The constitution question
The structure of a physical ontology is not exhausted by its mereology. In discussing the problem of composition, I’m clearly leaning towards mereological universalism. But I’ve performed a big sidestep to avoid considering constitution and identity right away.
What is constitution?
Mereology makes stipulations about what objects we can legally combine to make more objects, but is not too concerned about the nature of the result. That’s what constitution is about.
It seems reasonable to argue that if I have pieces of iron, then welding and bolting a bunch of them together would result into a bigger piece of iron. It so happens that in Paris, there is a specific assemblage of iron girders that most people consider to be a definite object named "the Eiffel tower". Yet the mereological sum of these same iron girders and iron bolts also makes up a big piece of iron. That doesn’t seem to be a problem since most people would agree the Eiffel tower is indeed a big piece of iron. But are we so sure about the relationship between "big piece of iron" and "Eiffel tower"? This is what we’ll explore here.
The main question about constitution is whether it is the same thing as identity...But what is identity? It is most often characterized by these two properties:
(Reflexivity): \(\forall a (a=a)\)
(Substitution): \(\forall (a,b) \forall F (a=b \rightarrow F(a)=F(b))\)
In the above, \(F\) represents any sort of expression. In a philosophical context, the substitution property is often called the indiscernability of identicals (thereafter I.I.), or Leibniz’s law. One corollary is that two identical objects share all of the same properties: if \(a=b\) and a given property is true of \(a\), then it is true of \(b\) as well.
From this characterization we can deduce more corollaries. Let’s call \(T(\cdot)\) the truth-value function, and define \(F(\cdot)=T(b=\cdot)\). It follows that:
(Symmetry): \(\forall (a,b) (a=b \rightarrow F(a)=F(b) \rightarrow T(b=a)=T(b=b)=\text{True} \rightarrow b=a)\)
(Transitivity): \(\forall (a,b,c) (a=c \text{ and } c=b \rightarrow F(a)=F(c) \rightarrow T(a=c)=T(b=c)=\text{True} \rightarrow a=c)\)
Reflexivity, symmetry and transitivity, mean that identity is by definition an equivalence relation.
Venus and the clay
Since ancient times, the problem of constitution has been discussed through a clichéd example: that of a statue; philosophers soon remarked that a statue differs in its properties from the brute matter it is made of.
Let’s set up our puzzle. On Monday, a sculptor bought a big lump of clay — we’ll call it "Clay". He brings it to his studio, and on Tuesday sculpts the clay into a representation of the goddess Venus — let’s just call the resulting statue "Venus". It’s pretty easy to find ways in which these two differ. First there’s a difference in kind: Clay is a lump, while Venus is a statue (of course this statement only makes sense if one wants to believe in kinds; if not, it’s fine to ignore this one). Another difference is in persistence conditions: Venus would stop existing if it was squashed multiple times with a hammer, while Clay would perdure. We’ll focus on another difference in particular: Venus did not exist on Monday, but Clay did.
We can then propose the following argument:
(VC1) Venus did not exist on Monday.
(VC2) Clay did exist on Monday.
(VC3) If (VC1) and (VC2), then Venus \(\neq\) Clay.
(VC4) So, Venus \(\neq\) Clay.
Let’s consider the possible reactions one by one:
Accept the conclusion: I’ve been careful to call this story a puzzle and not a paradox. There is no logical inconsistency in accepting the premises, the argument, and therefore the conclusion that Venus and Clay are not identical objects. The question that springs to mind is, what differentiates them, that they differ so much in properties while having the same weight, shape, components, etc. One ever-popular response is what Aristotle called hylomorphism: the Stagiryte argued that every object had material parts, and one immaterial part: its form.
Now, there are three main cases.
Venus and Clay both exist on Tuesday. In that case we have two different objects, sharing all material properties and with the same parts, occupying the same region of spacetime: coincident objects. On Tuesday, Venus and Clay share material and temporal parts, but have different forms.
The main issue with this view is profligacy rearing its head again. It’s one thing to be a mereological universalist and having to accept "high-level" infinities of objects. It’s another running the gamut of all possible forms, leading to scores of coincident objects all over the place. Where a cat is sitting, there would coincidentally be a lump of organic matter, a set of living cells, a pet, and many more.
Venus does not exist on Tuesday. That’s the nihilist view: if Venus doesn’t exist, then it seems hard to argue the lump kind is somehow privileged compared to the statue kind; all we have is a pile of mereological simples arranged lump-wise, then statue-wise.
Clay does not exist on Tuesday. In that case, Clay’s material parts persist, but the Clay-form has not survived the act of sculpture and has been replaced by a Venus-form. That is close to Aristotle’s view and is fine on paper, but carries unpalatable consequences. We’d like to say that Venus is a statue and a lump of clay at the same time, but that fails as some properties are incompatible (statues don’t survive being squashed, lumps of clay do). So, sculpting truly destroyed the Clay-form, even though sculpting does not appear to be something that could do that as obviously as, say, throwing it into the sun. Conversely, squashing Venus would somehow make the Clay-form pop back up into existence.
All of this becomes even trickier if you imagine the more subtle case of an artist who takes a rock and presents it to an audience as an artwork. Aesthetic conventionalists would agree the rock is now of the kind "art piece", but hylomorphists amongst them would need to agree the rock has disappeared. It doesn’t seem right that a speech can make a rock disappear; logical, perhaps, but unpractical as a model of object constitution that puts a premium on intuitiveness.
One way out of this is a theory called dominant kind. In that view, Venus is a statue and a lump of clay at the same time, so the Clay-form remains; the puzzle of inconsistent properties is solved by saying that "statue" is the dominant kind, therefore whenever there can be a conflict, Venus has statue properties rather than lump properties. This is quite attractive and more akin to how we think of objects, but difficult to implement for one basic reason: it’s not always as easy to define the dominant kind as in this textbook case.
Deny VC2: Again, this is the mereologically nihilist point of view that lumps of clay don’t exist (only mereological simples arranged lump-wise). Any constitution puzzle thus dissolves, since they are about objects, and objects don’t exist.
Deny VC1: How can Venus exist on Monday if that statue was only sculpted on Tuesday? Only proponents of mereological constancy have argued as much, assuming that Venus existed already insofar as all of its parts existed too. This turns out, in my opinion, to be a pure verbal game: if Venus existed on Monday then it doesn’t have any of the properties we associate with statues: that they need to be sculpted, that they cannot survive being squashed, that they are recognised as art pieces or representations, etc. Therefore Venus is totally identified with Clay.
This is another way of saying that statues can’t exist, and of circling back toward mereological nihilism (or to a constitution-less universalism that only admits raw compositions as objects — as we’ve already pointed out, nihilism and universalism are often two sides of the same coin).
Deny VC3: VC3 is a direct corollary from the inderscinability of identicals (I.I.). Denying it forces us to adopt an alternate concept of identity. It is precisely what Peter Geach proposed with relative identity.
From that perspective, it doesn’t make sense to make such statements as \(x=y\) or \(x\neq y\), instead we may be able to say that \(x=_Sy\), read as "\(x\) is the same \(S\) as \(y\)", where \(S\) is some type of thing. The relative identity relation \(=_S\) does not follow (I.I.), but it is (by definition) an equivalence relation. Furthermore, to say that \(x=_Sy\), one must first verify that "\(x\) and \(y\) are both \(S\)".
How does this help with our conundrum? Let’s start back from the beginning, where Clay is the object we start with on Monday, and Venus is the object we get on Tuesday after sculpting. Clay is a lump of clay, Venus is a lump of clay too. We can state "Clay and Venus are the same lump of clay". However Clay is not a statue, so it cannot be "the same statue as Venus".
We don’t have any issue with coincident objects here: on Tuesday there is only one object, Venus. However we also don’t have to deal with as much counter-intuiveness as before: sculpting the clay didn’t destroy Clay — Clay persists on Tuesday through the existence of Venus, they are one and the same lump of clay. We use a different proper name because Venus is a statue, so "not the same statue" as Clay. Throughout the week there’s been exactly one lump of clay, one statue, and no coincident objects at all. Difficulties with persistence properties also seem to dissolve; the property "can survive squashing" doesn’t make sense by itself since it appeals to a general concept of identity. One may say that Venus can survive squashing as a lump, but cannot survive squashing as a statue, so that if the result of Venus’s squashing is Clay-2, Clay-2 is the same lump as Clay and Venus, but not a statue at all.
If we imagine a scenario where a new statue is sculpted and then squashed ten times over, we will have had one lump and ten different statues in that room, which aligns well with intuition.
More puzzles
The debtor’s puzzle: One of Epicharmus’s comedies tells us a joke. Achilles owes Atreus a debt and is approached by him at a banquet. He tells him: "One man is growing, another is diminishing, and all are constantly in the process of change. You and I are different today from who we were yesterday, and by the same argument we will be different again and never the same in the future." Atreus agrees. Achilles then concludes that he is not the same man who contracted the debt yesterday; in that case he can hardly be held responsible for the debt. Atreus, exasperated, strikes Achilles a blow. Achilles protests, but Atreus points out that by now he is already quite different from the man who struck the blow a minute ago.
The type of puzzle time goes back a long way, arguably all the way to Heraclitus’s remark that one cannot bath twice in the same river. The simplest way to expose it in the context of absolute identity is as such:
(DP1) In 1986, Alice was 2 foot tall.
(DP2) In 2021, Alice is 6 foot tall.
(DP3) So, 1986-Alice \(\neq\) 2021-Alice.
Relative identity has no problem sidestepping this puzzle. 1986-Alice is not the same physical body as 2021-Alice (it may not have single cell in common), but it is the same person. Whatever the relation of "person-identity" is, none of the properties it preserves are material ones such as height or weight.
Tibs and Tail: Take a cat, Tibbles, and call Tibs the portion of that cat that excludes the tail. Tibbles is a cat with a tail, Tibs is a cat without a tail. Then amputate the tail. We end up with the now familiar set of uncomfortable options:
Two perfectly coincident cats exist at the same time and place,
Only Tibs exists— then Tibbles didn’t survive the loss of a tail,
Only Tibbles exists — then Tibs disappeared when the tail was cut, although it wasn’t his tail.
Again, relative identity seems able to save the day: Tibbles and Tibs are and have always been the same cat, but Tibbles and Tibs are different physical bodies (that is, because of their different history; they can be said to be "the same physical body at time t" if one wishes to introduce this concept).
The ship of Theseus: The ancient historian Plutarch recounts the story of the famous ship of Theseus, which was displayed in Athens for many centuries. "Over time, the ship’s planks wore down and were gradually replaced. The ship became a standing example among philosophers, for the logical question as to things that grow; one side holding that the ship remained the same, and the other contending it was not the same".
Interest in this story has persisted, owing in part to an additional twist imagined by Hobbes. Suppose that the original, worn-down planks were collected and stored in a warehouse, and much later on, were put back together by naval historians. Where, then, is the famous Ship of Theseus (SoT)?
Some would say that seafaring vessel is the one displayed in the museum ("the reconstructed ship"); they would argue that ships can survive the replacement of their parts, provided that the change is sufficiently gradual. Others would say it is in the warehouse ("the mended ship"), since ships can survive being dismantled and reassembled.
The complete range of options seems to be limited to those:
(1) The SoT is the reconstructed ship.
(2) The SoT is the mended ship.
(3) Both ships are the SoT.
(4) Neither ship is the SoT.
As it turns out, all of those are defendable options! Using relative identity helps highlight how, and leads us to conclude that the original puzzle is only a verbal game that stems from disagreements about what "being the same ship" means, and can be dispelled through rephrasing.
Studies at the Oak Ridge Atomic Research Center have revealed that "about 98 percent of all the atoms in a human body are replaced every year.... Experts have further concluded that there is a complete, 100 percent turnover of atoms in the body at least every five years". Yet "Alice" is clearly not identical to the mereological fusion of her atoms from 10 years ago (which are sprinkled within the ground, in the atmosphere, in other living beings’ bodies, etc.) — this takes us back to the notion of person-identity we evoked when discussing the debtor’s puzzle.
Intuitively, it seems possible to follow (1) in saying that the reconstructed ship is the Ship of Theseus if certain conditions are fulfilled, such that (a) the rate of replacement of parts be slow enough (if 9 planks out of 10 were replaced on the same day, the claim would be harder to support), and (b) there is some social recognition by humans that the identity of the object is unchanged (if the museum curator one day changed the label to say it is now "a replica of Theseus’s ship", claims that this is the SoT would be weakened). So using relative identity, we are able to define a relation of "being the same socially-recognized ship". But the criterias outlined should appear for what they are: fuzzy, imprecise and often mind-dependent. Relative identity can salvage identity statements about ordinary objects from paradoxes, but it is at the price of logical rigor.
Accepting (2) seems pretty straightforward in terms of relative identity: consensually, the mended ship is "the same physical ship as" the SoT. Again, by leaving aside absolute identity (out of necessity), we’re not in a perfectly rigorous domain. The old planks in the warehouse have gained and lost atoms, via rot and erosion. Radioactive decay has turned some atoms into others. "Same physical ship" is thus far from equated with "same physical body at a fundamental level"; instead we would need to agree on some reasonable criteria defining the relation "same plank" and say that the "same physical ship" is made from the same planks, arranged in the same shape.
(3) is compatible with (1) and (2) as we’ve just discussed them. The SoT is relatively identical to both the mended ship and the reconstructed ship, based on distinct identity relations, so transitivity doesn’t come into play; indeed we don’t think of the mended ship and the reconstructed ship, which both exist at the same time in different physical locations, as identical (note that would be possible with some very loose criteria, where "being the same ship" would only mean "having the same shape and materials, and being named the same by its owners").
Conversely, (4) is compatible with a very strict relative identity relation. We could demand that "being the same ship" mean: 90% of the planks are identical and there is no history of dismantling and re-assembling. In that case neither the mended ship nor the reconstructed ship qualify.