Paradox of Composite Objects
The Special Composition Question Given some x’s, what must be the case for them to compose a y? ◮ We typically believe in things that are made up of smaller things, like a water molecule made up of hydrogen and oxygen. ◮ 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? ◮ Answering this question should help inform how we answer what is going on with the statue and lump.
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?
The Special Composition Question Given some x’s, what must be the case for them to compose a y? One important step towards answering the question is to distinguish extreme answers from medium answers. The two extreme answers are: Nihilism There is only one x. 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? ◮ Medium answers try to say that there are some composite objects but not all the objects posited by universalism. ◮ One example of a medium answer is: Contact The x’s 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
The Special Composition Question Given some x’s, what must be the case for them to compose a y? Contact The x’s are in contact. ◮ 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 intuitive cases mostly right.
Other Answers Lots of people have attempted to specify medium answers of 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
Option 1: Accept Nihilism ◮ While there are some things where it is natural to just think of the collective term as really talking about the activities of the individuals, there are also lots of things for which that sounds less natural (e.g. the nihilist must say there is no spoon, only atoms that are shaped to look like a spoon). ◮ The nihlist has strategies for resisting the weirdness of these consequences ◮ When people would normally talk about tables and chairs, the nihlist can talk about particles arranged tablewise and particles arranged chairwise ◮ Notably, there is no object that holds me up when I sit down, but the particles arranged chairwise work together to collectively prevent me from falling to the ground (there is no chair-shaped or chair-colored object) ◮ While this is certainly a weird way of speaking, one might think that since the word “chair” was coined in the presence of particles arranged chairwise, we somehow manage to express the strictly true proposition with a sentence that is not strictly true. ◮
Option 1: Accept Nihilism ◮ One may or may not be happy with the “arranged x-wise” analysis ◮ We cannot say that “this is the same chair” that I sat in yesterday, since there is no chair to be the same from day to day (and it is highly unlikely these are all the same particles arranged chairwise that collectively held me up yesterday) ◮ The biggest problem for nihilsm, however, is that I exist, and it does not seem like I am particles arranged human-wise ◮ There is a unity to my thoughts and the things I do that seems like it could not be analyzed as simply the activities of many different things 1. Something is experiencing a thought (or feeling, emotion, belief, etc.) 2. No individual particle is experiencing a thought C. Therefore, a composite object is experiencing the thought.
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 ◮ Like nihilism, universalism has an attempt to make these seemingly bizarre consequences seem less bizarre. ◮ Consider the sentence “there is no more beer” ◮ Presumably, a person uttering that sentence would not mean that there was no more beer in the world, only that there was no more in their immediate vicinity ◮ Similarly, I can say “the red car is mine” and you understand what I say, even though there are lots of red cars in the world ◮ The phenomenon uniting these two examples is domain restriction
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