Abstract
The second alternative to universals that is considered in this work is the ontology of classes of tropes. Defenders of these ontologies have sustained that classes of tropes are free from the problems that affect resemblance nominalism while still evading universal entities. It is argued here that these supposed advantages are illusory. Resemblance classes of tropes have the same difficulties of resemblance classes of objects, because the relation of resemblance relevant is also in this case ‘external’ to tropes. Besides, an ontology of tropes without universals is inadequate for an actualist modal metaphysics. If resemblance classes of tropes are substituted with ‘natural’ classes, the situation does not improve.
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Notes
- 1.
Resemblance between ordered pairs of resemblance is designated as “resemblance+”. It may be the same relation applied to itself or a relation of higher ‘logical type’. In any of these cases, a vicious regress is generated.
- 2.
It should be noted, however, that there are forms of internal complexion that a trope can have. For example, a trope can be the mereological fusion of other tropes that are its parts. There are Gestalt or ‘structural’ tropes that result from the parts that make up that trope and from their mutual external relations—which must also be tropes and ordinarily consist of external relations between the objects that instantiate these tropes or of which those tropes are a part. If a macroscopic object has a certain length of n cm, this length is grounded on tropes of length of each of the parts of that object. The sum of the lenghts of each of these parts—that is, the respective tropes of those parts—must be the length of the whole, assuming the connection and continuity of all those parts. There are different ways in which the mereological structure of the particular objects that make these ‘structural’ tropes has been understood (see, for example, Campbell 1990, 135–155; Simons 1994, 569–574), but it is not necessary to enter into these differences here.
- 3.
- 4.
There are several additional difficulties that have to do with modal problems that are not relevant to discuss now. In the classical theories of tropes, such as those of Williams or Campbell, tropes are entities fundamental and independent among themselves. If one supposes, however, that the individuality of a trope is grounded on its location—with the other conditions indicated above, i. e., tropes are simple entities with a fundamental intrinsic qualitative nature—a trope would be essential for all tropes with which it is co-present. Thus, if an object is a perfect sphere of 10 gr of mass, it could not have more or less mass than it has, it could not have a different shape from the one it has, and it could not have a spacetime location different from the one it actually has, although the difference was infinitesimal.
- 5.
In effect, our commonsense conception is that the same object could be located in regions different from those in which it is actually located. In these ontologies of tropes, particular objects are mereological fusions of tropes co-present with each other (see Williams 1953a, 9–10). If each of these tropes could not have a different location from the one it has, then the object that has those tropes—which is, essentially, the mereological fusion of those tropes—could not have another location than it has.
- 6.
Moreland presents a different argument. He argues that it would be ‘unintelligible’ for two simple entities to be simultaneously under internal and external relationships (see Moreland 2001, 64). But there does not seem to be any difficulty with two substrata—something about which there are few doubts about their simplicity—that have the internal relation of being both substrata and that have also the external relationship of being 10 m away.
- 7.
As can be seen, in 1981, Campbell’s first conception, the situation is different. The location of something in the spacetime region r is dependent on that region. Regardless of whether one adopts a substantialist or relationalist conception of space and time, this involves other entities than the localized object. It would be, then, that the individuality of a trope would be something grounding extrinsic for the trope. Even in this case, however, the individual character of a trope would be combinatorially intrinsic.
- 8.
Could not this same argument apply to any pair of individuals, such as two substrata, for example? In effect, two substrata would be with each other in the internal relation of being both substrata and in the internal relation of being numerically different. But these internal relations are not ‘arbitrarily different from each other’, as the numerical difference between two entities of a certain category C must be grounded on facts about each of these entities being of category C.
- 9.
Faced with this type of problems, some have argued that the transitivity of the accessibility relations between possible worlds should be rejected (see Salmon 1989, 2005, 238–240). That is, although w2 is accessible to w1, and w3 is accessible to w2, it is not necessary that w3 be accessible to w1. This assumes that modal logics of type S4 or stronger would not be valid, and the characteristic axiom [□p → □□p] must be rejected. For many, a scenario in which something is metaphysically necessary, but it is metaphysically contingent that it is necessary, that is, a scenario in which something necessary might not have been necessary (see Plantinga 1974, 51–54; § 42) is very counterintuitive. Another alternative would be to postulate that modal facts relating to tropes are grounded on counterparts (see Lewis 1968). A counterpart of x is an entity y numerically different from x, but which is similar to x in important respects. Thus, it would be possible for the trope t1 in w1 to characterize a volume of n cm3 if and only if there is a trope t2 in w2 that characterizes a volume of n cm3 and that counts as ‘counterpart’ of t1. But many reasons have also been presented for rejecting the counterparts as determining modal facts in which one cannot enter here (see Plantinga 1974, 88–120; Fara and Williamson 2005).
- 10.
The examples that come to mind, in this case, are a bit more sophisticated. Every elementary physical particle in the Standard Model of particle physics has a volume of 0. They are treated as point particles. But they differ among themselves by their respective masses, their respective charges, and their respective spins. Thus, any trope of mass of 0.511 MeV/c2 (the mass of an electron) characterizes something with volume 0, although not every trope that characterizes a volume 0 grounds the character of having 0.511 MeV/c2 of mass.
- 11.
The situation would be different if modifier tropes had a fundamental intrinsic nature. This fundamental intrinsic nature would be what grounds, at the same time, the qualitative character of the objects that instantiate such tropes, as well as the internal similarities between tropes. Resemblances between objects would only be epistemologically prior to resemblances between tropes. But, as we have seen, tropes do not possess a fundamental intrinsic qualitative nature.
- 12.
Here too, there are no simple examples that come to mind. In the Standard Model, all elementary particles have volume 0. They are point particles. An electron has a mass of 0.511 MeV/c2, while—for example—a quark of the type ‘above’ has a mass of 2.4 MeV/c2. Any mass trope of 0.511 MeV/c2 is co-localized with something of volume 0, but not all that is co-localized with something of volume 0 is also co-localized with something of mass of 0.511 MeV/c2. Thus, some tropes do not belong to the class of mass tropes of 0.511 MeV/c2 that are similar to all tropes of this class, because they are co-located with something of volume 0.
- 13.
Propositions have also been understood as sets of possible worlds (see Lewis 1986, 53–55), but such a conception would be completely useless if the same possible worlds are reduced to maximally consistent sets of propositions or maximal propositions. A ‘maximal proposition’ or ‘world proposition’ is a proposition q such that: [∀p (☐(q → p) ∨ ☐(q → ¬p))], in a way analogous to how a ‘maximal state of affairs’ is a state of affairs S such that, for all state of affairs S’, either S includes S’, or S excludes S’.
- 14.
I owe this objection to Axel Barceló.
- 15.
To these difficulties must be added those that result from less ‘liberal’ conceptions about the mutual dependence of tropes among themselves. If, for example, the substratum in which it is instantiated is essential to a trope, then there are not many combinations in which a trope can enter. This trope could not be instantiated in another substratum. The only combinations in which it could enter is to be accompanied by other tropes instantiated on the same substratum. If one maintains, on the other hand, that the remaining tropes with which a trope form a bundle are essential to it, these combinatorial possibilities are reduced to zero.
- 16.
And, precisely, how easy it seems to generate possibilities in this conception is evidence of how unlikely these conceptions are as alternatives in modal metaphysics.
- 17.
More precisely, assuming that L is a well-regimented first-order language: [∃x ((x ≠ tm) ∧ (x is a trope of n gr of mass))].
- 18.
It is intriguing, on the other hand, that Ehring says that natural classes of tropes do not have the problems that the resemblance classes of tropes have, if the relation of resemblance is supposed to be not an internal relation, grounded on the intrinsic qualitative nature of the tropes (see § 26; Ehring 2011, 184–186). He cannot claim that tropes have an intrinsic qualitative nature for the same reasons. If tropes had an intrinsic qualitative nature—which grounded the ‘natural’ character of the classes that will fulfill the functions of a universal—then there would be more than one arbitrarily different internal relationship between two tropes, which is at odds with its simplicity. Ehring must maintain that a trope possesses the qualitative character that it possesses because it belongs to one natural class rather than another.
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Alvarado, J.T. (2020). The Superiority of Universals Over Classes of Tropes. In: A Metaphysics of Platonic Universals and their Instantiations. Synthese Library, vol 428. Springer, Cham. https://doi.org/10.1007/978-3-030-53393-9_4
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