Metaphysica

, Volume 11, Issue 1, pp 63–78

A Novel Interpretation of Plato’s Theory of Forms

Authors

    • Department of PhilosophyUniversity of Iowa
Article

DOI: 10.1007/s12133-010-0059-x

Cite this article as:
Monaghan, P.X. Int Ontology Metaphysics (2010) 11: 63. doi:10.1007/s12133-010-0059-x
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Abstract

In several recent issues of this journal, I argued for an account of property possession as strict, numerical identity. While this account has stuck some as being highly idiosyncratic in nature, it is not entirely something new under the sun, since as I will argue in this paper, it turns out to have a historic precedent in Plato’s theory of forms. Indeed, the purpose of this paper is twofold. The first is to show that my account of property possession can be utilized to provide a novel interpretation of Plato’s theory of forms. And the second is to show that once it has been divorced from a variety of implausible doctrines with which it has historically been wedded, Plato’s central insight that all properties possess themselves, far from being of mere historical interest, is independently plausible, ironically enough, even from an empirical point of view.

1 I

In several recent issues of this journal,1 I argued for an account of property possession as strict, numerical identity.2 While this account has stuck some as being highly idiosyncratic in nature,3 it is not entirely something new under the sun, since as I will argue in this paper, it turns out to have a historic precedent in Plato’s theory of forms. Indeed, the purpose of this paper is twofold. The first is to show that my account of property possession can be utilized to provide a novel interpretation of Plato’s theory of forms. And the second is to show that, once it has been divorced from a variety of implausible doctrines with which it has historically been wedded, Plato’s central insight that all properties possess themselves, far from being of mere historical interest, is independently plausible, ironically enough, even from an empirical point of view. I begin in the following section by highlighting several of the key components of my account of property possession, as well as several of the misconceptions one might have about it.

2 II

What is it for an entity to possess a property? Over the course of the history of western philosophy, two general answers to this question have been proposed. I refer to them as externalism and internalism about property possession.

On the one hand, externalism is the view that for x to possess a property is for x to bear a certain relation (to be specified relative to the version of externalism under consideration) to a certain entity y (also to be specified in such a manner) that is external to x in the sense that y is not a part of x.4 One version of externalism is Platonic transcendent realism, which is the view that for x to possess a property is for x to instantiate a transcendent (i.e., non-spatial) universal. For example, according to this view, for x to possess the property of being red is for x to instantiate the transcendent universal redness.5 Ironically enough, as far as I am able to determine, most other versions of externalism are also versions not of realism about universals, but of nominalism, or the view that there are no such things as universals. One such version is predicate nominalism, which is the view that for x to possess a property is for x to satisfy a predicate, e.g., the predicate “is red.”6 Another version is concept nominalism, which is the view that for x to possess a property is for x to fall under a certain concept, e.g., the concept of a red entity.7 Still another version is class nominalism, which is the view that for x to possess a property is for x to be a member of a certain class, e.g., the class of all and only red entities.8 And then there is resemblance nominalism, which is the view that for x to possess a property is for x to be a member of a certain resemblance community, e.g., the class of all and only red entities.9

On the other hand, internalism is the view that for x to possess a property is for x to bear a certain relation (to be specified relative to the instance of internalism under consideration) to a certain entity y (also to be specified in such a manner) that is internal to x in the sense that y is a proper part of x. One version of internalism is Aristotelian immanent realism, which is the view that for x to possess a property is for that property to be an immanent (i.e., spatial) universal that inheres in x. Another is the version of trope theory according to which for x to possess a property is for that property to be a trope that inheres in x.10

Given the general nature of externalism and internalism, one may be forgiven for thinking that whatever exactly the correct account of property possession turns out to be, it will inevitably be a version of either the one view or the other. But it is important for our purposes to note that whatever differences there may be between the various version of those two views, they all share a presupposition in common, which is that if x possesses y as a property, then x and y are numerically distinct from each other. Now this presupposition may seem innocuous at first, perhaps even self-evident. But as I have argued elsewhere, since externalism and internalism are both founded upon this presupposition, they are actually founded upon a mistake.11 Accordingly, I advocate an account of property possession as strict, numerical identity. According to this account, for x to possess y as a property is for x and y to be numerically identical to each other.

What does it mean to claim that for x to possess y as a property is for x and y to be numerically identical to each other? According to my initial answer to the question, it means that the following three claims are true. First, property possession is the relation that x bears to y only if y is a property that can be truly predicated of x.12 Second, identity is the relation that, necessarily, any given entity bears just to itself. And third, property possession and identity are one and the same relation.

To provide a more precise answer to the question, we must first take a short detour through mereology. Mereology is the logic of parts and wholes. It is usually formulated by taking the reflexive and symmetrical but non-transitive relation of overlap as a primitive, and by defining other mereological relations on the basis of it.13 One such relation is parthood: x is a part of y just in case y overlaps everything that x overlaps. Unlike overlap, the relation of parthood is transitive and reflexive but non-symmetric. To account for the non-symmetric nature of parthood, it is standard to draw a distinction between the relations of proper and non-proper parthood: x is a part of y just in case either x is a proper part of y, or else x is a non-proper part of y. On the one hand, x is a proper part of y just in case x is a part of y but y is not a part of y. Unlike overlap and parthood, the relation of proper parthood is transitive but anti-reflexive and anti-symmetrical. On the other hand, x is a non-proper part of y just in case x is a part of y and y is a part of x. Unlike overlap, parthood and proper parthood, the relation of non-proper parthood is transitive, symmetrical, and reflexive. Finally, x and y do not overlap each other just in case they are disjoint.

I will have more to say about mereology below. But in the meantime, there are several points concerning the metaphysics of mereology that should be noted prior to proceeding. The first is that on the standard interpretation of mereology, it is assumed that x is a non-proper part of y just in case x and y are numerically identical to each other.14 According to this assumption, whereas the proper parts of an entity are the parts of that entity to which it is not identical, the non-proper part of an entity is the part of that entity to which it is identical. In other words, according to this assumption, whereas nothing can have just one proper part, nothing can have more than one non-proper part. In this essay, I will not presuppose that this assumption is true. In fact, it seems obvious to me that it is false. On the one hand, I grant that if x and y are numerically identical to each other, then they are non-proper parts of one another. But, on the other hand, I deny that if and y are non-proper parts of each other, then they are automatically identical to one another. Now there is a rather large literature over the issue of whether there are certain objects that constitute a counter-example to the principle that x and y cannot be parts without being identical (e.g., the statue and the clay). But in my opinion, the clearest counter-examples to this principle are ones that are couched instead in terms of properties. For example, it seems obvious to me that while the color and shape of a red, rubber ball perfectly overlap each other, and so are non-proper parts of one another, they are nevertheless numerically distinct. After all, presumably that ball could still retain the very same shape even if it were painted blue.

The second point is that on the standard interpretation, the principle of mereological extensionalism is assumed to be true. According to this principle, if x and y have proper parts in the first place, then they are identical to each other just in case they share all such parts. It should be noted that this principle is to be distinguished from the more general one according to which, given any x and y, regardless of whether they have proper parts or not, they are identical to each other just in case they share all such parts; for even if there exist just two mereological atoms (i.e., entities with no proper parts), then whereas the existence of these atoms will constitute a counter-example to the latter principle, their existence will not constitute a counter-example to the former one. The principle of mereological extensionalism is also to be distinguished from the one according to which, given any x and y, they are identical to each other just in case they share all of the same parts; for if there are two mereological atoms that are parts of each other, then whereas the existence of these atoms will constitute a counter-example to the latter principle, their existence will not constitute a counter-example to the former one. Of course, if one believes that x cannot be a non-proper part of y without being identical to y, then one will reject out of hand the claim that two numerically distinct atoms can nevertheless be parts of each other. But in that case, whereas the latter principle will be trivially true, the former one will be substantively so, if true at all. Not surprisingly, I also reject the principle of mereological extensionalism as false. On the one hand, I grant that if x and y are identical to each other, then they share whatever proper parts they have in common. But, on the other hand, I deny that if x and y have all of the same proper parts, then they are automatically identical to each other, even assuming that they have proper parts in the first place. Here again the case of the color and of the red, rubber ball constitutes a counter-example.

The third and final point is that on the standard interpretation, the principle of unrestricted composition is assumed to be true. According to this principle, given any set of entities, all and only the elements of this set are the parts of some mereological whole. While I am inclined to believe that this principle is true, nothing of significance turns on this point.

We are now in a position to return to the question: What does it mean to claim that that for x to possess y as a property is for x and y to be numerically identical to each other? According to my account, to claim that for x to possess y as a property is for x and y to be numerically identical to each other is to claim that for x to possess y as a property is for y to be a specific part of x. To be sure, it is not to claim that y is a proper part of x, as some have thought.15 Rather, if one accepts the assumption that the relation of non-proper parthood only ever obtains between numerically identical entities, it is to claim that y is the non-proper part of x. Otherwise, if one rejects that assumption, as I do, it is to claim that y is the non-proper part of x to which x is identical.

To provide an even more precise answer to the question of what it means to claim that for x to possess y as a property is for x and y to be numerically identical to each other, I introduce the notion of the nature of an entity. As I define that notion, the nature of x is the more or less complex property possessed by x that is complete and total in the sense that it comprises as parts not only all of the properties that can be truly predicated of x, but also all of the properties that can be truly predicated of x (as well as whatever non-mereological relations there are that obtain between these various properties). So, for example, the nature of a red, rubber ball is the property possessed by that ball that has as parts a certain shape, size, mass, density, color, texture, and so forth. Given this definition, according to my account, for x to possess y as a property is for y to be the non-proper part of the nature of x (to which that nature is identical) and for that nature to be the non-proper part of x (to which x is identical).

At this point, there are several misconceptions concerning my account that should be noted prior to proceeding. The first is that one might believe that my account requires the identification of relatively complex material objects, such as a red, rubber ball, on the one hand, with relatively simple properties, such as the property of being red, on the other. But this belief is mistaken. It is based, of course, on the assumption that the red, rubber ball possesses the property of being red. But since the red, rubber ball obviously is not identical to the property of being red (given that there is more to that ball than that property), that ball cannot be said to possess that property on my account. Instead, according to my account, there is more to the property possessed by the red, rubber ball than the mere property of being red. According to my account, the property possessed by the ball is a relatively complex nature that has as parts not only a certain color, but also a certain shape, size, mass, density, texture, and so forth. Indeed, one might say that according to my account, for an entity to possess a property is for that entity to possess a more or less complex nature, as long as it is understood that there is nothing more to any given entity than the nature of that entity. But even though there is nothing more to the red, rubber ball than the nature of that ball, this does not entail that there is nothing more to that nature than the property of being red.

The second is that one might believe that if the red, rubber ball does not possess the property of being red, then we cannot truly predicate that property of that ball. That is to say, one might believe that we can truly say of the ball that it is red in the first place. But this belief is also mistaken. It is based on the assumption that the relation that an entity bears to a property just in case that entity possesses that property is the relation that an entity bears to a property just in case that property can be truly predicated of that entity. But these two relations need to be distinguished from each other. On the one hand, I grant that if an entity possesses a property, then that property can be truly predicated of that entity. But, on the other hand, I deny that if a property can be truly predicated of an entity, then that entity automatically possesses that property as one of its own. Instead, I claim that if a property can be truly predicated of an entity, then that property is a part of the nature of that entity. For example, the property of being red obviously can be truly predicated of a red, rubber ball. In other words, a red, rubber ball obviously is red. So according to my account, that property is a part of the nature of that ball. Thus, a red, rubber ball can still be red without possessing the property of being red. If that ball is red, then it possesses a nature with redness as a part.

The third is that one might believe that if no relatively complex material object possesses the property of being red, then nothing will do so. But this is a mistake as well. On the one hand, I grant that just like the red, rubber ball, no complex entity (e.g., a table or chair) will possess the property of being red on my account; for just like that ball, the nature of that complex entity will have two or more properties as parts. But, on the other hand, since the property of being red is self-identical, it follows that according to my account, that property possesses itself. In other words, according to my account, if x possesses the property of being red, then x is what I call an instance of redness. If x is an instance of redness, then there is nothing more to x than the property of being red that x possesses.16 And if x is an instance of redness, then x can either be a universal or a particular.17

Of course, at this point one might think that if x is a mere instance of redness, this implies that instances of redness are capable of existing utterly independently of all other entities—floating free, as it were. But this is mistaken. For according to my account, no property can exist without being a part of the nature of some entity or other. So if x is an instance of redness, then it must be a part of the nature of some entity, such as a red, rubber ball. On the other hand, one might also object that the claim that the property of being red possesses itself amounts to a kind of category mistake. But as we will see below, I have two replies to this objection. According to the first, if one only takes the time to examine the matter with some care, one sees that it is phenomenologically obvious that the property of being red is red (where, just to be sure, this “is” is the “is” of predication, not the “is” of identity). And according to the second, if the property of being red does not possess itself as a property, then we cannot truly predicate that property of any entity at all. In other words, according to the second, if the property of being red does not possess itself, then absolutely nothing at all in the world can be red.

Finally, there are three additional implications of my account that should be noted at this time, by way of conclusion. First, according to my account, given any property, x, the following two claims are true:
  1. (1)

    x possesses itself as a property.

     
  2. (2)

    x is self-identical.

     

Second, according to my account, both claims have the very same truth-maker. And third, according to my account, that truth-maker is none other than x itself. It is important to note that x serves as the truth-maker for both claims, regardless of whether x is a relatively complex property, such as the nature of a red, rubber ball, or whether x is a relatively simple property, such as the property of being red. The fact that x serves as the truth-maker for both claims will become important in the following section, when I argue that Plato’s theory of forms constitutes an historical precedent for my account of property possession.

3 III

In the previous section, I highlighted some of the key components of my account of property possession. In this section, I show how this account can be utilized to provide a novel interpretation of Plato’s theory of forms.

As I see it, Plato’s theory of forms divides into three component parts. The first is his view on what it is for a sensible, changing thing to possess a form as a property (e.g., what it is for a painting to be beautiful). The second is his view on what it is for one form to possess a second form as a property (e.g., what it is for the form of the just to be beautiful). And the third is his view on what it is for a form to possess itself as a property (e.g., what it is for the form of beauty to be beautiful). Traditionally, this last view has been referred to as Plato’s view on the self-predication of the forms. But it is important to note that whereas the predication of properties of entities is a mind-dependent phenomenon, the possession of properties is not, or at least not to the same extent.18 So for that reason, I will continue to refer to the last of these three views in the way in which I do.

There are a variety of passages in Plato’s writings in which he claims that various forms posses themselves as properties. For example, consider the following passage from the Protagoras:

Socrates: Suppose he questioned us further: “Do you also say there is a thing called piety?” We would say we do, right?

Protagoras: Right

Socrates: “Do you say this too is a thing?” We would say we do, wouldn’t we?

Protagoras: That too.

Socrates: “Do you say that this thing is by nature impious or pious?” Myself I would be irritated with this questions and would say, “Quiet, man! How could anything else be pious if piety itself is not?” What about you? Wouldn’t you answer in the same way?

Protagoras: Absolutely (330d1-e2).19

At the same time, however, there are scant few places in Plato’s writings in which he delves into the issue of exactly what it is for a form to possess itself as a property. Of course, at this point one might be inclined to put this down to the fact that whenever he attempts to do so, he runs smack into the problem of the third man regress. But as I will explain below, this problem is easily avoided if one adopts the interpretation of Plato’s theory of forms that is based on my account.

One of the few passages in which Plato explicitly discusses what it is for a form to possess itself as a property is the following one from the Parmenides:

And [the One] won’t be different from another, as long as it is one; for it is not proper to One to be different from something, but proper to Different-From-Another alone, and to nothing else.—That’s right.—Therefore it won’t be different by being one. Or do you think it will?—No indeed.—Yet if it isn’t different by being one, it will not be so by itself; and if it isn’t so by itself, it will not itself be so. And if it is itself in no way different, it will be different from nothing.—That’s right.—Nor will it be the Same as Itself.—Why not?—The nature of the One is not, of course, also that of the same.—Why?—Because it is not the case that, whenever a thing comes to be the same as something, it comes to be one.—But why?—If it comes to be the same as the many, it must come to be many, not one.—True.—But if the one and the same in no way differ, whenever something came to be the same, it would always come to be one; and whenever it came to be one, it would always come to be the same.—Certainly.—Therefore, if the One is to be same as itself, it couldn’t be one with itself; and thus it will be one and not one. But surely this is impossible. Therefore the One can’t be either different from another or the same as itself.—It can’t.—Thus the One could neither be different from nor the same as itself or another.—Yes, you’re quite right (139 c-d).

Now I admit that this is a difficult passage from an already difficult dialogue. But, nevertheless, in it Plato seems to be making the following two claims. The first is that even though the form of the One possesses what we might call the property of being different than another, that form’s possession of that property and that form’s being self-identical do not amount to one and the same phenomenon.20 Instead, it seems that the form of the different-than-another’s possession of itself as a property and its being self-identical amount to one and the same phenomenon. The second is that even though the form of the One also possesses what we might call the form of being the same as oneself, not even this form’s possession of this property and that form’s being self-identical amount to one and the same phenomenon. Instead, it seems that the form of the same-as-oneself’s possession of itself as a property and its being self-identical amount to one and the same phenomenon. Taken together, these two points seem to have the following two implications by parity of reasoning. The first is that the form of the One possesses itself as a property. And the second is that the form of the One’s possession of itself as a property and its being self-identical amount to one and the same phenomenon. And it is this notion (i.e., the notion of a form’s possession of itself as a property and its being self-identical amounting to one and the same phenomenon) that is the cornerstone of my interpretation of Plato’s theory of forms.

How is this notion to be analyzed? There are two reasons why I do not attempt to analyze it in terms of a form’s bearing the relation of participation to itself. The first is that, as far as I am able to determine, Plato regards the relation of participation as one that only ever obtains between entities that are numerically distinct from each other (i.e., between a sensible, changing thing and a form or between one form and another). This is a point to which I will return below. And the second is that I do not believe that this notion is to be analyzed in terms of a relation in the first place, regardless of whether this relation is identified with participation or not.

Instead, to analyze the notion, I utilize the idea of properties as truth-makers that was discussed in the previous section. On my interpretation, according to Plato, given any form, the claim that this form possesses itself as a property and the claim that this form is self-identical are both true. On my interpretation, according to him, both claims have the very same truth-maker. And on my interpretation, according to him, that truth-maker is none other than that form itself. So, for example, on my interpretation, according to Plato, the claim that the form of beauty is beautiful and the claim that the form of beauty is the form of beauty are both true. On my interpretation, according to him, both claims have the same truth-maker. And on my interpretation, according to him, that truth-maker just is the form of beauty. In other words, on my interpretation, according to Plato, the form of beauty is beautiful simply by virtue of its being the form of beauty. And in this sense, on my interpretation, according to him, it is beautiful intrinsically.

Given this analysis, my interpretation of Plato’s theory of forms can be stated quite simply as the conjunction of the following two claims. The first is that according to Plato, if a thing possesses a form as a property, then if that thing is numerically identical to that form, then that thing possesses that form as a property intrinsically in the manner described above. And the second is that according to him, if a thing possesses a form as a property, then if that thing is numerically distinct form that form (i.e., if it is a sensible, changing thing, or if it is a form other than the first one), then that thing possesses that form as a property extrinsically by bearing the relation of participation to it. As I said above, as far as I am able to determine, Plato regards the relation of participation as one that only ever obtains between numerically distinct entities. At the same time, however, on my interpretation, that relation is nevertheless one of resemblance in the sense that if one thing bears that relation to a second thing, then those two things will resemble each other in a certain respect. For example, on my interpretation, if a sensible, changing thing participates in the form of beauty, then that thing and that form will resemble each other in the respect that they are both beautiful. Now there are some occasions on which Plato seems to suggest that if a sensible, changing thing participates in (for example) the form of beauty, then that thing will be beautiful to the very same extent as that form. But there are other occasions on which he seems to suggest instead that even if a sensible, changing thing participates in the form of beauty, the beauty of that form will still surpass the beauty of that thing. Thus, it should be noted that my interpretation is neutral on this issue. In any case, in the end, on my interpretation, it turns out that Plato’s theory of forms is similar to the view known as Aristocratic resemblance nominalism. On this theory, if an object is beautiful, it is beautiful in virtue of its resembling a small subset of the set of all beautiful things, i.e., the resemblance paradigms (this view is to be contrasted with the one known as Egalitarian resemblance nominalism, according to which, if an object is beautiful, it is beautiful by virtue of its resembling all of the elements of the set of beautiful things).21 Of course, it should also be noted that on my interpretation, Plato’s theory of forms is not equivalent to Aristocratic resemblance nominalism. For whereas according to that version of nominalism, resemblance paradigms are not to be identified as properties, according to Plato’s theory, resemblance paradigms are to be identified as properties, given that they are to be identified with forms.

At this point, prior to proceeding, it is important to note what my interpretation of Plato’s theory does and does not imply. On the one hand, that interpretation implies that according to Plato, given any x, if x is identical to a form, then x possesses that form as a property. But, on the other hand, that interpretation does not imply that according to Plato, given any x, if x possesses a form as a property, then x is identical to that form. Again, there are two types of counter-example to this last claim. In the first, a sensible, changing thing possesses a form as a property by bearing the relation of participation to that form. And in the second, one form possesses a second form as a property also by bearing that relation to that form. Thus, even though on my interpretation, Plato regards all forms as possessing themselves as properties, he still believes that it is possible for one thing to possess a second thing as a property. And for this reason, his theory of forms cannot be taken as equivalent to my account of property possession as identity. This is a point to which I will return the following section.

Finally, it should be noted that on my interpretation of Plato’s theory of forms, that theory is able to avoid the third man regress.22 On the one hand, I grant that according to my interpretation of Plato’s theory, if a group of things are F (e.g., large) and if the form of the F (e.g., the form of the Large) is not a member of that group, then the members of that group are F by virtue of their partaking of or participating in something that is not a member of that group (i.e., the form of the F). But, on the other hand, I deny that according to my interpretation of Plato’s theory, if a group of things are F, and if the form of the F is a member of that group, then the members of that group are F by virtue of their participating in or partaking of something that is not a member of that group (i.e., some second form of the F). To be sure, according to my interpretation of his view, all of the members of that group other than the form of the F are F by virtue of participating in that form. But according to my interpretation, the form of the F itself is F by virtue of its possessing itself as a property. In other words, it is F intrinsically.

4 IV

In this section, I conclude by arguing that once it has been stripped from a variety of implausible doctrines with which it has been historically associated, Plato’s central insight that properties possess themselves, far from being of merely historical interest, is independently plausible, even from an empirical point of view.

Since my account of property possession as identity can be utilized to provide an alternative interpretation of Plato’s theory of forms, I regard that theory as a historical precedent for my account. At the same time, however, there are three reasons why my account and Plato’s theory are not equivalent to each other. The first is that whereas according to Plato’s theory, it is possible for one entity to possess a second entity as a property, according to my account, this is not possible. As we have seen, according to Plato, there are two cases in which one entity will possess a second entity as a property. In the first, a sensible, changing thing will participate in a form, and in the second, one form will participate in another. But as we have also seen, according to my account, given any entity, the only property that this entity will possess is the more or less complex nature to which that entity is numerically identical.

The second is that whereas Plato believes that a predicate is meaningful only if it corresponds to its own genuine property, I do not.23 For example, according to Plato’s theory, since the predicate “is a Chicago Cubs fan” is meaningful, it must correspond to the property of being a Cubs fan; since the predicate “is a nice guy” is meaningful, it must correspond to the property of being a nice guy; since the predicate “is a mathematically-gifted unicorn” is meaningful, it must correspond to the property of being a mathematically gifted unicorn; and so on and so forth. But not every meaningful predicate can correspond to its own genuine property. Consider the predicate “is a property that is possessed by all properties that do not possess themselves.” Even though this predicate is meaningful, it cannot correspond to a genuine property, given that if such a property existed, then since (1) either it would possess itself or else it would not do so and (2) it would possess itself just in case it did not, that property both would and would not possess itself, which is absurd. On my account, if the predicate “is a Cubs fan” applies to a person, it does so because that person gets a whoosh of certain chemicals in his or her bloodstream on those rare occasions on which the Cubs manage to win a game. It is not because that person participates in the form of Cubs fanhood.24

The third reason is that whereas Plato regard all properties as being non-spatial, I do not. In fact, I regard all of them as being spatial. As Aristotle reports, Plato’s philosophy is a combination of the influence of Heraclitus and Socrates.25 On the one hand, Plato agrees with the latter in thinking that there are some things that can be defined. But, on the other hand, he believed that sensible, changing things cannot be defined, since he agreed with the former in thinking that (as he puts it in the Timaeus) those things are continuously coming to be and passing away in such a manner that they never really are.26 Thus, according to Plato, things amenable to definition are somehow separate from sensible, changing things, and he referred to these things amenable to definition as the forms. Now I grant that Plato’s argument is valid, though there remains the issue of exactly what separation amounts to in this context.27 But I deny that it is sound, since I deny the truth of the Heraclitean premise. Instead, I take it as a datum of metaphysics that there are at least some entities that are ontologically stable enough to satisfy various predicates, e.g., “is red,” “is round”, and so forth. But if there are entities that are stable at least to this extent, it follows that they are stable enough to be defined (which, of course, is not to say that they are actually amenable to definition).

As far as I am able to determine, the strongest contemporary argument for the claim that all properties are non-spatial is the one offered by Evan Fales. He writes:

We do not wish to say that universals exist in space and time. If they did so exist, it would obviously be “as” their instances that they existed. Such instances can be created and destroyed; they can change their location. But these vicissitudes cannot be shared by the things which these instances have in common; for it is precisely in respect of their temporal duration and spatial location, that instances differ. And if universals are in space and time, then spatiotemporal relations characterize universals. Moreover, it will not do to say that spatial and temporal properties exist in space and time, for if they did so, they would themselves have spatial and temporal properties. It will not do to say that the property enduring for 1 s has the property of enduring for 1 s, nor of enduring for any other period of time. So universals—even physical properties—are not in themselves in space and time.28

It seems natural to regard Fales as offering three different arguments for his conclusion in the passage quoted. According to the first, since instances of properties are capable of being created and destroyed and are capable of changing their locations, whereas properties themselves are not, properties are non-spatial (given that they could be spatial in the first place only if they existed as their instances). But this argument is inadequate, since not only does it presuppose that properties are universals;29 if we assume that instances of properties completely overlap their spatiotemporal locations, then two instances of properties could still be individuated from each other in virtue of their locations, even if all properties have the very same spatiotemporal locations as the instances of which they are components.

According to Fales’ second argument, since properties can be spatial only if spatiotemporal relations characterize them, then since such relations do not characterize them, properties are non-spatial. Now, on the one hand, I grant that there is indeed a problem with the claim that universals can bear spatial relations to each other and to themselves. For example, as Ehring has argued, if we assume that one universal exists simultaneously at both the North and South Poles of the globe, then that universal will be both north and not north of itself.30 But, on the other hand, I deny that this problem besets the view that tropes can bear such relations to each other. After all, no one trope will be able to exist simultaneously at both the North and South Poles (putting aside the worry that time travel is possible). Thus, since this argument also presupposes that properties are universals, it too is inadequate.

Fales’ third argument is this: All properties are spatial only if spatial properties themselves have spatial and temporal properties. And all spatial properties have spatial and temporal properties only if the property of enduring for 1 s has spatial and temporal properties. But it will not do to say that the property of enduring for 1 s endures for just 1 s. So properties are non-spatial. But there are two reasons why this argument is inadequate as well. The first is that even if it will not do to say that the universal of enduring for 1 s endures for 1 s (provided that as one instance of this universal ceases to exist, another continues to do so), it is not at all clear why it will not do to say that a particular property of enduring for 1 s can endure only for that amount of time. Indeed, if the trope theorist claims that if there is some object that exists for only one instant, and if that object possesses a particular instance of the property of existing for one instant (i.e., a trope of existing for only one instant), then unless that theorist wishes to claim that when the object goes out of existence, that trope “jumps” to another object, presumably that theorist is committed to the claim that the trope also exists for only one instant. On the other hand, perhaps Fales’ judgment is based on the claim that properties do not possess themselves. But as I will argue below, that claim is false. The second reason is that it simply does not follow that if all properties are spatial, then the property of enduring for 1 s has spatial and temporal properties. After all, the claim that all properties are spatial is perfectly compatible with the claim that there is no such thing as the property of existing for 1 s in the first place.

It is interesting to note in passing that, despite Fales’ insistence that properties are non-spatial, he nevertheless insists that they are somehow “injected” into space-time via the relation of instantiation. He writes:

Instantiation, I wish to suggest, is in this sense a formal relation. In fact, in the case of physical particulars, it is the very relation previously mentioned between physical universals and identifiable space-time locations. Where such a relation obtains, we have a material particular. Universals “under the aspect” of space and time—that is in union with an anonymous spatial and temporal location “become” individual, distinguishable instances or tokens. They “become” universals “in” particular things.31

But there are two problems with the view expressed in this passage. The first is that if we claim that the relation of instantiation obtains between properties and space–time locations, which this view seems to do, then whereas this suggests that those properties are possessed by those locations themselves, as opposed to the material objects at those locations, presumably Fales’ wishes to claim just the opposite. Perhaps to combat this, he will assert that if the relation of instantiation obtains between a property and a space–time location, then this property will be possessed by the objects that overlap that location. But while this assertion entails that the physical universe as a whole will possess absolutely all of the properties that are tethered by the relation of instantiation to any space–time location contained within the universe, surely the universe does not possess all of the properties contained within it in this manner. The second problem is that, despite Fales’ attempt to explain the point, it really is quite difficult to see exactly what to make of the claim that while the properties possessed by spatial objects are in those objects, those properties themselves are non-spatial. If even some of the properties possessed by a spatial entity are themselves non-spatial, then that entity would be required somehow to straddle the divide between the spatial and non-spatial realms—with one foot in the one realm and the other foot in the other, as it were. But it seems much more plausible simply to assume that whereas all of the properties in the nature of any spatial entity are themselves spatial, all of the properties in the nature of whatever non-spatial entities exist are themselves non-spatial.

At this point, prior to proceeding, it should be noted that while my account of property possession is incompatible with the claim that all properties are non-spatial (given the obvious existence of at least some spatial entities), my account is perfectly compatible with the claim that whereas all of the properties in the nature of any spatial entity are themselves spatial, all of the properties in the nature of whatever non-spatial entities exist are themselves non-spatial. Indeed, my account is compatible with the claim that that there are even some properties that are simultaneously part of the natures of both spatial and non-spatial entities.

At this point, once we have shorn away the implausible doctrine that a predicate is meaningful only if it corresponds to its own genuine property, and once we have brought the remaining properties down to earth and made them spatial, we can see the truth of Plato’s central insight that all properties possess themselves. To be sure, some might object that the claim that properties possess themselves somehow involves a category mistake. Properties do not possess themselves; they are possessed by other things.32 But this objection is also implausible. For example, I claim that the property of being red possesses itself. Indeed, I claim that if the property of being red did not possess itself, then that property could not be truly predicated of anything at all. In other words, I claim that if the property of being red did not possess itself, then absolutely nothing in the world could be red.

To see this point clearly, let us engage in the following thought experiment. Let us imagine that God has reached the point in the creation of the world at which he is just about to create the first red entity. He has created the whole of space–time, he has populated it with a variety of non-red entities, but he has yet to create something that is red. For the sake of convenience, let us refer to this entity (i.e., the entity that is supposed to be the first red entity) as x. To make x red, he must first create the property of being red (or turn his attention to it, if we assume that this property exists externally or even necessarily), and then connect this property to x in the appropriate way. Perhaps he does this by placing the property of being red into space–time. Perhaps he even places that property within x itself, as a part of that entity. Or perhaps he leaves that property up in heaven with himself, and simply connects x to that property via some relation, such as instantiation. The details of this connection do not matter at the moment. Nor does it matter whether this property is assumed to be a universal, or whether it is assumed to be a particular. Now let us imagine that God has actually created the property of being red, or has turned his attention to it. Let us imagine that God has now connected that property to x in the appropriate sort of way. And, finally, let us imagine that this property does not possess itself. In that case, it is difficult to see how anything could be red. First of all, if the property of being red does not possess itself, it seems clear that this property itself is not red. Certainly one might object that this property is red in virtue of its possessing some property other than itself. But this objection leads straightforwardly to the third man regress. On the other hand, taking a page from my view, one might object that it is red in virtue of having another property of being red as a part of its nature. But then I will just argue that this other property of being red possesses itself. Second, if the property of being red is not red, then it is difficult to see how x could be red. After all, if the property of being red is not red, then it is difficult to see how even God could take this non-red entity and connect it to a second non-red entity in such a way that, by doing so, he thereby succeeds in making the second entity red. And this holds even if we assume that God places the property of being red within x itself, as a part of that entity. For it is difficult to see how x could be red simply in virtue of having a non-red entity, any non-red entity, as a part, regardless of whether we refer to that second non-red entity as the property of being red or not. It can’t be that the relation of instantiation conducts redness from the property of being red to x like an electrical line conducting electricity, since unlike electrical conductivity, the transference of redness is not something we ever seem to perceive. But, third, if x is not red, then no entity will be red at all. Again, if the property of being red is not red, then even if God manages somehow to bring that property down to earth, by doing so he only succeeds in adding one more non-red entity to a world already cluttered with them. Thus, if the property of being red does not possess itself, then nothing will be red.

Finally, I submit that once the doctrine that all meaningful predicates correspond to genuine properties has been discarded, and once the remaining properties have been brought down to earth, the claim that all properties posses themselves is plausible from an empirical point of view. Consider the redness of a red, rubber ball. (This property may be construed either as a particular or as a universal.) I claim that the redness of the red, rubber ball is red (where this “is” is the “is” of predication, not the “is” of identity). Certainly one might object once again that I am making a category mistake here. But if the color of the red, rubber ball does not possess itself, we are left only with some very implausible alternatives. For it seems very strange to say that the color of the ball possesses a color other than itself, especially if this implies that the color of the color of the ball is different than the color of the ball itself. It sounds even stranger still to claim that the color of the ball possesses no color at all. If one does not think that this sounds strange, presumably one is still operating under the assumption that all properties are non-spatial. But the color of the ball is a spatial entity, and every spatial entity seems to have some shape or other, unless it is diaphanous. And, finally, one cannot attempt to avoid these alternatives by claiming that there really is no such thing as the color of the ball in the first place; for here I claim the mantle of common sense: If the ball has a color in the first place, then there is such a thing as the color of the ball. Or consider the shape of the ball. It seems implausible to claim that it has some shape other than itself, and even more implausible to claim that it has no shape at all, given that every spatial entity has some shape or other. Or consider the size, mass, or density of the ball. Much the same result will be achieved. In general, I submit that once a suitably empirically austere conception of properties has been adopted, the claim that all properties possess themselves will become plausible from an empirical point of view. Indeed, I submit that the claim is phenomenologically obvious. For the fact that properties possess themselves is something that we can readily perceive, if we only take the time to examine the matter with some care.

Footnotes
1

See my (2005) and (2007). References omitted from the works cited page for the sake of blind review.

 
2

In this essay, I will use the term “entity” technically in such a way that an entity is any existing thing, regardless of the ontological category to which it belongs, and I will use the variables “x,” “y,” and “z” to quantify overall entities.

 
3

See Dufour (2005). This reference has also been omitted.

 
4

The mereological relations of parthood and proper parthood will be defined below.

 
5

I do not presuppose that Platonic transcendent realism is equivalent to Plato’s own view. Obviously, I will have more to say about the latter below.

 
6

Armstrong attributes this view to John Searle. See Armstrong (1978a, p. 14).

 
7

For more on this view, see Armstrong (1978a, pp. 25–27).

 
8

Rodriguez-Pereyra attributes this view to David Lewis. See Rodriguez-Pereyra (2002, p. 25, n. 4). Obviously, to avoid the charge of circularity, the class nominalist must insist that this class be “given in extension.” Similar remarks apply to resemblance nominalism.

 
9

For a recent defense of resemblance nominalism, see Rodriguez-Pereyra (2002).

 
10

For a recent defense of this view, see Bacon (1995).

 
11

See my (2007).

 
12

Below I will explain why I do not claim that property possession is the relation that x bears to y just in case y is a property that can be truly predicated of x, though probably it is clear enough already.

 
13

As I understand the notions, relation R is transitive just in case, for all x, y, and z, if x bears R to y and y bears R to z, then x bears R to z. R is non-transitive just in case, for some but not all x, y, and z, x bears R to y, y bears R to z, and x bears R to z. And R is anti-transitive just in case for all x, y, and z, if x bears R to y, and y bears R to z, then x does not bear R to z. Similar remarks apply with the appropriate changes made to reflexive and symmetrical relations.

 
14

This standard interpretation is usually referred to as classical extensional mereology. For more on this interpretation, see Simons (1987).

 
15

For example, see Paul (2002).

 
16

This is not to say that the nature of this property does not have other properties as proper parts, such as a hue, a shade, etc.

 
17

As I explained in my (2007), my account is compatible both with trope theory and with realism about universals, as long as that view is construed in a certain way.

 
18

The possession of properties by entities is mind-dependent precisely in those cases in which those properties are possessed by minds.

 
19

See also the Phaedo 100c-d, where Plato seems to suggest that the form of beauty is itself beautiful.

 
20

I speak to the issue of exactly how to explicate this notion of phenomenon below.

 
21

For more on these views, see Rodriguez-Pereyra (2002).

 
22

For a discussion of this regress in terms of the form of the Large, see the Parmenides 132a-b.

 
23

See the Parmenides 135c, where it seems to be suggested that discourse will be meaningful only if the full plurality of forms exist.

 
24

For a discussion semantic relations that obtain between predicates and properties with which I largely agree, see Armstrong (1978b).

 
25

See Aristotle’s (1966) Metaphysics book I, chapter 6.

 
26

See Timaeus 27d.

 
27

For a discussion of this issue that makes Aristotle’s view out to be similar (though not equivalent) to my own, see Spellman (1995).

 
28

See Fales (1990, pp. 189–190).

 
29

This is what is implied by the claim that properties are shared in common.

 
30

See Ehring (2002).

 
31

See Fales (1990, p. 191).

 
32

As far as I am able to determine, this sentiment can be traced back to Aristotle’s insistence in the Categories that everything other than primary substance can be said of or is present in such substance.

 

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