Some Questions About the Exemplification Tie Between Universals and Particulars

Jeffrey Grupp

Abstract

A connection between things and properties is required to hold things and properties together. Exemplification is such a connection. Exemplification is usually considered primitive, and therefore analysis of exemplification is nearly absent from the literature. I maintain that exemplification might not be primitive; and in giving a description of exemplification, I point out a new problem having to do with the issue of how things are tied to properties.

1. Exemplification

Many theories of universals and physical particulars have been developed by platonic realists from Plato to contemporary philosophers such as Michael Loux and Michael Tooley, but few accounts of the exemplification ties between universals and physical particulars have been presented or discussed. In this paper, I am not addressing the problems of whether or not platonic universals exist or of the specific nature or structure of spatially located physical particulars. Rather, I am focusing on platonist exemplification, and its alleged capacity to connect located and unlocated entities. Platonic realists typically hold that universals are spatially unlocated and physical particulars spatially located. They claim that exemplification connects, in some sense, spatially unlocated universals to spatially located physical particulars, and thereby connect what are, according to Russell, “radically different” types of entities. Russell makes this claim when referring to the relation “is north of.” Being a universal, this relation is, according to Russell, “radically different… [from] everything that can be apprehended by the senses or by introspection…” (p. 98) On page 93 Russell states what he means by everything apprehended by senses or by introspection: “We speak of whatever is given in sensation, or is of the same nature as things given in sensation, as a particular; by opposition to this, a universal will be anything which may be shared by many particulars…” [1] .

A perceived need for exemplification arose from the theories of abstract objects that originated with Plato in his discussion of Forms (or Ideas) [2] , and with the debates between Aristotle and Plato. Aristotle held that a universal, say circularity, is located where the circular entity is, and Plato held that a Form is unlocated. The Aristotelian-based idea of located universals (“universals in things” [3] ) gives rise to an apparently problematic issue—the problem of multiply located entities—which is allegedly solved by introducing an ontology where universals are not in physical particulars but are connected to physical particulars by exemplification. Armstrong writes:

Plato appears to be raising this difficulty in the Philebus, 15b-c. There he asked about a Form: “Can it be as a whole outside itself, and thus come to be one and identical in one thing and in several at once,—a view which might be thought to be the most impossible of all?” … A theory that kept universals in a separate realm from particulars would at least avoid this difficulty! [4]

According to most accounts of Aristotelian realism, a single entity can simultaneously exists at more than one spatial location: Sphericity, for example, is a single abstract entity, but exists in many different places. Many philosophers have found this problematic since it may be troublesome to consider that one entity is at two locations [5] . Armstrong, writes:

One thing that has worried many philosophers, including perhaps Plato, is that on [the Aristotelian view, where universals are in things,] we appear to have multiple location of the same thing. Suppose a is F and b is also F, with F a property universal. The very same entity has to be part of the structure of two things at two places. How can the universal be in two places at once? [6] (Emphasis mine.)

“One entity located at two places” arguably is not a description of one entity but of two entities; and it is thus arguable that a universal, being one entity multiply located, is self-contradictory inasmuch as it is both one entity and more than one entity simultaneously.

Therefore, a need was felt to solve this prima facie problem by maintaining that an apparently multiply-located entity is not in fact multiply-located. This can be done by espousing a metaphysics where (1) universals are unlocated, and (2) universals are exemplified by located physical particulars. A universal can be exemplified without being where the physical particulars are, thus explaining circularity’s merely apparent multiple locatedness in nature. This scenario seems to solve the problem of multiply-located entities, but further examination shows that this scenario—the platonist scenario—being dependent on the notion of exemplification, has serious problems of its own, as will be discussed below.

Contemporary platonism (a descendent of Plato’s old theory of Forms) is briefly described by Jubien, where “having” is used to mean exemplifying.

For a Platonist, properties are entities that exist apart from and independently of the things that have [exemplify] them. So, if a thing has [exemplifies] a property, it must be that the having [exemplifying] is a certain relation that holds between the thing and the property. [7] (Emphasis mine.)

Spatially unlocated platonic universals are still widely assumed to exist by such present platonists as Plantinga [8] , Tooley [9] , Bealer [10] , Hale [11] , Butchvarov [12] , L. Nathan Oaklander and Quentin Smith [13] , Craig [14] , Hochberg [15] , Grossman [16] , Leftow [17] , and many others. (Theistic platonists, such as Alvin Plantinga and Brian Leftow, hold that platonic abstract entities exist independently of the human mind, but exist in God’s mind. Atheist platonists, such as Michael Tooley and George Bealer, hold that universals exist independently of any mind.) Despite the fact that such platonist universals are unlocated and thus are “radically different” types of entities than the physical particulars to which they are tied, platonists apparently do not consider the exemplification connection problematic, perhaps due to the fact that exemplification is held to be primitive. In discussing platonism in his lucid book Metaphysics: A Contemporary Introduction [18] , Michael Loux discusses exemplification’s primitivism, as given by the platonist position: “[platonists] will insist that, on their view, the nexus of exemplification serves to tie universals and particulars, and they will claim that… this notion is ontologically basic or primitive...” [19] (Emphasis mine.) Reinhardt Grossman also says exemplification is indefinable:

What relationship, then, does the property have to different things? Well, it is precisely that unique relationship which properties generally have to the things that have them. I called this indefinable relation… exemplification. Plato is a human being, that is, he exemplifies this property; Aristotle is a human being, and this means that he, too, exemplifies the very same property. [20] (Grossman’s emphasis.)

(Whether or not Plato and Aristotle are nothing but spatially unlocated “souls” that exemplify spatially unlocated properties is an issue I need not address. If there is any difficulty on this score, substitute examples of mindless physical particulars.)

Whether exemplification is considered primitive or not, platonic exemplification may leave one puzzled as to how exactly it can tie or connect unlocated (~L) universals to located (L) physical particulars. Such a capacity apparently implies that exemplification’s ontological role is to connect items across realms, from the realm of the unlocated (~L) to the opposite realm of the located (L). Some philosophers have made note of this puzzling yet remarkable capacity having to do with exemplification. Armstrong writes:

Once you have uninstantiated [or unlocated] universals you need somewhere to put them, a “Platonic heaven,” as philosophers often say. They are not to be found in the ordinary world of space and time. And since it seems that any instantiated universal might have been uninstantiated… then if uninstantiated universals are in a Platonic heaven, it will be natural to place all universals in that heaven. The result is that we get two realms: the realm of universals and the realm of particulars, the latter being ordinary things in space and time… Instantiation then becomes a very big deal: a relation between universals and particulars that crosses realms. [21] (Emphasis mine.)

A description of how exactly exemplification ties or connects universals and physical particulars across these two realms is presently unavailable due to the fact that any description or analysis of the nature of exemplification is absent in the philosophical literature. It is likely that one reason for the absence of this sort of analysis or description is due to the widespread view that exemplification is primitive. The supposed primitivism of exemplification might consequently lead one to inadvertently pass over this remarkable capacity that exemplification has to tie two kinds of ontological items across the ontological realms of the unlocated and the located and yet be simple (partless), uniform, and continuous from one realm to the other. An interesting example of this absence of discussion is Shoemaker’s “Causality and Properties” [22] , where throughout his well-known article universals and particular objects are considered in different contexts, yet exemplification is not addressed anywhere in the paper. Another example of this absence is found in Russell’s The Problems of Philosophy [23] , Chapter 9, where universals and relations are discussed in detail, but where no mention is made of exemplification. [24]

We must be clear that this ontological realm-crossing tie is not a normal relation or property; for it is precisely these normal relations and properties that are tied to the located physical particulars by the tie of exemplification. The relation besides is not a realm-crossing relation or dyadic property; rather, according to the platonist, this dyadic property exists only in the realm of the unlocated and it is connected to located physical particulars by the exemplification tie. The dyadic property besides does not exist in both realms or connect the two realms; rather, it exists only in the unlocated realm and is connected to the located realm by means of an exemplification tie whose ontological role is to tie something unlocated (e.g., besides) to something located (e.g., my chair and my computer). The dyadic property besides is not directly attached to the chair and computer; rather the dyadic property is directly attached to the exemplification tie. Likewise, the chair and computer are also not directly attached to the dyadic property, besides; they are directly tied to the exemplification tie, which itself is directly attached to the chair and computer. We have four distinct entities (in the broadest possible sense of this term), the dyadic properties besides, the particular, the chair, a second particular, the computer, and the exemplification tie. The dyadic property, besides, the chair and the computer are not directly attached to each other; rather these three together merely form an unordered set [chair, computer, besides]. The three members of this set are directly attached to the exemplification tie, in such a way as constitute the chair’s being besides the computer. Here “being” in “being besides” expresses the exemplification tie. “Being” is here the “being” of n-adic predication (or, as we more normally talk, the “is” of predication, except by talking of n-adic predication I am using “predication” in a wider sense that includes predicating  relations (polyadic properties)).

Exemplification is not an n-adic property precisely because exemplification does not itself need to be exemplified by an n-adic property to the particular; instead it directly attaches to both the property and the particular. 

On the typical platonic theory, it is false that the tomato exemplifies exemplifies redness, since exemplification is directly attached to redness and is also directly attached to the tomato; the tomato exemplifies redness.  The phrase “exemplifies exemplifies redness” is either a category mistake or is a redundant way of saying “exemplifies redness”.

It is worth emphasizing these distinctions for the sake of further clarifying what is meant by “exemplification”. It is this exemplification tie that we refer when we say that the chair has the relation of besides to the computer (. . .has . . . to . . ). It is also expressed by the predicative “is” when we say “the chair is besides the computer”. And when we say that the chair stands in a relation or dyadic property, namely, besides, to the computer, we use “stands in a relation . . .to” to designate the exemplification that is directly attached to besides, the chair and computer. “Two things x and y stand in the relation R” means (in my terminology) “the two things exemplify the dyadic property R”.

My basic thesis can now be re-emphasized: the connection of the unlocated to the located is not a problem about the unlocated n-adic properties and the located particulars that exemplify them. Rather, the problem is how exemplification is able to tie the unlocated to the located.

Platonic realists note that there is a difference between exemplification and normal relations and properties, but do not go beyond merely noting this difference.

For example, Loux writes:

Realists… generally concede that realism would be viciously regressive were exemplification a relation notion categorically like the more familiar relations to which it applies, realists take this claim to provide the parameters for formulating a theoretically adequate version of realism rather than a refutation of their view. What the claim shows, realists tell us, is that exemplification is a tie or a nexus rather than a relation. Now, nominalists may find the different version of the objection that realism is regressive more powerful than realists themselves claim they are; and they may find the realist’s denial that exemplification is a relation ad hoc and the distinction between ties or nexus and relations artificial. [25]

Regarding the ad hoc charge, it may be said that platonic realists have merely asserted that exemplification is different than n-adic properties and things, but have not explained how this is the case. If exemplification is propertyless, some might find it difficult to consider that, for instance, exemplification does not have the property of being itself, does not have the property of being exemplification, and does not have the property of being propertyless. If a given exemplification, call it exemplification₁, does have properties, it would exemplify properties by way of a different exemplification tie, exemplification₂. If exemplification₂ exemplifies properties, exemplification₃ would be needed to tie exemplification₂ with its properties, and an infinite regress ensues. But these are not the only troubling questions that arise, or even the most fundamental ones. 

2.  Some Questions about Exemplification

Platonic exemplification has two direct attachments—for lack of a better word: a universal, which is unlocated (~L), and a physical particular, which is located (L). Exemplification must directly connect to each attachment in order that there be a continuous and uniform connection between n-adic universals and physical particulars. [26] Since the platonist typically asserts, without further explanation, that exemplification is primitive, platonists might have to explain how exemplification is continuous and uniform, and yet at the same time reaches across ontological realms from the located to the unlocated to thereby connect the two.  

In contrast to the widespread philosophical position that exemplification is primitive, I will argue that exemplification may not be primitive. Although exemplification is an integral element in the platonist model of reality, there have been virtually no articles written about it. What literature does exist, as far as I can tell, is confined to short passages in books, which usually make it known in short fashion that exemplification is primitive, but where no reasoning follows to explain why this is the case. Therefore, platonists have not justified why exemplification is primitive, but have simply asserted it to be so. Primitivist exemplification has thereby remained unquestioned, but I intend to question it in this section.

Since any entity is either L v ~L, then exemplification is L v ~L. And since exemplification is purported to be a continuous (unbroken) and uniform connection between unlocated (~L) universals and located (L) physical particulars, then exemplification would involve a continuous and uniform connection between an L entity and a ~L entity. If coherent, this could only occur in one of two ways:

1. Exemplification is partless, and thus is either a wholly located or wholly unlocated entity. In order that exemplification be a continuous and uniform connection of universals to physical particulars, exemplification, which is L v ~L, would have to connect to both L and ~L entities.

2. Another possibility is that exemplification is both located and unlocated, and therefore is composed of two or more parts: where at least one part is located (and directly connected to the located physical particulars), and where at least one part is unlocated (and directly connected to the unlocated universal). In order that exemplification give rise to a continuous and uniform connection of universals to physical particulars, these located and unlocated parts of exemplification would somehow connect to each other.

Since exemplification is a continuous and uniform connection between universals and physical particulars, points 1 and 2 suggest that exemplification involves some means where L and ~L are continuously integrated. Platonists, however, have not explained or rendered intelligible how exemplification could have such a capacity. Such a connection seems problematic, for the following two reasons.

Unlocated entities do not have surfaces. But since humans understand connections between physical entities according to surfaces and extensions, it is unclear how surfaceless and unextended entities (universals or exemplification) can be connected or attached to entities with surfaces and spatial extensions (physical particulars). There is no understood mechanism of uniform and continuous connecting of unextended and unlocated entities with extended and located physical things. Platonists may have to outline and justify a mechanism of the connecting of unextended, surfaceless, spatially unlocated entities to physical entities, since without such a mechanism, it is unclear how exemplification can connect or tie properties to located things.

The situation I am delineating is perhaps analogous to the problem Descartes encountered in his attempt, and failure, to maintain that cogitans (immaterial and unextended) interact or communicate with existans (material and extended). Descartes understood that physical things impact one another through contiguity, but Descartes could not explain a mechanism for how nonphysical and unextended entities (cogitans) contact, influence, or connect to physical entities (existans). As seen with the work of Descartes, this problem has no solution.

Unlike Descartes, platonists have not attempted to show that unlocated and unextended entities directly connect to physical particulars. Rather, they assert that the exemplification tie, acting as a primitive intermediary, directly attaches to universals and physical particulars, in order that universals tie to physical particulars. But this is of no consolation, since problems, such as those which Descartes faced, arise with the problem of exemplification. Exemplification does not avoid the dilemma Descartes came to, but hides it, and exemplification takes on the problem of somehow providing a continuous and uniform connection of the immaterial (abstracta) to the material (concreta). Platonists must justify how the immaterial can directly connect, via exemplification, to the material.

I will now put aside the problems of surfaceless and unextended connections, and consider a different problem having to do with exemplification, and the circumstances of 1 and 2 above. It is difficult to understand how a continuous and uniform connection might take place at all between located and unlocated entities. It appears that if a located entity is to connect to an unlocated entity, these entities must somehow continuously and uniformly connect. Such a continuous and uniform connection would require either that the unlocated entity “reach across” the realms in order to be at a place and to thus attach to or connect to the located entity, or vice versa. Since the located cannot fail to be at a place, what is unlocated then must indeed “reach across” to the located, in order to connect to the located. Since the located can only be at a place, the unlocated must become located, or must somehow be at a place, if it is to connect to a located entity. Similarly, located entities would have to “reach across” the realms in order to become unlocated, if they were to connect to the unlocated. However, how this occurs is not only unexplained, it is also apparently self-contradictory: in order that such a continuous and uniform connection occur between a located and unlocated entity, either a located entity must not be at a place, or an unlocated entity must be at a place. But by the definition of “unlocated”, what is unlocated cannot be at a place lest it be located; and by the definition of “located”, what is located cannot fail to be at a place lest it be unlocated. If exemplification is indeed a continuous and uniform connection between properties and things, exemplification apparently involves such contradictory features. Platonists however have not outlined or justified a means by which such an apparently self-contradictory connection can occur. It is simply assumed that exemplification somehow connects with both physical particulars and universals.

For a reader who objects, wishing to state, for example, that “unlocated universals just simply can and do attach to located physical particulars, period,” this reader will have to present some justification for this assertion, since it is certainly not self-evident. This reader will need to show how exemplification avoids the difficulties and apparent contradictions, which I have discussed above, that arise when one postulates a connection between located and unlocated entities. If another reader objects by maintaining that “exemplification” is a metaphor that refers to a primitive relationship that is not spatial, this still would not avoid the basic problem which I have explained up to this point: How can a given entity, of any sort—metaphorically described or nonmetaphorically described, spatial or nonspatial—directly attach to an unlocated entity (an universal) and to a located entity (a physical particular) in a way that avoids or overcomes the problems just discussed?

3. Conclusion

The problem of exemplification I have discussed in this paper is a problem to which I see no solution. My intention in this essay has been to bring this problem to the attention of platonists. I am interested in seeing if or how platonists, such as Evan Fales, Alvin Plantinga, Brian Leftow, Nicholas Wolterstorff, Michael Tooley, George Bealer, Panayot Butchvarov, etc., can solve this problem. Until it is resolved, it appears that metaphysical theories, such as nonreductive possible world metaphysics, may be unjustified, as they as make use of platonism, which is an apparently self-contradictory ontology. [27]  

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