Paradox of Composite Objects

Paradox of Composite Objects

Composition The Special Composition Question Given some x s, what must be the case for them to compose a y? We all believe in things that are made up of smaller things, like a chair that has legs, a seat, and a back as parts. This naturally raises the question, when should we think that some things are parts of a bigger thing, and when should we think they are just separate objects? The x s just refers to any things, be they people, trees, legos, cells, leptons, etc. y is whatever we want it to be, such as an army, a forest, an x-wing, an organism, a molecule, etc. The SCQ thus helps to precisely ask, when (or in what circumstances) does composition occur?

Examples of Composition Questions If the French Foreign Legion pushes some sand to make bunkers, have they made something, or merely rearranged the things that were already there? For that matter, is there even a French Foreign Legion? If someone builds something out of legos, when have they actually made something? When the first two pieces are connected? When it looks like the final product? When they are done building? Is a hunk of stone an object, or is it merely some particles that happen to be attached? In either case, when has a sculptor made something with that hunk of stone? When do trees make up a forests? Can a forest be split into two forests?

Composition The Special Composition Question Given some x s, what must be the case for them to compose a y? There are three important answers to this question which can be used as reference points: Nihilism There is only one x. Contact The x s are in contact. Universalism Nothing Nihilism says there are no composite objects. Only simple, small, sub-atomic particles exist. Universalism, says that for any objects whatsoever there is a composite object. Thus, there are forests, trout-turkeys, and combinations of my left pinkie and the Eiffel tower.

The Special Composition Question Given some x s, what must be the case for them to compose a y? Contact says that objects compose something if and only if they are in contact. This has some highly implausible results, which we should discuss, but it is meant only as an example of how we could give a middle answer in between the two extremes of Nihilism and Universalism. The nice thing about Contact is that it affirms the existence of people while denying the existence of trout-turkeys and other weird things One can however object that it excludes things it should include like schools, armies, forests, clubs, and other separated things. One can also object that it includes things it shouldn t like the combination of you and the chair, the combination of two people when they shake hands, etc. One of the main challenges of the SCQ is finding an answer that seems to get these inuitive cases mostly right.

Other Answers Lots of people have attempted to specify when objects compose things. Some suggestion include: The x s are connected and are disposed to stay connected. When the activity of the x s constitutes a life. When the x s have causal powers that are not the sum of the causal powers of the individual x s When there is a collective term for the x s And many more...

The Problem for Medium Answers Most people think that the answer to the Special Composition Question has to be somewhere between Nihilism and Universalism. However, any medium answer seems to face a sorites paradox For instance, if spatial proximity is important for composition, we can imagine you, and a scenario in which every quark, lepton, and other particle composing you is spread to the farthest reaches of the universe. Those two scenarios are connected by a very long series of circumstances in which the only difference between two circumstances in that series is that one particle is moved on nanometer.

The Problem for Medium Answers As we have seen, there are lots of Sorites paradoxes out there. What is unique about this one, is that it seems to be able to be stated without any vague language whatsoever Suppose for the sake of simplicity that there is a composite object composed of two things and that it is the only thing in the universe. Then either of the following two statements is sufficient to define when composition occurs: (1) There are exactly 3 things. (2) There is an it x an it y and an it z such that it x is not identical to it y, it y is not identical to it z, and it x is not identical to it z ( x,y,z x y, y z, x z). If (1) or (2) goes from false to true, then composition has occurred, but neither one has any vague terms, so stating whether or not composition occurs is not vague.

The Problem for Medium Answers We can summarize this problem in the following argument: 1. If composition sometimes but not always occurs, then there is a continuous series of situations connecting situations in which composition occurs to situations in which composition does not occur. 2. If X occurs at one point in a continuous series and not at another, then either there are two arbitrarily similar situations which are such that X occurs at one and not at the other, or there are situations at which it is vague whether or not X is occurs. 3. There are no arbitrarily similar situations which are such that composition occurs at one and not at the other. 4. Therefore, if composition sometimes but not always occurs, there are situations at which it is vague whether or not composition has occurred. (1, 2, 3) 5. It is never vague whether or not composition has occurred. C. Therefore, composition either always occurs or never occurs. (4, 5)

Option 1: Accept Nihilism One option is always just to accept the conclusion by denying composite objects there are only fundamental particles arranged in various ways For a lot of seemingly composite things we want to talk about, it makes sense to view the language of the composite as just a shorthand way of expressing something about the various parts. For instance, when we say the marching band formed an aircraft carrier, it kinda seems like we are saying that one band member was a spot 1, one was at spot 2, etc. such that together their positioning represented the shape of an aircraft carrier The point is, the actions of a band seem to be nothing more than the actions of the various members of the band While some people will already be dissatisfied with this analysis, the biggest problem for the analysis is that it does not seem like we can say a similar thing for you and I talking about the things I do is not a veiled way of talking about the things my various cells do.

Option 2: Accept Universalism A different way to accept the conclusion is to accept that any combination of things is a composite object including trout-turkeys, pinky-eiffel Towers, and the rest While this is incredibly un-intuitive in general, it also has trouble making sense of the existence of composite human persons Consider the problem of whether or not there is a cloud in the sky: Think of a cloud just one cloud, and around it a clear blue sky. Seen from the ground, the cloud may seem to have a sharp boundary. Not so. The cloud is a swarm of water droplets. At the outskirts of the cloud, the density of the droplets falls off. Eventually they are so few and far between that we may hesitate to say that the outlying droplets are still part of the cloud at all; perhaps we might better say only that they are near the cloud. But the transition is gradual. Many surfaces are equally good candidates to be the boundary of the cloud. Therefore many aggregates of droplets, some more inclusive and some less inclusive (and some inclusive in different ways than others), are equally good candidates to be the cloud. Since they have equal claim, how can we say that the cloud is one of these aggregates rather than another? But if all of them count as clouds, then we have many clouds rather than one. And if none of them count, each one being ruled out because of the competition from the others, then we have no cloud. How is it, then, that we have just one cloud? And yet we do. (Lewis 1993: 164)

Option 2: Accept Universalism The problem of the borders of the cloud is known as the Problem of the Many Importantly, it primarily seems to arise if we accept Universalism Also importantly, it seems to apply to humans Consider one dead skin cell on you which is sort of attached to the rest. Given universalism, there is one composite object that includes that dead skin cell, and one that does not. Which one is you? Ramping up, it seems like if we accept Universalism we have to accept that there are in fact millions of humans in the general vicinity of you, but this is absurd. It can t be the case that millions of people think, I want a cup of coffee ; then those same millions all simultaneously stand up and walk over to the coffee pot.

We can thus expand the paradox: 1. If composition sometimes but not always occurs, then there is a continuous series of situations connecting situations in which composition occurs to situations in which composition does not occur. 2. If X occurs at one point in a continuous series and not at another, then either there are two arbitrarily similar situations which are such that X occurs at one and not at the other, or there are situations at which it is vague whether or not X is occurs. 3. There are no arbitrarily similar situations which are such that composition occurs at one and not at the other. 4. Therefore, if composition sometimes but not always occurs, there are situations at which it is vague whether or not composition has occurred. (1, 2, 3) 5. It is never vague whether or not composition has occurred. 6. Therefore, composition either always occurs or never occurs. (4, 5) 7. I am a unique, composite object. 8. If I am a unique composite object, then composition occurs sometimes but not always. 9. Composition occurs sometimes but not always (7, 8)

Option 3: Accept Vague Existence (or Vague Identity) There are two different ways of stating when composition occurs, and the only thing they have in common is that they talk about existence. If the problem is linguistic vagueness, one could try to say that the word exists or the words there is or there are are vague. However, these words seem to just be the broadest generic category there can be. If something can be referred to, or if there are more than 0 of that thing, or if it could be what is meant by a pronoun, we just say there is that thing, so how could that be vague either it is there to be referred to, or it isn t The only other way to say that it is linguistic vagueness is to say that both identity and numbers are vague, which is difficult

Option 4: Make Sense of a Sharp Cutoff The remaining option is to give a theory of composition which makes composition non-problematic. One way to do this is to say that the difference between composition and non-composition is based on something that cannot be put into a Sorites paradox It is, however, hard to find any physical facts about the world which cannot be put into a Sorites The other way to do this is to say that two arbitrarily similar situations are such that one contains a composite object and the other does not. However, it strongly seems like there needs to be a reason for thinking of two situations differently.