To be clear, however, it is not the supervenient Gestalt qualities that are the structural universals. Rather, we need structural universals to be the bearers or supervenience bases for these Gestalt qualities. It is the resemblance between the structural universals that grounds or corresponds to the instantiation of the Gestalt quality by the particular whole. The simplest account of Gestalt qualities would be to take them to be simple, natural qualities of the structural universals themselves. Then it would follow that the Gestalt quality is realized in a particular whole whenever that whole instantiates one of the quality-bearing structural universals.
Accounting for possibilities. Peter Forrest (1986) has suggested that we identify possible worlds with structural universals (world-properties). We'll take up this suggestion again in Chapter 15, on Abstractionism (14.1T.1A = 15.1T). This requires a moderately abundant theory of structural universals. We don't need disjunctive structural universals (like RED OR SQUARE), but we will need structural universals that are conjunctions and amalgamations of properties and properties of parts if we are to have enough structural universals to supply at least one for each possible state of affairs.
We will also need something on the level of particulars (perhaps bare particulars?) to perform the job of making possible situations actual. We will need such ultimate actualizers as the things that instantiate those possible situations that are actual.
Providing resources for Strong Nomism (4.4A.2). If there are structural universals, then we could represent each causal law of nature as simply connecting one such structure (the initial situation) with a second structure (the resulting situation). There is, however, an alternative. We could instead posit a family of lawmaking relations, one for each logical form of a law (this was Tooley's original proposal in Tooley 1977).
Accounting for inclusion and incompatibility among universals. Using structural universals, we can easily explain why, for example, the universal RED AND ROUND includes the universal REDNESS and excludes the universal RED AND NOT ROUND. However, this sort of explanation doesn't apply to logically simple universals. Some philosophers, such as Wittgenstein at the time of writing the Tractatus (1921), have thought that all simple universals are mutually compatible and no set of simple universals ever entails the instantiation of other universals. But this is quite a controversial position. There do seem to be cases of incompatible simples, such as incompatible sensory qualities (color, smell, texture).
The possibility that there are no simple universals. At the very least, there might be some structural universals that are “structures all the way down”, structural universals such that each part of the structure would be another complex structure, with still more parts. The world could contain infinitely complex properties. Lewis considered this to be the strongest argument for structural universals. If it is possible that some structures have no simple parts, then, if there are to be universals that are shareable in such cases, the universals must be complex.
There are two additional arguments (our seventh and eighth arguments) that Lewis did not consider. The seventh (emergent holistic powers) looms large in light of our consideration of causal powers (Chapters 4–6). As we will see in Chapters 22 and 25, there are good grounds for thinking that there may be emergent or holistic powers of composite things, powers that are not wholly grounded in the powers of their microscopic parts. This is most plausible in the case of sentient or rational beings. The whole organism in some cases transforms the nature of its parts, altering fundamentally the powers of those parts. Powerism entails that powers are internal to the properties that confer them. Thus, there must be structural universals that can confer these emergent or holistic powers on the composite particulars that instantiate them (or to the proper parts of those particulars).
The eighth argument also concerns composite material things. As we discussed in Chapter 9 and will examine again in Chapters 25, there are cases of composite things that seem to violate Mereological Constancy (25.1A). Such things are mereologically inconstant: they can continue to exist despite gaining or losing some of their constituent parts. Organisms, for example, are constantly exchanging material particles with their environment. Some artifacts can survive the loss or replacement of some of their parts (think of a car that survives the replacement of its spark plugs). If a composite thing is to survive such change, there must be a principle of unity that persists despite the substitution of some of the participants in that unity, and structural universals are plausible candidates to play such a unifying role. Katherine Ritchie has been investigating this use of structures in her recent work on social groups (Ritchie 2013, 2015).
Despite these advantages, structural universals are somewhat mysterious. Consider the structure of an H2O molecule. Since water molecules contain two hydrogen atoms, the universal corresponding to being an H2O molecule must have two “parts” each of which is the relatively simple universal HYDROGEN ATOM. How can this universal be present “twice over” in the H2O universal? There is only one HYDROGEN ATOM, which must either be a part or not a part of the H2O universal. It's not at all clear what being present “twice” could mean.
Even if we could solve this problem, a deeper mystery remains. Some structures have exactly the same parts assembled in different ways. For example, the hydrocarbon structures normal butane and isobutane both contain four carbon atoms, ten hydrogen atoms, and 13 chemical bonds. In normal butane, the four carbon atoms are in a chain, while in isobutane there is a central carbon atom with the other three carbon atoms and a hydrogen atom bound to it. Since there is only one universal CARBON ATOM, how can the two structures (normal butane and isobutane) put that one universal into two different relations to itself and to the hydrogen-atom universal?
In response, Lewis offers the theory of amphibians, on behalf of Constituent Ontologists who want to posit structural universals.4 On this view, there are amphibious entities that are partly universal and partly particular, in addition to universals and particulars. The hydrogen structure contains one oxygen amphibian and two hydrogen amphibians. The two hydrogen amphibians are distinct duplicates, each of which instantiates the common universal HYDROGEN ATOM. However, hydrogen amphibians are not particulars, since they are themselves instantiated by parts of particular water molecules. They both instantiate and are instantiated.
Amphibians are like particulars in another way: they can stand in the same relations to one another that particulars do. Thus, the two hydrogen amphibians in the H2O structure are chemically bonded to the oxygen amphibian, in the very same way that particular hydrogen atoms are bonded to particular oxygen atoms in actual water. In fact, when a particular water molecule instantiates this structure, the chemical bonds between the particular atoms are identical to the chemical bonds between the instantiated atom-amphibians.
Constituent Connectionism would require bare amphibians, elements whose metaphysical function is to distinguish each amphibian from all of the qualitatively indiscernible amphibians. Bare amphibians are thus analogous to bare particulars.
Structures are often organized hierarchically, with some structures serving as components of still larger structures. Such hierarchical nesting of structures requires a similar nesting of structural universals. For example, just as there are atom-amphibians in the structure of the water molecule, there can also be water-molecule-amphibians in the structure of the ice crystal. Likewise, we should find atom-amphibians in the structure of amino acids, amino-acid-amphibians in protein structures, protein-amphibians in the structure of cellular organelles, organelle-amphibians in cell structures, cell-amphibians in organ structures, organ-amphibians in the structure of organisms, and organism-amphibians in social structures. A universal is a constituent of an amphibian; that amphibian is within another amphibian, and so on, finally reaching a particular. In other words, a particular hydrogen atom could realize an amphibian role A1 within an organism, while A1 realizes an amphibian role A2 within a cell, which in turn realizes a third amphibian role A3 within
a protein, which in turn realizes a fourth amphibian role A4 within an amino acid, which in turn realizes the universal of being a hydrogen atom. For Constituent Ontologists, this requires a nesting of amphibians within amphibians, with a universal at the bottom and a particular at the top.
Amphibian theory will come in two varieties, depending on the roles that we want structural universals to play. These two varieties are the very sparse and moderately abundant types. If we rely on Gestalt qualities, holistic powers or incontinent wholes (arguments 2, 7 or 8) as our basis for Realism about structural universals, then we will want to adopt a very sparse theory of structural universals. We should posit structural universals only when the structures are associated with emergent qualities or powers or with the kind of unity required for inconstant persistence.
In contrast, if our motivation for structural universals depends on Forrest's idea of possible worlds as structural universals (argument 3), then we will need to have a moderately abundant theory of structural universals. We will need one structural universal for every possible situation, including whole possible worlds.
If we adopt the sparse version of amphibian theory, then we will recognize three types of entities in the world: universals, amphibians, and particulars. Universals are instantiated (by amphibians and particulars), amphibians both instantiate universals and other amphibians and are instantiated by both particulars and other amphibians, and particulars instantiate universals and amphibians. If we adopt Substrate Theory, we will need both bare amphibians and either bare particulars or modular substrates as the ultimate ground of distinctness among amphibians and particulars. In addition, Constituent Ontology alone requires some entity to play the role of distinguishing particulars (that are essentially incapable of being instantitated by anything else) from amphibians (that are essentially capable of being instantiated by other things). We could give this role to bare particulars or modular substrates, or we could introduce some new kind of entity—an ultimate actualizer or particularizer—to do this job.
The moderately abundant amphibian theory would be especially attractive as a version of Bundle Realism: Amphibian Bundle Theory. On this view, the actual world consists entirely of universals and amphibians. A particular is simply a structure that is not in fact (in the actual world) duplicated. Duplication occurs only when a universal is instantiated by more than one amphibian within some actual or realized structure. Thus, a particular is either a maximal actual structure (one that isn't in fact a proper part of any other structure) or a unique (un-duplicated) part of such a maximal actual structure. We might imagine that there is a single structure—the cosmic structure—that includes all of the facts about the locations, properties, and relations of the whole physical universe. This might be the only maximal actual structure, which would give us a version of metaphysical Monism (11.2A). As we shall see in the next chapter, such a theory offers an attractive interpretation of the Monism of F.H. Bradley. Alternatively, we could suppose the cosmic structure is only one of many maximal actual structures, the other structures being partly physical (thus overlapping with the cosmic structure) and partly non-physical (including mental, ethical, or biological features not included in the physical world). This version of Bundle Theory would avoid the problem of individuation that plagued Classical Bundle Theory (9.1T.1T.1A), since bare amphibians would ground the distinctness of indistinguishable parts of a structure (as bare particulars do in Bare Particular Theory 9.1T.1A.2A). This account will require some way of distinguishing merely possible structures from actual ones, a problem we return to in Chapter 15.
10.4 Determinables, Quantities, and Real Numbers
As we have already seen, some properties stand in the determinate-determinable relation.5 There is for example, the determinable property of color, and there are a large number of determinate colors (scarlet, periwinkle, mauve, and so on). In physics, we have such determinable properties as mass, charge, and velocity, and we also have determinate masses, quantities of charge, and velocities (e.g., 2 kilograms, 5 coulombs, or one-half the speed of light). There are four basic facts about determinables and determinates to be explained:
If anything instantiates a determinable property, it must also instantiate one of the determinates. Anything that is colored must have some specific color.
If anything instantiates a determinate property, it must also instantiate each of its determinables. Anything that is scarlet is colored and reddish.
If P and Q are both determinates of the same determinable, then it is impossible for something to instantiate both P and Q at the same time. It is impossible to instantiate two distinct, specific quantities of mass at the same time.6
The determinates of a single determinable can be ordered along one or more dimensions of similarity. For example, 1 kilogram is more similar to 2 kilograms than it is to 3 kilograms, and red is more similar to orange than it is to green.
In many cases (physical quantities), these similarity orderings make possible a precise measurement of the determinates of a determinable. That is, the determinates can be assigned unique real numbers (or complex numbers) as measurements (e.g., 3.7 grams, 5 meters/second, etc.), relative to certain conventions about units of measurement and (possibly) a conventional coordinate system (such as latitude and longitude).
These facts can be explained by Realists and by Trope Nominalists in several ways. We will consider three popular theories: Determinate Universal Theory, Simple Intensity Theory, and Composite Intensity Theory. Determinate Universal Theory supposes that each determinate property corresponds to a single universal (or, for Trope Nominalists, to a class of exactly similar tropes). Real numbers on this view are second-order properties, natural properties that are instantiated by ordered pairs of determinate universals. Simple Intensity Theory makes do with a single class of quantitative intensities, while supposing that it is the determinables that are universals. On the Simple Intensity Theory, a substance instantiates a determinate property by jointly instantiating both a determinable (like mass) and a specific intensity. Composite Intensity Theory supposes that each degree of intensity contains all lesser degrees as proper parts. A determinate property of a substance corresponds to the largest or maximal intensity that is instantiated in conjunction with some determinable by the substance.
10.4.1 Determinate Universal Theory
Real numbers are used as measures of quantities, both extensive (distance, duration) and intensive (mass, charge, energy). A measure is something essentially relational. Consequently, we could propose, following John Bigelow (1988), that the fundamental role of real numbers is as relations between physical quantities. Thus, real numbers are relational properties. (More precisely, real numbers are relations between scalar quantities. Relations among vector quantities include the complex numbers.)
What are the quantities that real numbers relate? They could either be universals of a kind (exactly so-much mass, exactly so-much charge) or tropes (either modifying or modular).
10.2T Real numbers are universals.
10.2A Real numbers are not universals.
10.2A.1T Real numbers are tropes.
If we are Realists, we could suppose that each real number is a relational universal, one instantiated by pairs of quantities, taken in the not-less-than/not-greater-than order.
10.2T.1 Determinate Universal Theory. Real numbers are relational universals, each instantiated by ordered pairs of quantities.
For Modifying Trope Nominalists, when two quantity-tropes q1 and q2 stand in the real-number relation r, then r is a modifying trope that modifies jointly q1 and q2 in the not-less-than/not-greater-than order.
10.2A.1T.1 Determinate Trope Theory. Real numbers are natural resemblance classes of relational modifying tropes, each of which modifies an ordered pair of quantities.
How does Determinate Universal Theory explain the four facts about determinates and determinables? First, determinable properties correspond to classes of determinate universals that stand in real-numbered
relations to one another. Consequently, if a substance instantiates one of those determinate universals, then it will automatically possess the determinable property. Conversely, a substance cannot possess the determinable property without instantiating one of the associated determinate properties. Third, the mutual exclusion of pairs of determinates will have to be treated either as a brute metaphysical necessity or as the consequence of a special law of nature. Finally, the natural ordering of the real numbers corresponds to the similarity ordering of the determinates.
There are thus two major costs to Determinate Universal Theory. First, it requires laws or brute necessities corresponding to the mutual exclusion of distinct determinates of the same determinable (the mutual exclusion of having exactly 1 gram of mass and having exactly 2 grams, for example). Second, it requires a large class of brute facts. There are so many families of properties (mass, charge, volume, velocity, and so on) that are interrelated in the right way by the entire field of real (or complex) numbers. Both costs involve the postulation of a vast number of brute facts of a surprisingly convenient sort.
The Atlas of Reality Page 36
