Problems with the

Platonist Exemplification Tie between Located

Entities and an Unlocated Entity

JEFFREY GRUPP   Western Michigan University

1. The Platonist Exemplification Tie

Although this paper is about platonism, I do not address commonly discussed platonic ontological issues, such as whether or not spatially unlocated platonic universals exist, or the specific nature of spatially located physical particulars. Rather, I concentrate on the platonist exemplification tie between a spatially unlocated platonic universal and spatially located physical particulars, and the platonist exemplifications tie’s alleged capacity to connect, in some sense, located entities and an unlocated entity. Many theories about spatially unlocated platonic universals and spatially located physical particulars have been developed by platonic realists, but few accounts of the platonist exemplification tie that connects them have been offered. Platonic realists, such as Bealer (1982), Butchvarov (1979),

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Craig (2000), Grossman (1992), Hale (1987), Hochberg (1981), Leftow (1991), Moreland (2001), Oaklander and Smith (1994), Plantinga (1974), Tooley (1987), and many others, do not appear to find the platonist exemplification tie problematic, despite its remarkable capacity to connect spatially located entities to a spatially unlocated entity.

Despite the importance of the platonist exemplification tie’s role of holding a universal and particulars together, there has been virtually nothing written about it. What literature does exist is confined to short passages, which usually make it known in short fashion that the platonist exemplification tie is primitive (eg., Grossman 1992, p. 20), but where no reasoning follows to explain why this is the case, or to explain what precisely exemplification’s primitivism involves (for example, does primitiveness require exemplification to be partless, even though exemplification connects to distinct, non-collocated spatial particulars?). It is perhaps for reasons such as these that the platonist exemplification tie remains unquestioned. I argue here that platonists might have to explain how exemplification is a continuous and uniform entity (where I use the word “entity” in the broadest sense of the word), while also having the capacity to connect spatially located entities to a spatially unlocated entity.

When the platonist exemplification tie is mentioned, philosophers frequently ignore its noteworthy capacity to connect an item in the realm of the unlocated to items in the realm of the located. An exception is Armstrong, an Aristotelian realist (Aristotelian realism is also called moderate, or minimalist realism), who discussed it in an interesting passage:

Once you have uninstantiated universals [spatially unlocated, unexemplified 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. (Armstrong, 1989, p. 76, my emphasis)

A realm-crossing tie is not part of Aristotelian realism, since the latter does not involve uninstantiated, unlocated universals connecting to what could be located particulars. Aristotelian realism involves the Aristotelian-based idea of located (immanent) universals (“universals in things”). (Armstrong, 1989, p. 77, and 2001, p. 66; Price, 2001, p. 23). But located universals lead to an apparently problematic issue—the problem of a multiply located entity—which is allegedly solved with an ontology where universals are not in physical particulars, but are unlocated, and connected

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to physical particulars via a realm-crossing tie. Accordingly, a universal can be exemplified without being where the physical particulars are, thus explaining a universal’s merely apparent multiple locatedness in nature. But while placing universals outside of space may solve various ontological problems, the platonist exemplification tie needed to connect them to located particulars leads to other problems, which I discuss below.

The platonist exemplification tie may leave some philosophers wondering exactly what the mechanism is involved in the connecting of unlocated and located entities, and what the specific nature of the platonist exemplification tie is. The realm-crossing tie, platonists tell us, is not an ordinary platonic n-adic property, since ordinary platonic n-adic properties do not cross realms. Also, platonist exemplification is not an ordinary platonic n-adic property precisely because it does not itself need to be exemplified by an ordinary platonic n-adic property to the particular. On the typical platonist theory, it is false that a lion exemplifies exemplifies ferocity, since exemplification is directly attached to ferocity and is also directly attached to the lion. The phrase “exemplifies exemplifies ferocity” is either a category mistake or is a redundant way of saying “exemplifies ferocity”.

     Some philosophers hold that the platonist exemplification tie is a special relation;[1] others hold that it is an infinite regress of relations,[2] and others may argue it is a non-relational tie.[3] I am not concerned here with which of these positions is correct. Rather, my concerns are merely to establish that the platonist exemplification tie is an entity (in the broadest sense of the world “entity”) and that the platonist exemplification tie, whatever its nature, connects a spatially unlocated universal to spatially located physical particulars by directly attaching to both the universal and particulars.

2.  Exemplification and the Connection of Located and Unlocated Entities

I have been using “connection” to denote the tie between a universal and particulars, between an unlocated entity and located entities, where unlocated entity and located entities are not directly attached, but are mediated by the exemplification tie. In this section, I use “direct attachment” to express the concept of a connection between entities which does not involve an intermediary. Direct attachment is how the exemplification tie attaches to the property and particulars. (Loux 1998, 38-41).

The platonist exemplification tie has two direct attachments: a platonic universal, which is unlocated, and at least one physical particular, which is located, and it must directly attach to each attachment in order that there be an intermediary connection between the unlocated universal and the located physical particular(s). The connection between property and particular across the realms of the unlocated and the located is not an issue having to do with the attachments (property and particulars); rather, it involves the realm-crossing exemplification tie: how the platonic exemplification tie is able to connect an unlocated entity to located entities.

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       Since the platonist exemplification tie is purported to be a continuous (unbroken) and uniform connection between a spatially unlocated universal and spatially located physical particulars, and since the platonist exemplification tie would involve a direct attachment to the spatially located entities and to the spatially unlocated entity, the exemplification of a platonic universal by a physical particular involves direct attachments of wholly located and wholly unlocated entities for the following reasons:

(1)   If the platonist exemplification tie is partless (simple), it is either wholly located or wholly unlocated. In order that the platonist exemplification tie be a continuous and uniform connection between a platonic universal and physical particulars, the platonist exemplification tie would have to directly attach to both an unlocated entity and to located entities, where one of these direct attachments is a direct attachment of located and unlocated entities.

(2)   Another possibility is that the platonist exemplification tie is both located and unlocated, and therefore is composed of two or more parts, where at least one part is spatially located (and directly attached to physical particulars) and where at least one part is spatially unlocated (and directly attached to the platonic universal). In order that the platonist exemplification tie give rise to a continuous and uniform connection between the platonic universal and physical particulars, these located and unlocated parts of the platonist exemplification tie would somehow directly attach.

Since the platonist exemplification tie is a connection between a platonic universal and physical particulars, both points suggest that the platonist exemplification tie involves some means by which a spatially located entity and a spatially unlocated entity are directly attached. Platonists, however, have not explained or rendered intelligible how the platonist exemplification tie could involve such a capacity. My recent article (2003) however, argues that a direct attachment of a located entity and an unlocated entity, such as the direct attachments described in points (1) and (2), is impossible, since such an attachment requires the unlocated entity to be in space, at a spatial place, since the located entity is necessarily spatially located. In order for the unlocated entity to directly attach to the located entity, the unlocated entity must be where the located entity is—by definition, in space. But it is a contradiction for an entity to be unlocated and located at the same time. I will, however, ignore this argument, and follow the complaints of some philosophers who may object to its reasoning, for the very reason that platonistic exemplification need not involve discussion of such “realm crossing” intermediaries, or “direct attachments across realms”, and need not involve any discussion at all, since the platonist exemplifica-

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tion tie is ontologically primitive. But a primitivist platonist property exemplification may be impossible, for the following reasons.

     Consider an exemplification tie between a wholly spatially located entity, L, a lion,[4] and a wholly spatially unlocated platonic universal, S, sublimity, which the lion has (exemplifies): L has S. Being a physical object, L cannot fail to be at a spatial location, x. This implies that L only exemplifies n-adic properties (such as, exemplifying the property, sublimity) at x and nowhere else, since wholly located entity L is nowhere else but at x. An exemplification not at x is an exemplification that does not have to do with L. S, being a wholly spatially unlocated entity, cannot fail to be spatially unlocated—call this being at y—and this implies that S only involves a direct attachment to the exemplification tie while at y, since S is nowhere else but at y. A direct attaching with the exemplification tie that is not at y is a direct attaching that does not have to do with S. This implies that L and S could not be tied by exemplification, according to the typical account of platonistic metaphysics, for the following reasons. If L exemplifies n-adic properties only at x, if S involves a direct attachment to the exemplification tie only at y, and if the exemplification tie does not cross realms, since x≠y, then L and S apparently cannot have any sort of dealings with one another (such as being tied by the tie of exemplification). It appears that in order for L to tie to S, S, which is wholly at y, must be at x, and thus must apparently take on characteristics that are self-contradictory; or L, which is wholly spatially located at x, must be spatially unlocated at y, and thus must take on characteristics that are self-contradictory. (This apparent contradiction ensues regardless of whether or not exemplification is considered primitive and unanalyzable.)   

Platonists have not outlined or justified a means by which such an apparently self-contradictory connection can occur between property and particular. Without a coherent mechanism of direct attachment of located and unlocated entities, the platonist exemplification tie cannot be a connection of a spatially unlocated platonic universal and spatially located particulars, and properties and things apparently are not held together according to platonism.

A reader who objects, wishing to state, for example, that “an unlocated universal unequivocally can and does attach to located physical particulars,” will have to present some justification for this assertion, since it is certainly not self-evident. This reader will need to show how the platonist exemplification tie avoids the difficulties and apparent contradictions that arise when one postulates either a connection via an intermediary, or a direct attachment, between located and unlocated entities. If another reader objects by maintaining that “the platonist exemplification tie” is a metaphor that refers to a primitive relationship that is not spatial, this still would not avoid the basic problem, i.e., how can a given entity, of any sort—metaphorically described or non-metaphorically described, spatial or

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non-spatial—can directly attach to an unlocated entity (a universal) and to located entities (physical particular) in a way that avoids or overcomes the problems just discussed?

3. Conclusion

The problem of the platonist exemplification tie is one to which I see no solution since a continuous and uniform integration between spatially located and spatially unlocated entities apparently involves contradictions. My intention in this essay has been to express this problem for platonists to work out. I am interested in learning how or if platonist philosophers, such as Smith, Oaklander, Craig, Fales, Hochberg, Plantinga, Grossman, Leftow, Wolterstorff, Tooley, Bealer, Butchvarov, etc., can solve this problem. Until it is resolved, it appears that not only do platonists have a contradictory description of how properties and things hold together, but also the metaphysical theories that make use of platonism, such as Plantigan possible world metaphysics or platonist ontologies of mathematical objects, might also be considered contradictory.

       The problem I outline here might be applicable to any philosophical work that maintains a continuous and uniform integration between spatially located and spatially unlocated entities. Examples are easy to find, particularly in the metaphysics of time, numbers, mind, causation, ordinary objects, and religion, where philosophers often allow or argue for a connection between located and unlocated entities. For example, in a recent article, Markosian briefly discusses an aspect of the long-standing philosophical position that a human being has unlocated (nonphysical) and located (physical) parts, which appears to affirm a connection or continuous integration between a located entity and an unlocated entity:

[T]he best account of physical objects is this: a physical object is an object with a spatial location… The intuitive idea [involved here] is this. Objects from all of the different ontological categories—physical objects; non-physical objects like souls, if there are any; propositions; universals; etc.—have this much in common: they all exist in time. But not all of them exist in space. The ones that exist in space, i.e., the ones that have spatial location are the ones that count as physical objects. Thus souls, if there are any, are objects with temporal locations but without spatial locations. They might interact with objects in space. And if it turns out that a living person is a composite object, with one physical part (i.e., spatially located) part and one non-physical (i.e., not spatially located) part, then [this criterion] will entail that living people are partly physical and partly nonphysical. (2000, p. 377;my emphasis)

           My criticism of platonism in this article involves what appears to be a contradictory connection between physical particulars and platonist universals. But this objection is apparently applicable to any philosophical

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theorization that asserts, or implies, or argues for, a direct attachment or continuous connecting between a spatially located entity and a spatially unlocated entity. Such philosophical work, whether presented as platonist or not, by my argumentation in this paper, appears to be contradictory. Perhaps new work in philosophy will result from the possibility that my conclusions show that either there is only a located realm, or if there are both unlocated and located realms, these realms cannot influence each other.[5]

Notes

References

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