The Atlas of Reality
Page 83
Def D22.6 Atom. x is an atom if and only if x has no proper parts.
Def D22.12 Maximally Fastened. The x's are maximally fastened if and only if they are fastened, and there are no y's such that the y's are fastened and the x's are among the y's, unless the x's just are the y's (van Inwagen 1990a: 63).
22.8T.1A.7 Democritean Composites. The x's compose something if and only if they are all atoms and the x's are maximally fastened.
If two people are fastened together, Democritean Composites still gives the intuitively wrong answer that a new composite thing has come into existence. Still worse, it now entails that neither of the two people exist, since neither is composed of atoms that are maximally fastened to each other, since the atoms in one are fastened to the atoms in the other.
Perhaps the right solution is to build up the world of composite things in a step-by-step, hierarchical fashion, beginning with the atoms and building progressively larger and more complex entities. In this way, we might get chemical atoms, molecules, organisms, planets, star systems, and galaxies, without getting any of the bizarre entities we want to avoid, like the supposed thing that results when two people are fastened or fused together. This is Serial Bonding:
22.8T.1A.8 Serial Bonding. The x's compose something if and only if the x's are atoms bonded in ways R1 or R1′ or R1″, and so on, or the x's are things composed of atoms bonded in way R2 or R2′, and so on, or the x's are things composed of things composed of atoms bonded in way R3, and so on, or ….
So, protons and neutrons have to be bonded in a certain way to make nuclei, and nuclei and electrons are bonded in a different way to make chemical atoms, and chemical atoms are bonded in a third way to make molecules, and so on up to rocks, clouds, organisms, planets and stars, solar systems, galaxies, galaxy clusters, and even the universe!
Van Inwagen offers a number of worries about and objections to Serial Bonding. First, since ‘atom’ is defined in mereological terms (i.e., as not having a proper part), van Inwagen rules out both Serial Bonding and Democritean Composites as satisfactory answers to the Special Composition Question on the grounds of circularity. However, it is not clear that Heapists must propose a non-circular answer, so long as there is a finite and intelligible principle of the composition of heaps.7
Second, Serial Bonding violates the transitivity of parthood, since an atom can be part of a composite of level 1, and a composite of level 1 be a part of a composite of level 2, but the atom will not, according to Serial Bonding, be a part of the composite of level 3, contrary to axiom MA3 of mereology (see Section 23.1). This doesn't seem to be a difficult objection to meet, since Heapists could take Serial Bonding to define a ‘part*’ relation, and then could define the ‘part’ relation as what is called the ‘transitive closure’ of the part* relation. Roughly, x is a part of y if and only if x is a part* of y or x is a part* of a part* of y or ….
Third, even if a version of Serial Bonding could be constructed that would work in our world, given the kinds of matter we actually have and the sorts of bonding permitted by the actual laws of nature, it would seem to tell us nothing about what sort of things might exist in worlds with different kinds of matter and different laws of nature. Serial Bonding is too parochial a principle to serve as a metaphysical account of composite entities.
Fourth, if Serial Bonding is going to avoid the counterexamples involving fused persons and organisms, it will have to explain in a principled way why fusing together some crystals produces a composite rock, but fusing together two or more organisms produces no composite entity at all. It is hard to see how this explanation could avoid being ad hoc and therefore implausible.
Finally, Serial Bonding, like Universalism, faces a serious challenge in accounting for the persistence and non-persistence of things through time. We take up this issue in Chapters 24 and 25.
We need to consider one final principle, one not mentioned by van Inwagen. This principle seems to be implicit in much of Aristotle's work:
Def D22.13 Homogeneity. x is homogeneous if and only if x has proper parts, and any two parts of x of the same size and shape are perfect duplicates (intrinsically indistinguishable).
22.8T.1A.9 Homogeneous Continua. The x's compose something if and only if they form a homogeneous material continuum (a material thing with no sharp internal boundaries).
Homogeneous Continua avoids van Inwagen's test case, since it is impossible for a living organism to be a homogeneous continuum. Consequently, two organisms fused together will also fail to form such a continuum. However, Homogeneous Continua will entail that no composite organisms exist, since organisms are never perfectly homogeneous. We could modify Homogeneous Continua to guarantee that all organisms count as composite things:
22.8T.1A.10 Homogeneous Continua Plus Organisms. The x's compose something if and only if they form an organism or a homogeneous material continuum.
However, this principle involves a significant departure from common sense. Few of the world's heaps are homogeneous continua. Neither rocks nor clouds nor bodies of water live up to this standard. Still, we might point out that many of them are approximately homogeneous and appear to the naked eye to be homogeneous. Perhaps common sense simply ignores the deviation of many heaps from the standard of homogeneous continua, indulging in the useful fiction that they are homogeneous and continuous or being satisfied with the quasi-truth that they are.
Thus, Homogeneous Continua seems to avoid the usual challenges to answers to the Special Composition Question. However, would material continua of this kind really be heaps? Would they really be composite things at all? Do homogeneous continua have actual parts or only potential ones? Since no sharp boundaries articulate a material continuum into ready-made parts, it seems natural to think that the parts of such a continuum are only potential. If this is so, then material continua are really metaphysical atoms of a certain kind, which we could call ‘Aristotelian atoms’, to distinguish them from the absolutely indivisible Democritean atoms.
Def D22.14 Aristotelian Atom. x is an Aristotelian atom if and only if x is an atom (with no actual proper parts) and x has the passive power of bringing into existence one or more fission products.
Def D22.14 Fission Product. y is a fission product of x if and only if x has a passive power P such that, as a matter of necessity, when P is exercised, x ceases to exist, y begins to exist, and y occupies part of the former location of x.
Def D22.16 Democritean Atom. x is a Democritean atom if and only if x is an atom but not an Aristotelian atom.
If all homogeneous continua are Aristotelian atoms, then the two versions of Homogeneous Continua will be empty, since there will never be a number of actual distinct things that together make up a single continuum of this kind. Aristotelian atoms are not heaps at all, since they lack actual proper parts. If all homogeneous continua are Aristotelian atoms, then none of them are heaps. Once again, we have failed to come up with a principle of composition that gives us precisely the heaps that common sense wants, undermining the legitimacy of an appeal to common sense.
22.7.3 Do artifacts exist?
Consider again the thesis of Extreme Anti-Artifactualism:
22.10T Extreme Anti-Artifactualism. No composite material artifacts exist.
As in the case of heaps, the main argument against Extreme Anti-Artifactualism is an appeal to common sense. If we claim that there are no forks or spoons, automobiles or ships, tables or chairs, we are likely to be met with an incredulous stare. How could we possibly deny the existence of such familiar, everyday objects? Anti-Artifactualists can appeal to the same strategies here as Anti-Heapists: paraphrase, useful fiction, and quasi-truth. (5), for example, can be paraphrased as (6):
(5) THP is sitting on a chair.
(6) THP is sitting on some particles arranged chair-wise.
Finally, we might suppose that we can give a coherent answer to van Inwagen's Special Composition Question insofar as it applies to artifacts. The answer might go something like th
is:
22.8T.1A.11 Composition of Artifacts (1). Some material things compose a mere material artifact if and only if they have been altered or arranged by some intelligent agent (or group of agents) for a single purpose or interdependent set of purposes, and they do not compose a living thing.
However, is it really necessary for some things to be altered or arranged in order to constitute an artifact? There are such things as found artifacts. We could find a stump in the woods and make it into a chair simply by using it as such.
In addition, is arrangement sufficient to constitute an artifact? Consider a broken and abandoned watch. Is it still an artifact or is it now a mere heap of metal parts? The parts were altered and arranged for a purpose, but the watch no longer serves that purpose. To overcome these challenges, we might try an alternative principle of composition:
22.8T.1A.12 Composition of Artifacts (2). Some material things compose a mere material artifact if and only if they are used and maintained by some intelligent agent (or group of agents) for a single purpose or interdependent set of purposes, and they do not compose a living thing.
1. Immaterial artifacts. Let's suppose that holes, shadows, and spots of light on a wall, for example, are not material things. Artifacts can be made of such immaterial entities. For example, Alexander Pruss has pointed out that one could make a chess set simply by forming holes in a thick, viscous mound of jelly. One moves one's queen in this set by inserting a tool into the hole in the jelly that is the queen and slowly moving the hole to a 1new position on the chessboard, and then removing the tool. The pieces of such a chess set cannot be material entities, since their parts are not material entities. But if this holey chess set is not a (composite) material thing, then we shouldn't suppose that an ordinary chess set is, simply by virtue of its being composed of different things.
There are even simpler examples of the same phenomenon. A trench is an artifact, but a trench consists simply in a long, narrow hole that is produced by digging. In addition, there are works of art that consist entirely of shadows or points of light.
Some ordinary artifacts, like works of literature (poems, plays, novels) and musical compositions, seem to be wholly abstract. A musical composition is just a sequence of notes, an abstract entity that is not located in space. Do we really believe that a musical composer alters the world of abstract objects, bringing into existence a new sequence? Surely not. But if the creation of a new thing is not required for such musical or literary creating, why think that an act of manual creation involves the coming into being of an entity, as opposed to the mere re-arrangement of existing things?
2. Making artifacts out of living things. Van Inwagen (1990a: 126–127) asks us to imagine an artifact made entirely of a living thing. For example, we could imagine making a very long snake into a hammock by tying it together into a network of knots. Doing this to the snake would not bring into existence a new thing nor would it destroy the snake. This isn't a case in which the living thing counts, all by itself, as a material artifact (as a bonsai tree or an artificial organism might). Since the hammock is neither an old nor a new material thing, it seems that it cannot be a material thing at all. If we appeal again to Functionality the Essence of Artifacts, no hammock could be a material thing, since any hammock is functionally equivalent to any other.
We might suppose that turning the snake into a hammock fails to produce a new material thing precisely because the snake already existed. However, this seems an entirely ad hoc solution. How can arranging a rope in a certain way bring into existence a new material entity if arranging the rope-like snake in precisely the same way for the same purpose fails to do so?
Notes
1. As we saw in Section 3.4, there are two further sub-questions: When can the truths about composite things be conceptually grounded in facts about their parts? and, When can the facts about composite things be non-conceptually grounded in facts about their parts?
2. Compare Definition D11.1, gunky body. A body that is spatially gunk will satisfy D11.1.
3. We write this section, as well as the one one below about free will, in the first-person singular, for ease of exposition.
4. Merricks considers it an open empirical question whether there are emergent powers possessed by other composite things, including molecules and sub-personal organisms.
5. See Merricks (2003), Chapters 2 and 7.
6. To be precise, it is not missing anything that can be expressed in a non-mereological vocabulary.
7. Van Inwagen defines the Special Composition Question in such a way as to require a non-circular answer (one that doesn't include mereological vocabulary). The defender of Serial Bonding could challenge the appropriateness of that requirement.
23
Composition: The General Question
In this chapter, we take up issues to do with van Inwagen's (1990a) General Composition Question: what is it for one thing to be a part of another? We begin in Section 23.1 with some background to do with formal mereology, the study of parts and wholes. We identify four answers to the General Composition Question in Section 23.2, though we discuss only three in detail, and in Section 23.3 we consider whether those answers can supply a ground for the correct principles of mereology. Finally, in Section 23.4, we briefly consider the connection between parthood and truthmaker, which in part prompts the discussion of Section 25.1, on whether wholes can change their parts.
23.1 Formal Mereology: Leśniewski, Goodman, and Leonard
In discussing the metaphysics of parts and wholes, it is helpful to have some specialized vocabulary, as well as a well thought-out mathematical model of a very broad, inclusive theory. The theory of mereology, proposed by the logician Stanislaw Leśniewski (1916) and introduced to the wider world by Goodman and Leonard in an article in the Journal of Symbolic Logic (1940), provides that vocabulary and such a model. These mereologists proposed some basic axioms for the part-whole relation. First, they assumed that the part-whole relation is reflexive, antisymmetric, and transitive. Reflexive relations are relations such that everything stands in the relation to itself; antisymmetric relations are relations such that if a thing A stands in the relation to a thing B and if B stands in the relation to A, then A just is B, A and B are identical; transitive relations are relations such that if a thing stands in the relation to a thing B, and if B stands in the relation to a thing C, then A stands in the relation to C. In the case of parthood then, Leśniewski, Goodman, and Leonard proposed these axioms:
(MA1) Mereological Reflexivity. Everything is a part of itself.
(MA2) Mereological Anti-Symmetry. If x is a part of y, and y is a part of x, then x = y.
(MA3) Mereological Transitivity. If x is a part of y, and y is a part of z, then x is a part of z.
Figure 23.1 Mereological Transitivity
Mereological Reflexivity seems an odd requirement, since we do not usually speak as though anything were a part of itself. However, it is convenient for technical reasons to use ‘part’ in this slightly odd way. (We needn't worry about these reasons at this stage.) Whenever we want to say that x is a part of y but not identical to y itself, we shall say that x is a ‘proper part’ of y. A ‘proper part’ is just defined as: a part of but not identical to the whole.
Def D23.1 Proper Part. x is a proper part of y if and only if x is a part of y and x ≠ y.
Once we understand the distinction between part and proper part, the reflexivity of parthood is unproblematic. Reflexivity is simply a consequence of the reflexivity of identity. Everything is identical to itself, so everything is a part (in this sense) of itself.
Anti-Symmetry makes parthood like the subset relation and the greater-than-or-equal-to relation from mathematics. If x is greater than or equal to y, and y is greater than or equal to x, then x and y must be identical. It is impossible for two distinct numbers each to be greater than or equal to each other. Similarly, mereologists assume that it is impossible for two distinct things each to be a part of the other. T
here are no part-whole loops involving two different entities. This seems a reasonable principle. At least, it is hard to think of any clear counterexamples.
Transitivity is somewhat more problematic. There do seem to be cases in which one thing is part of a second, the second a part of a third, and yet we do not want to say that the first is a part of the third. For example, the quarterback's left earlobe is part of the quarterback, the quarterback is part of the football team, and yet it would be strange to say that the quarterback's left earlobe is part of the football team.
Mereologists have two possible responses to these apparent counterexamples to Mereological Transitivity. First, they could suppose that in certain contexts we use ‘part’ to refer to only special, salient parts of the whole. For example, when we talk about the ‘parts’ of a football team, we normally mean the team's members, and we don't intend to include all of the parts of those members, even though, strictly speaking, the parts of the members are really parts of the team.
Second, mereologists could admit that the metaphysically most basic relation is non-transitive or even intransitive. If we have a non-transitive relation R, it is easy to define a new relation R*, the ancestral or transitive closure of R, that is transitive. For example, the relation of being a parent is obviously not transitive: the parent of a parent is not normally a parent. However, we can define the relation of being an ancestor as the transitive closure of being a parent: x is an ancestor of y if and only if x is a parent of y or there is some z such that x is a parent of z and z is a parent of y or there are a z and z′ such that … The relation of being an ancestor is necessarily transitive. Similarly, we could let the logic of mereology apply to the transitive closure of whatever parthood relation is metaphysically fundamental or natural. This option comes at a cost, however. If the fundamental relation is non-transitive, then each of the other axioms of mereology have to be strengthened in order to apply to the transitive closure of parthood.