Abstract
Three alternatives to universals are discussed in this work: resemblance nominalism, trope theories and theological nominalism. This chapter discusses resemblance nominalism, especially in its strongest formulation by Gonzalo Rodriguez-Pereyra. It is argued that there are important difficulties for resemblance nominalism because it requires to postulate primitive and complicated facts of resemblance, it requires an inversion of the direction of ontological priority, it cannot explain structures of determination of properties, it cannot explain adequately causal powers, natural laws, or the reliability of our inductive practices, and it requires a possibilist modal metaphysics. Besides, resemblance nominalism under the specific formulation of Rodriguez-Pereyra suffers from a vicious regress.
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Notes
- 1.
My experience, moreover, with common people, without previous philosophical training, is that once the pros and cons of the different positions in metaphysics of properties are explained to them, they are usually inclined to accept the existence of universals.
- 2.
The relation of resemblance is not generally transitive. This here presents no problem, however, since for objects belonging to a resemblance class according to requirements (A) and (B), there are no cases in which, for x, y, z: x is similar to y, y is similar to z, but x is not similar to z. By construction, if x were not similar to z, either x or z should not belong to the resemblance class.
- 3.
Which seems false, indeed. There are human beings without kidneys—which must be dialyzed regularly—but with a heart. There are human beings without hearts—with an artificial device that circulates their blood—but with kidneys. A resemblance nominalist could also differentiate between the resemblance class assigned to having a heart and the resemblance class assigned to having kidneys. See Rodriguez-Pereyra 2002, 97–98. The classic example will be maintained, however, to simplify the discussion.
- 4.
The problem of the company has been confused many times with the problem of co-extensive classes. A precise formulation of this problem has only been made in Rodriguez-Pereyra 2002, 149–155.
- 5.
The examples that come to mind when a resemblance class has a ‘companion’ are cases like the property of having a perfectly spherical shape and the determinable property of having a form. If one wants to restrict the examples to super-determinate properties, however, it is more difficult to find examples. There would be cases of this kind in particle physics if it were accepted that natural laws are necessary. Every quark of the type ‘down’ has a mass of 4.8 MeV/c2 and an electromagnetic charge of −1/3, but not every particle with a charge of −1/3 has such a mass.
- 6.
One could define, in effect, the similarity* of n objects to each other as the conjunctive fact that: x1 is similar to x2, and x2 is similar to x3, and … and xn-1 is similar to xn. A notion of similarity* defined in this way in terms of the dyadic notion of resemblance, however, could not evade the problem of the imperfect community, since objects that are similar to each other without sharing the same nature would count as similar* to each other.
- 7.
Something similar happens with the variant of resemblance nominalism proposed by Paseau (2015, 110–115). He postulates a relation of similarity of comparative character that has pluralities as arguments. The form of the basic resemblance facts is the following: the X1s are more similar to the X2s than the X3s are similar to the X4s. Here the variables ‘X1’ to ‘X4’ range over pluralities. The details of this alternative will not be discussed here.
- 8.
In Rodriguez-Pereyra’s theory, an additional requirement is added to distinguish the classes of similarity that fulfill the functions of universals from mere intersections of classes of similarity (see Rodriguez-Pereyra 2002, 186–198). These sophistications will not be considered here.
- 9.
A nominalist will probably protest against this formulation. It is not the case, he will say, that similarities between objects are postulated, but simply that the objects are (or are not) similar to each other. But it is an acceptable paraphrase of “a is similar to b” to say that “there is a similarity between a and b”. The nominalist will agree that, for example, (i) it is a fact that a is similar to b, and (ii) that this fact is not the existence of an internal relationship between a and b. This is all that is required for what is held here.
- 10.
Let inst be the universal relation of instantiation. The explanation of why there is a state of affairs of a1 having universal U1 is given by inst (a1, U1). But inst is a universal relationship, so it should be explained why it is instantiated in the pair <a1, U1> rather than in any other ordered pair. One could appeal here to the same universal relation of instantiation inst or a relation of instantiation of a higher logical type. In the first case, it is generated inst (inst, (a1, U1)), which then requires inst (inst, (inst, (a1, U1))), and so on. In the second case, a relation inst1 would be required assuming that inst is of the lowest type, be inst0. What explains inst0 (a1, U1) is inst1 (inst0, (a1, U1)). And what explains inst1 (inst0, (a1, U1)) is then inst2 (inst1, (inst0, (a1, U1))) and so on. The first alternative has the drawback that there would be a universal of being an X such that: ¬inst (X, X). That is, the universal of not be instantiated in itself, that it is inconsistent, because if it were instantiated in itself, it would not be instantiated in itself, and if it were not instantiated in itself, then it would be instantiated in itself. The second alternative avoids this incoherent universal, but it is much less economical since it is necessary to postulate an infinite sequence of different universal relations of instantiation for each logical type. In either case, it is a vicious regress because there is an infinite chain of grounding relationships without a first element.
- 11.
Although, of course, if it is an ‘immanent’ universal, it must have some instance, although not one or another in particular. If it is a transcendent universal, it is merely accidental to have instances.
- 12.
This presupposes that every physical object has arbitrary proper parts that occupy exactly one arbitrary spatial region that is a sub-region of the spatial region that the object occupies. Such an assumption has been called into question. Armstrong’s position would also require that there are ‘minimal’ properties that must be instantiated in the atomic parts of an object. If there are no mereological atoms, it is also doubtful that there are ‘minimal’ properties and, with that, that there is partial unity in the terms contemplated by Armstrong for all those determinate properties under a determinable.
- 13.
Another proposal is that of Evan Fales in which a determinable property is fixed by classes of causal powers (see Fales 1990, 166–178). Neither will the details of this proposal be discussed.
- 14.
Something similar happens with the relationship that may exist between the conjunctive property being F and G and the property of being F.
- 15.
Although it has been common to maintain that natural laws must, at least, imply regularities, this is not the case—a point that Daniel von Wachter has insisted on for years. Armstrong distinguishes between ‘iron’ laws without exceptions and ‘oaken’ laws that admit being overridden (see Armstrong 1983, 147–150). But natural laws, as they are ordinarily understood, do not imply regularities. If it is a natural law, for example, that opposite charges are attracted, and there are objects with charges of +q and –q, respectively, they will not necessarily come closer together. Some additional force could be exerted to prevent the deployment of that force of attraction. What the law predicts is the existence of a tendency that may or may not be reflected in the phenomena, according to what other forces are operating in the circumstances. In any real physical system, there is a multitude of forces operating. Since many of these forces can be neglected, our mathematical models that ignore them have sufficient predictive value. Strictly, however, none of the laws implies a regularity.
- 16.
This is what happens with the Lewis-Ramsey theory in which natural laws are those statements that achieve the axiomatization of everything that happens in a possible world that best satisfies the requirements of simplicity and informativeness (see Lewis 1973, 73). Note that here, the laws are ‘statements’ in a theory that describes how things are in a possible world. They do not have any regulatory function. Laws are those statements that fulfill a systematic function in such a description. In the theories of natural laws that give to these a regulatory role, laws are not statements, but entities that can be described in many different ways.
- 17.
And it is not necessary that laws are deterministic. Stochastic laws—insofar as determinate objective probabilities can be assigned for the process in question—also allow for such ‘unification’.
- 18.
As far as can be supposed. Recall that ‘similarities’ are primitive external relationships, whose intelligibility is already a significant problem, as explained in § 18.
- 19.
Anyone who has some familiarity with the discussion of Armstrong, Tooley, and Dretske’s theory of natural laws will note that an objection of this kind has been directed precisely against it: why would there be a necessary connection between different universals? Calling this relationship “necessitation” does not really make the universals to be connected in the way intended (see Lewis 1983, 40). This lack of connection has been one of the reasons why the most recent defenders of non-Humean conceptions of natural laws have preferred to maintain that laws are simply primitive causal powers. No second-order relationship is required to ‘connect’ universals with each other and to bring about a natural law. It is part of the essence of a universal to confer on its instantiations specific powers to enter certain causal relationships (see Mumford 2004, 143–159). The universal by itself is already the natural law. Defenders of non-Humean conceptions are well aware of the difficulty and have proposed feasible solutions.
- 20.
Recall that an ‘event’ has usually been understood as the instantiation of a property in an object at a time, or as the instantiation of a relationship in several objects—according to the adicity of the relationship—at a time. This specification of what is an event should be taken cum grano salis. In principle, ‘instantiation’ should be taken here in a way that does not prejudge against nominalist or the defender of tropes. In the same way, ‘object’ should not be taken here in a way that prejudges against the defender of trope bundles.
- 21.
This requirement of ‘locality’ is much weaker than the requirement usually presented under that name. It is not required that the event cause and the event effect be mutually contiguous (see Lange 2002, 1–25). Nothing prevents, for example, phenomena of quantum entanglement (see Lange 2002, 280–299). What is required, however, is that a causal connection between the events c and e involves the spatiotemporal regions occupied by c and e, along—eventually—with the distance between such regions and no other.
- 22.
Or of the union of such regions, if a set-theoretic perspective is adopted and regions are conceived as sets of points with topological properties. A region r is said to be “disconnected” if and only if it is the union of at least two disjoint and closed regions.
- 23.
A structure of this type in which the similarities of the hereditary pairs ground the ‘natures’ of the objects and, in turn, the ‘nature’ of the objects ground the similarities of the hereditary pairs would be a structure in which both the similarities of the hereditary pairs and the ‘natures’ of the objects would be grounded on themselves. This reflexive grounding is unacceptable if it is a relation of strict grounding that is irreflexive and transitive—and, therefore, asymmetric. It would be acceptable if it were weak grounding, but it would require to assume that ‘natures’ and similarities of hereditary pairs are identical. As indicated above (see § 19) the nominalist must identify the natures with the similarity classes, but not with the similarities which ground such classes. But why not also identify the class of similarity with the similarities that ground it? The problem is that no singular entity—a class—can be identified with a plurality. A statement like “α = the Fs” does not make sense, because “the Fs” designates collectively, in effect, a plurality of entities. A statement like “the Fs = the Gs” in which the sign of identity is flanked by designations of pluralities makes sense, but the meaning of such a statement is derivative of the identity between individuals, because:
$$ \left(F\mathrm{s}=G\mathrm{s}\right){=}_{\mathrm{df}}\left(\left({x}_1={y}_1\right)\wedge \left({x}_2={y}_2\right)\wedge \dots \wedge \left({x}_{\mathrm{n}}={y}_{\mathrm{n}}\right)\right) $$Here, “the Fs” is a plural designation of x1, x2, …, xn; and “the Gs” is a plural designation of y1, y2, …, yn. Thus, it would make sense to state that, for example, “α = x1” where x1 is one of the Fs, but cannot be identified with the plurality of the Fs. The similarity class α could not be identified either with the plurality of similarities between hereditary pairs.
- 24.
- 25.
Unless, of course, the nominalist accepts possible worlds and their inhabitants as Lewis conceives them. What is at issue here, however, is to consider whether resemblance nominalism could work without such an ontological commitment.
- 26.
A possible state of affairs S is ‘maximal’, according to the definition of Plantinga, if and only if, for every possible state of affairs S′, either S includes S′, or S excludes S′. In general, a state of affairs S includes S′ if and only if it is not possible for S to obtain and S′ not. A state of affairs S excludes S′ if and only if it is not possible that S and S′ both obtain (see Plantinga 1974, 45).
- 27.
A property is called “alien” if and only if it is not instantiated in the actual world, nor is it constituted by properties instantiated in the actual world (see Lewis 1983, 37).
- 28.
More perspicuously, using quantified modal logic: [⃟∃x (Fx ∧ ¬Gx ∧ A∀y (x ≠ y))]. The operator A of actuality restricts the value of what is within its scope to the actual world.
- 29.
A useful presentation of the criticisms against Lewis’s extreme modal realism can be found in Pruss (2011), 63–123. Lewis argues that the modal facts—i. e., the facts about what is necessary, possible or contingent—are grounded on a plurality of ‘possible worlds’, understood as entities of the same nature as the actual world. A possible world is a mereological fusion of all objects that are at a spatial or temporal distance between them. These are concrete entities (pace Lewis 1986, 81–86). How could we know such concrete entities if there is no causal connection with them? Furthermore, how does Lewis claim that such worlds obey a ‘principle of recombination’ by which anything can exist together or separated from any other (see Lewis 1986, 86–92)? Indeed, it cannot be known that the space of possible worlds satisfies that principle by inspection of those worlds.
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Alvarado, J.T. (2020). The Superiority of Universals Over Resemblance Nominalism. 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_3
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