The composition question
For the moment, we’ll consider the question under its most general guise: "Given a class of objects \(\{y\}\), under what conditions is \(x=\sum{y}\) an object too?". We take \(\Sigma\) to represent a mereological sum or fusion, where mereology refers to the study of parts and parthood. Mereological parthood is superficially similar to set-theoretic inclusion (the differences are not integral to our discussion here).
Three broad views about mereology can be outlined:
Mereological conservatism: only ordinary fusions exist.
Mereological universalism: all possible fusions exist.
Mereological nihilism: no fusion exists.
We will examine each one in turn.
Mereological conservatism
has it that some collections of objects form other objects, while others do not. The sole motivation is to create an ontology that’s as close as possible to common sense.
Glancing around me, I’m naturally inclined to say there are a table, a computer, a notebook, a pen. I haven’t really considered whether it would be difficult to separate the tabletop from the legs, or whether the table has a removable extension. I’m typing on the computers’ keys and turning the notebook’s pages, so those might be considered as distinct objects, proper parts of their respective fusions.
In Giza, Egypt, there is a specific pile of limestone blocks known as the Great Pyramid of Giza. Most people would agree that the blocks are objects, and that they compose a larger object: the pyramid. On the site of Chichen Itza in Mexico, there are other limestone blocks that make up an object, the Temple of Kukulcàn, a step-pyramid. Yet, the collection of limestone blocks from Giza and from Chichen Itza does not compose any object — there is no "bi-pyramid of Giza-Kukulcàn".
Cars are objects with many parts: an engine, seats, wheels, windows, a driving stick, etc. However if I affix my bike on the car’s roof for a trip, they don’t compose a new object, nor does the bike become a proper part of the car.
It is clear that mereological conservatives need to present their assessments of objects as brute facts and adopt as their motto: "I know it when I see it".
Needless, to say, there are some major problems with this position:
Arbitrariness: I can only agree with Ned Markosian, who proposed that there is "no true, non-trivial, and finitely long answer to the composition question"— as long as one doesn’t go with mereological universalism or nihilism, there can be no easy formula to define objects.
Some properties are promising candidates, but they usually don’t sustain a closer examination. Take the notion of cohesiveness: it seems fair to say an object is something that’s made of one physically connex piece. But when two men shake hands, they don’t become a single object. If one super-glued their hands, or nailed them together, they wouldn’t become one object either. To take a less grisly example: I can very easily unscrew my living-room table’s legs, yet they’re part of the table; but if the table was nailed to the floor as sometimes happens in public places, and extremely hard to detach, it would not be considered a part of the floor. So, cohesiveness is not a sufficient solution. But it’s not a necessary one either: a bikini or a suit are commonly seen as items rather than collections (if a shopper were to purchase a bikini, a polo and a three-piece suit, they’re bound to say they got three items, not four, five or six).
Conversely, some properties seem preposterous in the general case but work, arbitrarily, for specific classes of objects. Take the incar: it is a hypothetical object that is colocated with my car when it’s in a garage, but the incar ceases to exist as soon as the car comes out. Incars are not even close to the ordinary objects from our daily language. Yet an island is colocated with a portion of the lithosphere when its highest point is above sea level, and ceases to exist when it is below; yet islands’ existence is generally accepted as sound.
All those concerns about arbitrariness can be attributed to a nagging worry that those distinctions come down to either purely linguistic or cultural grounds. Even if we could settle on a finitely long criteria, it’s hard to dispel a sense that it could not survive the evolution of our culture, or a modal shift of perspective ("what would an alien think?"). A typical case is when objecthood is grounded in function: in some cars it might be easier to dismount a seat than to dis-attach a bike from the roof-rack. Yet only the seat is part of the car. This comes down to the seat being delivered with the car, and helping fulfil a basic function of the car (to seat passengers). The function of the bike itself is unrelated to the car. But a human from a few centuries ago wouldn’t know that, and their hunch on objecthood may differ.
Sorites paradox: in addition, conservative accounts in mereology are extremely vulnerable to a class of paradoxes known as sorites.
They typically take the following form.
A chair has a finite number of atoms.
If \(C\) is a chair, has n atoms, and we remove a single atom to create a new object \(C^{-}\) , then \(C^-\) is also a chair.
No object with fewer than 2 atoms can be a chair.
So, there are no chairs.
Sorites paradoxes are a stake through the heart of any attempt at rigorously approaching ordinary objects. With some tweaks they can be applied to properties or processes, so long as they are ground in vagueness ("how many hairs does one need to not be bald?", "what height is tall?", etc.). Naturally, there have been rigorous proposals to circumvent the issue, the point is that they can hardly accommodate a strictly bivalent logic with a unique existence quantifier, which is the standard formulation of ontology: a mereologist cannot have her cake and eat it too.
Problem of coincidence : If I caress a merino sheep, am I touching (1) a pile of wool that happens to be on an animal’s back, (2) an animal or (3) both? On a drive, I am sitting (1) on a car seat, (2) in a car, or (3) both?
(1) seems hard to argue for: ordinary objects are grounded in common sense and nobody would look at a sheep and say there are two objects there (an animal and some wool). (2) is typical of a maximalist account that precludes proper parts: there’s only a sheep, only a car there. This seems quite neat for a snapshot, but places the bar very low in terms of unfastening: simple actions like detaching a wiper, shearing a sheep, can conjure new objects out of existence. A bit of wool that sheds naturally comes into objecthood only at that very moment. (3) can seem more flexible: it accepts the existence of proper parts — the car, its seats, wipers, wheels, etc. all exist simultaneously. This wreaks havoc with traditional accounts of coincidence ("there cannot be two objects at the same time and the same place"), countability ("if there’s a car in the garage, is there one object or fifty?"), and causality ("did the car cause the damage, or was it the front bumper?").
This is not a crippling issue; we can do without these concepts, argue they are ill-defined and not suitable to our ontology. In doing so, we are firmly moving towards mereological universalism. This may not lead to any logical inconsistency, but it somewhat contradicts the mission that conservatism set for itself, to stick with common-sense accounts of objects.
All in all, mereological conservatism suffers from such serious issues, the reader may understandably wonder: have I taken us on a useless detour, leading up to a predictable cul-de-sac? Shouldn’t the topic of ordinary objects be left to psychologists and anthropologists? That may well be. But as we shall see, alternative accounts have their own issues. Better to highlight conservatism’s problems now to make the alternatives more palatable when we come to them.
Mereological universalism
is one of the main revisionist positions, in the sense that it rejects common-sense accounts of objecthood. Instead it advocates for a principle of unrestricted composition. All fusions, complements, intersections of objects are valid objects themselves. We could say that this mereology is a representation of discrete topology: any part of the physical universe, however defined, constitutes an object that we can talk about or quantify over.
This view has one important merit: clarity. However it can be challenged from several angles as well.
Counter-intuitiveness is sometimes mentioned as a drawback. Universalism accepts a variety of exotic objects, like the aforementioned "incars", or the proverbial "trouturkeys" (creatures made from the front half of a trout and the rear half of a turkey). There’s no limit to the kind of silly spatio-temporal combination that can be conjured into existence ("the fusion of Joe Biden between the years 1975 and 1978 and all Helium nuclei in Proxima Centauri 1,000 years ago").
The brand of critics this attracts is frequently flying the banner of common sense. But it seems that the only way to introduce common sense as a factor in ontological discussions about objecthood is to adhere to conservatism.
Yet from my perspective, the weaknesses of conservatism are quite insurmountable. If it is the only solution to the perceived counter-intuitiveness of universalism, then the remedy is probably worse than the disease. This is not to say we can’t define or talk about ordinary objects — restricted quantification or relative identity (more on this one later) allow just that — but their special status of "common-sense acceptability" doesn’t make them ontologically different from the most outlandish compositions.
Profuseness is another oft-mentioned drawback. Universalist mereology is tremendously profligate: consider a toy universe with one ordinary object, a bottle of water, at a single point in time, and whose basic bricks are \(\text{H\_2}O\) molecules (for 1 liter, around \(3\cdot10^{25}\) of them). The number of possible molecule combinations (legitimate objects according to the universalist) is on the order of \(10^{10^{25}}\), an unthinkably high number (there are around \(10^{81}\) elementary particles in the physical universe). And that’s just from one instantaneous snapshot of some small amount of water...
Most arguments against the gratuitousness of universalism seem to stem from some aesthetic preference for ontological parsimony. That is not very convincing to me. There are sets in mathematics that are several "orders of infinity" larger than the natural numbers, and yet humans have been doing arithmetics just fine without worrying too much about them.
Ockham’s razor arguments carry more weight: do we really need all these objects? Unless there’s some revolutionary position in the works, it appears that we do, save one case: it is possible to wield the razor and sheath the unseemly googolplexes of objects crowding our ontology, but the shave will be extremely close, so much so that only nihilism remains. We’ll discuss this position in the next section.
The problem of identity is not specific to universalism. It is an impediment to any view that accept composite objects, including conservatism (I didn’t mention it then — that view had enough issues of its own). We’ll need to come back to the topics of identity and constitution later as it warrants a whole section in itself.
Mereological nihilism
is the polar opposite of universalism: it posits a principle of impossible composition. In that view, there are no composite objects, only simples — object with no proper parts. Two main flavors of nihilism can be distinguished:
Atomism: this covers a family of views whereby there are many simples. Of course this is the intuitively "correct" position to us moderns given the spectacular success of atomic models and particle physics in the past century and a half (although physical atomism and mereological atomism should not be confused).
In an atomist picture, a mereological nihilist would say that there are no dogs nor tables, only "heaps of simples arranged dog-wise or table-wise".
Stuff: we’ve been spontaneously speaking of objects in our foray into the physical world. But to proponents of stuff ontologies (as opposed to thing ontologies, there is simply no such thing as a thing. Instead there is really only stuff, whilst objects are illusions emerging from the properties of stuff.
The world can be made of one stuff (mereological monism), in which case there is but one simple, or of several (mereological pluralism). Think of the pre-Socratics and of arguments whether the world was made of water, of air, or of four elements. According to Anaximenes, "air can apparently take on various properties of color, temperature, humidity, motion, taste, and smell". Moreover, "it is the condensation and rarefaction of air that naturally determine the particular characters of the things produced from the originating stuff. Rarified, air becomes fire; more and more condensed, it becomes progressively wind, cloud, water, earth, and finally stones..
This is strictly illustrative; I do know that Anaximenes’s ideas are not the best account of matter that we have today. But think of one our best accounts: quantum field theory. A direct consequence thereof is that many-particles systems need to be represented as single wavefunctions. Ultimately, physics can be said to describe the evolution of a single "wavefunction of the universe". The resulting system might be deemed a two-simples ontology: the universal wavefunction, and spacetime.
As I’ve mentioned above, mereology and physics are orthogonal, but if physical intuition must at least serve as a guide, one can see that contrary to atomist doxa, stuff ontologies have assets too.
In any of its guises, mereological nihilism has some powerful arguments in it favour. First it is, by definition, parsimonious, and thus completely bulletproof to the kind of criticism levied against universalism’s profligacy. Second, it simply dissolves all paradoxes of identity. These all start by asking whether certain composite objects are identical, and then evidence some contradiction. Nihilism simply states there are no composite objects, and therefore no paradox.
Be that as it may, there are also issues — big ones — with this account:
Atomless gunk: objects with proper parts have been christened with the poetic-sounding name of "gunk" by David Lewis. The concern here is that we’ve posited the existence of simples, but have conveniently ignored the possibility they might not exist. Nihilism, at least as presented here, would simply crumble then. I feel pretty confident in dismissing this. It is generally assumed that spacetime is ultimately quantized in some way, and can be represented as a lattice with Planck length/time periods. In addition, the nature of quantum theory precludes the possibility of atomless gunk — even if it was discovered that quarks have sub-components, which themselves are made of more fundamental particles, and so on ad infinitum, all possible many-particle systems could be represented by a common wavefunction which could act as the ultimate simple. One may dislike the wavefunction-as-stuff conceit, but it seems to show that bottomless gunk is not a logical wrench in nihilism’s gears.
Emergence: it’s all well and good to talk of "simples arranged woman-wise" when talking about a friend, but (1) it sounds quite rude, and (2) it makes one wonder about all the properties that I would normally associate with my friend, such as being tall, or being 30 years old.
Clearly, none of the electrons and quarks making her up are tall nor 30 years old. If she, as a composite object, does not exist, she can’t instantiate these properties either. There are three responses to this.
The first is to deny these properties exist. It’s an entirely consistent position, however most would say — I certainly would — that no composite object nor complex properties makes for a very poor ontology, that’s basically thankless to talk about and honestly quite useless.
The second response is to drop the atomist posit and to adopt monism. In this instance, when I say my friend is tall, I’m actually saying that the universe instantiates the property: "has a restriction to this specific region of spacetime that has the characteristics of a tall person". This can be made consistent too but ultimately takes ontology far away from notions borne out of our experience and into a purely mathematical viewpoint.
Finally the last attempt at a response is to accept both atomic simples and properties, but to try and develop a model of "collective instantiation" of those properties. The difficulty is to show how that’s actually different from having composite objects, and not just a verbal conceit...
Mereological nihilism has strong assets in principle, but it’s really hard to shake the challenge of emergent properties. Even more concerning is the diffuse feeling that the whole position amounts to a verbal game rather than a robust ontological position.
I can declare that my table doesn’t exist, nothing will fall on the floor — it’s all firmly supported by a group of simples arranged table-wise. Conservatism is a far cry from universalism in that it considers ordinary objects as a class of ontological import. Nihilism feels more like the mirror image, and ultimately exact equivalent, of universalism, a switch of perspective to artfully swerve from the problems of identity, in a way which I suspect could just be spurious. Agreeing as much could be seen as a form of mereological deflationism.