The Atlas of Reality
Page 61
17.1T.1A Spatial Particularism. Places are ordinary particulars (not properties or qualities), and location is an external relation between fundamental particulars (between locations and the occupiers of those locations).
There is a second question, though, one concerning the nature of places' relations to one another. In particular, the question is whether places are related internally, externally, or neither. Clearly, this question requires an understanding of this threefold distinction. We have already discussed internal relations; here again is the definition:
Def D2.2 Internal Relation. R is an internal relation if and only if necessarily, for every x and y, whether R holds between x and y depends only on the intrinsic properties of x and of y.2
An external relation will obviously not be internal. The holding of external relations depends on factors beyond the intrinsic character of the relata (taken individually). But David Lewis (1986a: 62–63) has suggested that we make a more fine-grained distinction. He takes an external relation to be one that is intrinsic to the pair of the relata, treated as a whole or composite.
Def D17.1 External Relation. R is an external relation if and only if R is not internal, and necessarily, for every x and y, whether R holds of x and y depends only on the intrinsic properties of the pair of x and y (taken together).
If we adopt this definition, there will be relations that are neither internal nor external. (We supply examples below.) We have, then, a three-way distinction between internal relations, external relations, and relations that are neither internal nor external. There are a number of examples of relations that are uncontroversially internal: for example, the relation of being twice as massive as would seem to be internal. Given the intrinsic properties (including the exact mass) of two bodies, we can always determine whether or not this relation holds between them. If one book has a mass of 200 grams, and the second book has a mass of 400 grams, then it necessarily follows that the second is twice as massive as the first. The relations of being the same color as, being happier than, and being denser than are also plausibly internal.
It is also easy to find examples of relations that are neither internal nor external. The third category of relations always involves some kind of reference to a third, independent standard or reference point. So, for example, the relation of having an earlier number in the Dewey decimal library catalog is neither internal nor external. Whether one book's numbers is earlier than another is not fixed by any property intrinsic to the books themselves, whether taken individually or as a pair. We can only tell if the relation holds by consulting a third thing, in this case the library catalog. The relations of having a smaller Social Security number than, being better liked by most people than, and being better known than are also neither internal nor external.
An external relation is intrinsic to each related pair, not taken separately and individually but as a pair. Consider the set of metal rings. Most rings are unconnected, in the sense that neither ring passes through the hole of the other. Some pairs of rings are directly interconnected, however, in the way that successive links in a chain are intertwined. Being connected in this way is not intrinsic to either ring taken individually, but it does seem to be an intrinsic property of the pair. It is something to do with the way in which the pair is in itself.
Are spatial relations like distance and contiguity (or contact) internal relations, external or neither? It seems clear that spatial relations are either internal or external. It is hard to see how spatial relations between places could depend on something outside of space (assuming that we have already ruled out Idealism, which makes distance and other spatial relations mind-dependent). So the question is whether distance and contiguity are internal or external. We thus get a distinction between Spatial Externalism and Spatial Internalism:
17.1T.2T Spatial Externalism. Spatial distance and contiguity are external relations between places.
17.1T.2A Spatial Internalism. Spatial distance and contiguity are internal relations between places.
Spatial Homogeneity. If places exist and are not qualities, then any two places are intrinsically indistinguishable.
Given Spatial Homogeneity, the Theory of Spatial Qualities and Spatial Internalism entail each other. Suppose the Theory of Spatial Qualities is true. Then places must form a natural “quality space”, similar to the “space” of colors. The “distance” in hue between any two colors (such as scarlet and purple) is internal to those colors. Given the two colors and their natures, their hue-distance is fixed. Similarly, if places are a kind of quality, then any two places must be distinguishable from one another by their qualitative difference, a qualitative difference that fixes their mutual distance. The story might go like this. Two places are in the same neighborhood if and only if they strongly resemble each other intrinsically. Two places are far apart if they are very dissimilar. Spatial distance is measured by degree of similarity. In order to provide a basis for a metric of distance, we need the following sort of primitive relation between places:
Place x is more similar to y than it is to z.
We can then define ‘closer to’ in terms of ‘more similar to’:
Place x is closer to y than it is to z if and only if x is more similar to y than it is to z.
We apparently have no experience of these qualitative differences—one place seems intrinsically exactly like any other—but the Spatial Qualities Theorists must hold that such internal differences nonetheless exist. Which is just to say that Spatial Internalism is true.
Conversely, if places are ordinary particulars—that is, if the Theory of Spatial Qualities is false—then Spatial Homogeneity requires that every place is intrinsically indistinguishable from every other place. Further, if places are not properties but particulars, then location must be an external relation between things and their places. Nothing about the intrinsic nature of individuals fixes where they are (if they are things that occupy space) or what they contain (if they are themselves regions of space). Distance and contiguity (the absence of distance) would then have to be external relations between those places because the indistinguishable intrinsic natures of places could not determine what relations hold between the places. Two regions of space with the same shape and volume would seem to be intrinsically indistinguishable from each other, no matter what their relative locations. (Importantly, we have already ruled out that these relations are neither internal nor external.) Part/whole relations are internal because whether place A is or is not a part of place B is fixed by their intrinsic natures. But we cannot reconstruct the topological and metrical features of space based solely on these part/whole (mereological) relations. If distance is an external relation between places, then Spatial Internalism is false. This establishes that given Spatial Homogeneity, if the Theory of Spatial Qualities is false, then Spatial Internalism is false. By contraposition, Spatial Internalism entails the Theory of Spatial Qualities (again, given Spatial Homogeneity).
Defenders of Substantivalism (whether the Theory of Spatial Qualities or Spatial Particularism) must immediately confront an important question, namely, how to square Substantivalism with special relativity. Substantivalism makes distance something absolute, not relative to one's frame of reference, and this seems to contradict special relativity. One could solve this by moving to spacetime points (rather than mere spatial points) and by making the basic relation not distance but spacetime interval, a distance-like quantity that is independent of frame of reference. In other words, Substantivalists could move from Spatial Substantivalism to Spacetime Substantivalism.
Spacetime Substantivalism has the further advantage that Einstein's general theory of relativity treats spacetime as a real thing with its own “curvature”, corresponding to the gravitational force of massive bodies.
17.2.1 Theory of Spatial Qualities: Advantages and disadvantages
Bertrand Russell (1927) first proposed the Theory of Spatial Qualities. It has at least four potential advantages. First, it gives an account of w
hat places are and what location is. Second, it gives an account of the nature of spatial relations like neighborhood and distance. Relative distance becomes a kind of internal relation among places. Third, it explains why something cannot be located in more than one place, since doing so would be to possess different, presumably incompatible qualities. Fourth, it doesn't multiply particular entities, and so is quantitatively simpler (PMeth 1.4).
But the Theory of Spatial Qualities also has some potential disadvantages. Here are three. First, it is not clear how degrees of similarity between spatial points are to be understood. There are some clear cases in the color case; yellow is more similar to red than it is to blue. But what does degree of similarity really amount to in the case of space? Second, how can the Theory of Spatial Qualities deal with vacuums? What possesses the spatial quality, when no physical body occupies the space? Do we need to posit uninstantiated qualities and merely possible bodies? (We will discuss this problem in more detail in Section 17.4.) Third, it brings with it an ontological commitment to properties. It is incompatible with Ostrich Nominalism (7.1A.1A).
17.2.2 Spatial Particularism: Distance as an essential but external relation
It seems that the distance between two places is essential to those places. It doesn't seem to make much sense to suppose that two places, P1 and P2, might have been closer together or farther apart. Is there a connection between internal relations and essential relations? Some philosophers have thought so, that external relations hold contingently while internal relations hold necessarily. If these philosophers are correct, one could argue to the falsity of Spatial Externalism on the basis of the necessity of relations of spatial distance. For if external relations hold contingently, and if Spatial Externalism is true, then relations of distance among places are contingent. But such relations are necessary, so Spatial Externalism is false.
However, the distinction between internal and external relations is independent of the distinction between necessary and contingent relations. The internality of a relation has to do with its being guaranteed to hold by the intrinsic natures of the relata, not with its being essential to the relata that they stand in that relation.
First, then, there may be essential relations that are not internal. For example, it might be essential to Queen Elizabeth II that she was the daughter of George VI (any daughter of anyone else wouldn't have been that very woman), but the intrinsic natures of Elizabeth II and George VI do not seem to guarantee that they stand in this relation. We can easily imagine intrinsic duplicates of these two that do not stand in a father-daughter relation. Imagine, for example, that George VI had an intrinsically identical twin; it is an external matter that one rather than the other is the father of Elizabeth II. The father-daughter relation is, thus, external, despite that the relation is plausibly essential to at least one of the relata.
Conversely, a relation might be internal without being essential. The relation of being twice as large as is an internal relation. It holds by virtue of the sizes of the two relata, and size is an intrinsic feature of a thing. But we need not assume that anything has its size (either relative or absolute) essentially. Thus, it is possible for something to stand in the relation of being twice as large as to something contingently. THP's wife Jamie, for example, is currently about twice as large as their three-year-old daughter, Gretchen. But Gretchen is still growing; she is only contingently 39 inches tall. Soon, therefore, Jamie will not be twice as large as Gretchen, and so she will not stand in this relation to her. Despite the fact that the relation is internal—that is, guaranteed to hold given the current intrinsic natures of Jamie and Gretchen—it is nonetheless contingent that they stand in it.
Although, as we have seen, it is possible to distinguish internality from essentiality and externality from accidentality, nonetheless, this separation comes at a cost. To suppose that some external relations are essential, then we must posit brute necessities of some kind, like the brute necessity of Elizabeth's having George IV as a father. If the distance between two places is indeed an external but essential relation between them (as Spatial Externalism requires), then this involves a necessary connection between two separate things: the two places cannot exist without standing in their essential distance relation to one another. To emphasize, though, this necessity is not grounded in the intrinsic natures of the two places. In general, we should prefer a theory that posits fewer such necessary connections, according to Ockham's Razor (PMeth 1.2). External but necessary spatial relations should, then, be counted a cost of Spatial Externalism.
TWO VERSIONS OF SPATIAL PARTICULARISM: BODY-SPACE DUALISM AND SPATIAL MONISM There are two versions of Spatial Particularism: Body-Space Dualism and Spatial Monism.
17.1T.1A.1T Body-Space Dualism. Both bodies and places are fundamental particulars of different kinds, with location being an external relation between bodies and places.
17.1T.1A.1A Spatial Monism. The only concrete particulars are places (parts of space). A body is simply a special kind of place—one that is characterized by a quality of being massive, body-ish or en-mattered.
RELATIONS BETWEEN THINGS AND THEIR PLACES The Theory of Spatial Qualities has a relatively clear account of the relation of location, that is, the relation that a thing holds to the place it occupies. For Spatial Qualities Theorists, this relation is that of predication. Locations are properties of things. This makes location an internal relation, since it is the qualitative character of the located thing that fixes its location, and a thing's location is simply one of those qualities.
Spatial Monists have a similarly simple theory. A body is simply identical to a place that has a special kind of body-ish quality or associated quantity (like mass or charge). On Spatial Monism, places that are the fundamental particulars, and bodies are modifications of space, like waves or disturbances passing through a constant medium.
In contrast, Body-Space Dualists need some further account of location. They could hold that location is an additional, fundamental relation between things. This comes with some theoretical cost, since we should prefer theories that posit the smallest class of fundamental properties and relations (PMeth 1.4). But Body-Space Dualism also has two putative advantages. First, there is something intuitive about thinking of places as things, and in thinking of both location and spatial distance as external relations. Second, one can avoid any ontological commitment to properties or qualities. Everything that exists is a particular.
But Body-Space Dualism has at least two further disadvantages. First, places seem to be superfluous. Given that distance is an external relation, why not make it a relation between ordinary things, non-places (e.g., bodies or particles)? The resulting Relationist account seems simpler. Second, Body-Space Dualism has difficulty explaining why a material object and the space it occupies must both have the same shape. The fact that a thing and its place must always be of the same shape seems to be yet another brute metaphysical necessity. Body-Space Dualists could hold that a thing derives its shape entirely from the shape of the spatial region it occupies. But this makes shape an extrinsic rather than intrinsic property of material bodies, which seems wrong.
This objection can be mitigated to some extent by supposing that the fundamental sort of body is that of point-sized or dimensionless bodies, and the fundamental sort of place is that of points. On this Pointillist (18.1T) view, extended bodies are nothing but sets or pluralities of point-sized bodies, and regions of space are nothing but sets or pluralities of points. Neither points nor point-sized bodies have any shape in any interesting sense, so the fact that each point-sized body “fits” into a point is not problematic. The shape of an extended body would then simply consist in the shape of the totality of points that its point-sized bodies occupy. Strictly speaking, the shape of such extended bodies wouldn't be intrinsic to them, since it depends on the relations of the ultimate parts of those bodies to spatial points, but in this case the extrinsicality of shape doesn't seem troubling.
Let's compare
Body-Space Dualism with Spatial Monism, the alternative form of Spatial Particularism. Spatial Monists can appeal to Ockham's Razor (PMeth 1.4), since they posit fewer entities and fewer fundamental kinds of entities. In addition, they need not posit any relation of location, nor do they need to worry about the coincidence between the shapes of bodies and the shapes of their places. There are only places (parts of space). Some places are vacuum-ish or empty, and other places are body-ish or en-mattered. What we call a moving body is nothing more than the successive loss of body-ishness by some places and the gain of body-ishness by other, neighboring places. A moving body is something like a moving wave on the ocean's surface or the movement of an illuminated spot on a wall. Nothing is literally moving in the direction of the body's movement. The water particles are moving up and down, and not laterally, and the wall is not moving at all. Similarly, space never moves. What “moves” is merely the pattern of realization of some quality by various parts of an immobile space. So the principal advantage of Spatial Monism is ontological and metaphysical simplicity.
Spatial Monism's major disadvantage lies in its account of the persistence of material bodies, including people and other organisms. Spatial Monists must deny that each of us is literally the same thing as any person existing an hour ago. An hour ago, the region of space that RCK occupies, which is the only thing that RCK could be identical to, was not a person at all but exhibited quite a different pattern of en-matterment. Each time one of us moves in space, one region of space ceases to be a person and another region of space becomes a person. The two persons are numerically distinct, since each is identical to a different part of space. Spatial Monists must adopt a version of Perdurantism (24.1T.1T.1A.1T) as their account of what it is for bodies to persist through time. We will take up questions to do with persistence in Chapter 24.