is that space cannot be divided up into discrete, infinitesimal points. Space is, by its nature, continuous. As such, even if the universe is finite in volume, there exist an (uncountably) infinite number of places at which an object can be. This being the case, even a universe containing only 2 ontologically simple objects would require us to define an infinite number of kinds under the assumption that arrangements are spatial. I see no reason why we should accept this in a universe with a multitude of objects much less a universe with only 2. Certainly, the number of possible functional arrangements far outweighs the number of objects, but the infinite number mandated by Rea's assertion and a spatial understanding of arrangements seems wholly unnecessary.
With this clarification taken care of, I have few remaining qualms with Rea's argument for Mereological Universalism. Chiefly, I wonder how non-physical objects work into his ontology – things like numbers and music. While we do discuss composite numbers in mathematics, they are not composite in the way used here; and I while I am willing to hesitantly accept that the toes on my left foot jointly compose an object along with Big Ben, I remain unconvinced that they can do so with a diminished G7 chord. These are things that many philosophers studying ontology have insisted do exist. Numbers, particularly, are often held to exist essentially. What does Rea do with them? Does he deny their existence? Is there some tacit substance dualism going on here, wherein the material and immaterial can only composite larger objects with like members? Where Rea to expound on this topic, we would certainly all benefit, but any further conjecture would be useless without further input from Rea.
Ultimately, my concerns about the immaterial are not grave enough for me to discount Rea over them. Truly, I believe that the rest of Rea's argument works rather beautifully. His introduction of dominant kinds serves well enough to remove the problem of co-location, and with the two severe ambiguities I mentioned cleaned up, I can find little to debate in his deductive argument for Mereological Universalism. I would like to believe that the argument that all arrangements can be kind constituting is something of a slippery slope, but I can see no other way to avoid an entirely anthropocentric understanding or listing of kinds, so I will accept it. As such, while I am not likely to champion Mereological Universalism over conventional wisdom to my friends or family; I will admit that Rea has convinced me that it is a more viable choice than the incredibly limited universes generated by Unger's or van Inwagen's arguments.
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