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Nominalism and Abstract Reference

J.P. Moreland, American Philosophical Quarterly: Volume 27, Number 4 (October 1990).

What kinds of things are redness, hairiness, and humanness. We take such things for granted. And yet, there is great controversy about the ontological nature of such properties. There are three basic approaches: “Extreme Nominalism (properties do not exist), Nominalism (properties exist and are themselves particulars), and Realism (properties exist and are universals).” Moreland argues for the superior explanatory power of Realism in accounting for these realities. While this argument may seem academic, there is a lot at stake for the Naturalistic world view in at least one respect. If, in fact, non-physical properties exist, then the universe is not comprised solely of matter and energy. The door creaks open for other kinds of non-physical entities like numbers, consciousness, and perhaps even God. ~ Afterall

Most people would grant that certain sentences are true which appear to involve reference to universals. Among those sentences are these:

(1) Red resembles orange more than it resembles blue.

(2) Red is a color

(3) Humanity is a substance-kind.

The Realist has a relatively straightforward way of accounting for the truth of these sentences. She can argue that the subject terms refer to a universal. This can be made explicit by the following paraphrases:

(1a) Redness resembles orangeness more than it resembles blueness.

(2a) Redness is a color.

(3a) Mankind is a substance-kind.

The Realist argues that there are states of affairs that obtain in the world which are accurately described by (1a)-(3a). This point can be made more linguistically by claiming that these sentences incorporate terms which refer to universals and, further, that these terms play essential roles in these sentences and cannot be eliminated through paraphrase. Thus, the truth of these sentences presupposes the existence of universals.2 The terms that allegedly refer to universals in sentences (1a)-(3a) are called abstract singular terms, e.g., “redness,” “orangeness,’ “blueness,” and “mankind.”

The Realist, then, challenges those who deny the existence of universals to account for sentences (1)-(3) in such a way that they still make plausible claims about the world without entailing the existence of universals. Now it is generally agreed that there are three major schools of thought regarding the nature of properties — Extreme Nominalism (properties do not exist), Nominalism (properties exist and are themselves particulars), and Realism (properties exist and are universals). Further, it is generally agreed that, whereas sentences which exhibit abstract reference like (1)-(3) are problematic for Extreme Nominalism, they can be adequately handled by Nominalism and, thus, abstract reference cannot be used as an argument for or against Nominalism vis-à-vis Realism.

The purpose of this article is to refute that claim. Specifically, I will show that sentences like (1)-(3) are equally troublesome for Nominalism and Extreme Nominalism, and that the phenomenon of abstract reference does lend support to a Realist interpretation of properties. First, a brief sketch of Extreme Nominalism, Nominalism, and Realism will be given. Second, we will investigate Extreme Nominalist and Nominalist arguments which seem to show that abstract singular terms refer to sets of concrete or abstract particulars. Finally, we will consider Extreme Nominalist and Nominalist attempts to offer reductive paraphrases of sentences which incorporate abstract singular terms.

I. Extreme Nominalism, Nominalism, and Realism

A helpful way to compare and contrast different view about universals is to consider a case of quality-agreement. Let us limit our discussion to monadic, first-order properties. Suppose we have before us two round, red spots where each has the same infimae species of color and shape. Let us call our spots Socrates and Plato. How are we to account for this example of quality-agreement?

Extreme Nominalism is one answer to this question. Extreme Nominalists deny the existence of qualities altogether by giving them a reductive analysis as follows: a has the quality F~P.

For example, P could be replaced by “a is a member of the set of F-things.” Thus, Extreme Nominalists deny an ontology of qualities and quality-instances and only allow for concrete particulars — red spots, individual humans — and sets (predicates, concepts) of concrete particulars. The color agreement between Socrates and Plato is to be explained by the fact that they are both members of the set of red-things. W. V. O. Quine and Wilfrid Sellars are examples of Extreme Nominalists.

A second school of thought is Nominalism. A Nominalist acknowledges the existence of qualities but denies that quality agreement is to be explained along Realist lines wherein qualities are taken to be universals. The Nominalist denies that the-redness-of-Socrates (red1) and the-redness-of-Plato (red2) is a numerically identical entity (the universal, redness) in each. Rather, each spot has its own little redness in it, viz. a particularized quality. Particularized qualities have been given a number of different names, among which are these: “tropes,” “perfect particulars,” “abstract particulars,” “cases,” “unit properties,” “moments,” and “quality instances.” Advocates of Nominalism include D. C. Williams, G. F. Stout, and Keith Campbell.3 In my view, Campbell is the most articulate contemporary proponent of Nominalism. He calls a particularized quality a trope, and since Campbell has worked out a Nominalist ontology more than anyone else in the current literature, it will be helpful later if we spell out his doctrine of tropes in more detail.4

According to Campbell, “Socrates is red” should be analyzed in this manner: The simple trope, ‘red’, which is a member of the set, redness — the set of all and only red tropes which stand to red’ in the primitive relation of exact similarity — is a part of the compresent bundle of tropes, Socrates.

Three features of tropes bear special mention. First, a trope is a particular, that is, it is exhausted in one embodiment. It is not multiply exemplifiable. A trope is an infinite species taken as a particular. Second, a trope is a basic, primitive, simple entity. For Campbell, this means the following: a trope is simple in that it is not a whole with more basic parts in it, a trope is fundamental in that its existence is not dependent on anything else (e.g. Socrates’ existence depends on the existence of red’ but the existence of red~ is not dependent on anything else), and a trope is independent in that a given trope could be the only thing in the universe. Tropes, then, are basic, simple entities which altogether lack complexity.

A third important feature of a trope is the central role that space (or space-time) plays in spelling out what a trope is. Tropes are essentially regional, that is, they exist at specific times and specific places. A trope is a quality-at-a-place. This should not be taken to imply, for example, that the redness of red1 and the location of red2 are two different constituents in red1. Tropes are simple entities and not complex entities. Rather the place or formed-volume (Campbell uses these synonymously) of a trope like red1 is identical to the redness of red2; they differ only by a distinction of reason and not by a real distinction. The location and color of red are merely different ways of thinking about the same trope and differ from one another only in thought.

The third view of qualities is Realism. Realists may differ over a number of issues, e.g. the existence of uninstantiated universals, but they are agreed on their analysis of quality-agreement. Socrates and Plato agree in color because each has a multiply exemplifiable entity, redness, which is literally in red1 and red2 as a constituent. Red1 and red2 are complex entities which have the same nature (redness) in each. Gustav Bergmann, Edwin B. Allaire, and D. M. Armstrong are proponents of Realism.5

It has already been pointed out that most philosophers who work on problems involving universals believe that Nominalism is superior to Extreme Nominalism when it comes to the phenomenon of abstract reference. D. C. Williams confidently asserted that ‘all the paradoxes which attend the fashionable effort to equate the universal Humanity, for example, with the class of concrete men…disappear when we equate it with our new set, the class of abstract humanities…the class whose members are not Socrates, Napoleon, and so forth, but the human trope in Socrates, the one in Napoleon, and so forth.”6 Nicholas Wolterstorff claims that “in general, it would seem that for every sentence containing singular terms standing for predicables, one can easily produce, as replacement, a sentence containing general terms true of cases [tropes] of predicables. All reference to predicables can be eliminated.”7 D. M. Armstrong and Michael Loux have made similar statements.8 Let us see why these statements cannot be sustained.

II. Abstract Singular Terms Refer to Sets of Tropes

Let us recall sentence (1):

(1) Red resembles orange more than it resembles blue.

Extreme Nominalism

How might an Extreme Nominalist explain the truth of (1)?9 An Extreme Nominalist could propose the following:

(1b) Anything red resembles anything orange more than it resembles anything blue.

But (1b) is not equivalent to (1). It could be the case that some red things resemble some blue things more than they resemble orange things. A red rubber ball would resemble a blue rubber ball more than it would resemble an orange tent. The problem for the Extreme Nominalist is that red things are complex in a way in which redness is not.10 So there are other aspects in which red things could resemble blue things (size, shape, hardness, etc.) besides color.

An Extreme Nominalist could respond by asserting:

(1c) Any thing red color-resembles anything orange more than it color-resembles anything blue.

A number of problems can be raised against (1c). First, Realists like Armstrong have pointed out that “color-resembles” is likely to be a fabricated predicate like ‘believes-that-tile-cat-is-on-the-mat,” and not a predicate that is really primitive.” The predicate “color-resembles” does not stand on its own. A whole variety of shapes, smells, and other qualities will resemble one another as do red, orange, and blue. But if (1c) is correct, each of these cases of resemblance will require a new primitive predicate. But it seems clear that we understand the pattern that is common to all these predicates and this understanding is what permits us to form new resemblance-predicates in new cases. And this ability is best explained by arguing that what is common to these predicates is resemblance and what is unique is the respect of resemblance. Thus, the best way to understand the predicate “color-resembles” is to hold that when it is true that x color-resembles y, then this means that x resembles y in color.

A second objection to (1c) can be brought out by considering a possible world where “red” and “triangular” are coextensive, “orange” and “sweet” are coextensive, and “blue” and “square” are coextensive. In this world, anything triangular color resembles anything sweet more than it does anything square. But it would not be the case that triangularity would resemble sweetness more than it does squareness. There is more to red resembling orange more than it does blue than what (1c) captures, and thus, (1c) is inadequate.

Trope Nominalism

Armstrong argues that these arguments succeed against Extreme Nominalism (he calls it Orthodox Nominalism), but not against Nominalism (he calls it Particularism): “We see, then, that the arguments of this section, though very powerful against orthodox Nominalism, fail against Nominalism when it is combined with Particularism.”22 But this is not the case.

Let us first consider Nominalist paraphrases that take “red,” “orange,” and “blue” to refer to sets, that is, sets of tropes. The Nominalist might offer the following:

(1d) The set composed of red tropes resembles the set composed of orange tropes more than it resembles the set of blue tropes.

By using (ld), the Nominalist treats “red,” “orange, ‘ and “blue” as singular referring terms which name three different sets of tropes.~3 But is it true to say that these three sets (not their members, but the sets themselves) resemble one another in the way that red, orange, and blue do in (l)? If sets exist at all, they are not colors or qualities. Two sets may resemble one another in being sets, in being abstract objects, in having members, and the like. But these respects of resemblance have nothing to do with color. Sets are just not the sorts of things that are colored.

In this regard, consider the following case. Suppose that the number of red and blue tropes were the same and the number of orange tropes were half this number. Then the set of red tropes would resemble the set of blue tropes (in the respect of having ,’ members) more than it would resemble the set of orange tropes. But redness would not resemble blueness more than orangeness. So (1) and (ld) are not the same.

The Nominalist cannot respond by using the primitive predicate “color-resembles.” Sets do not “color-resemble” one another. And there would still be the problem raised against Extreme Nominalism regardirtg the art)ficial nature of this predicate. The Nominalist could argue that (ld) is using terms which refer not to the sets themselves, but to the various members of those sets. But this move shifts strategies. Now “red,” “orange,” and “blue” are not abstract singular terms, but rather general terms which serve as abbreviations for disenurce s~hot~t various tropes. We will consider this strategy in the next section.

Perhaps enough has been said about (Id). Let us move on to another Nominalist paraphrase which attempts to avoid the objections that have been raised against (ld). Consider this paraphrase:

(1e) The set composed of red tropes and the set composed of orange tropes are comembers of more natural sets that are the set composed of red tropes and the set composed of blue tropes.

This paraphrase is an attempt to remove an appeal to resemblance and substitute for it some reference to set membership. Sentence (ld) failed, in part, because it substituted sets for Realist qualities in (1), but kept resemblance intact. So (le) is an attempt to be consistent. It substitutes sets for Realist qualities and set membership for resemblance.

This paraphrase also tries to capture a certah1 group of facts that the Realist captures itl (la)’For example, the set of red tropes might itself be a member of some higher order set, say, the set of sets whose elements occur in the lower end of the color spectrum. Since orange is, but blue is not in this end of the spectrum, then the set of orange tropes would also be a member of this set and the set of blue tropes would not. The word ‘natural” in (le) is an attempt to capture the fact that certain elements, as an ultimate, brute fact, simply fall into certain sets and others do not. If “natural” was not added, then (le) would clearly fail. For there could be an indefinite number of arbitrary sets in which the set of red tropes and the set of blue tropes were members. Likewise, with the set of red tropes and the set of’ orange tropes. In that case, there would be no way of saying the set of red tropes and the set of orange tropes were comembers of more sets than the set of blue tropes.

Unfortunately, (1e) fails as an adequate paraphrase.14 First, a set’s identity is in its members. A set cannot change membership and be the same set since a necessary feature of a set is that it have just the members it does, itl fact, have. However, consider the possibility that there might have been more red tropes than there senselessly are. In that case, the new set of red tropes would be different from the one referred to in (1e). Sentence (1e) would use the term “the set composed of red tropes” to refer to a different entity than would be the case if (1e) were used to refer to the set of red tropes that senselessly obtain in the actual world. But, then, (1e) would be describing a different state of affairs than originally designated. But nothing would have changed regarding the relations of resemblance between redness, orangeness, and blueness for these resemblance relations do not vary with the number of instances of redness, orangeness, or blueness.

In order to avoid this problem it would seem that the Nominalist would have to hold that it is an essential feature of redness that it have just the members it does. But, then, since red objects are red in virtue of having red tropes in them, this would amount to the claim that there could not have been more or less red objects. But this is absurd.

Second, consider a world where all the red tropes are copresent with strawberry taste tropes, all blue tropes are copresent with raspberry taste tropes, and all orange tropes are copresent with the taste tropes of a bitter orange flower. Recall that a trope is a simple entity wherein the nature and location of a trope are identical—they differ only by a distinction of reason. By the transitivity of identity, if the color of a trope is identical to its location, and if the taste of a trope is identical to its location, then if the two tropes are at the same location, they must be identical.

In the world just described, the red tropes would be identical to the strawberry taste tropes and, likewise, the blue and orange tropes would be identical to the raspberry taste tropes and the bitter orange tropes, respectively. But, then, the set of red tropes and the set of blue tropes could be comembers of more natural sets (say, the set of sets whose members are tart tasting tropes) than either would be with the set of orange tropes (which would be in the set of sets whose members are bitter tasting “ropes). But redness would not resemble blueness more than orangeness.

This same objection could be raised in a world where red tropes are located nearer blue tropes than orange tropes. In this case, the set of red tropes and the set of blue tropes could be comembers of more natural sets (say, the set of sets whose members were in a certain spatial region) than the set of orange tropes.

Third, suppose there were a world where there was a missing shade of color between red and orange, e.g. red-orange or pink. In this world there would be no red-orange or pink tropes. In this case, the set of sets whose members were at the lower end of the spectrum would be a different set, since it would not have as members the set of red-orange tropes or the set of pink tropes. Now, it may still be the case that the set of red tropes would be comembers with the set of orange tropes in more natural sets than would be the case between either and the set of blue tropes, although examples could be set up where this would not be true (by postulating a world where a number of color tropes were absent).

Nevertheless, (1e) spells out resemblance as comembership in natural sets, and in this possible world, there would be less natural sets in which the set of red tropes and the set of orange tropes would be comembers. Thus, red and orange would bear a different resemblance to one another in this world than they do in the actual world because resemblance is treated by the Nominalist as comembership in sets. But how can the presence or absence of red-orange or pink have any bearing on the resemblance between red and orange?15

In summary, it seems that the Nominalist strategy of paraphrasing (1) in terms of abstract singular terms referring to sets fails. There may be other paraphrases a Nominalist could offer. But I believe these would fail like (1d) and (1e) for three reasons. First, universal qualities are just not sets, and if sets do, in fact, exist and resemble one another, then the way sets resemble is not the way red, orange, and blue resemble. Sets are not colors. Second, universals such as redness, orangeness, and blueness and their resemblances are features of the world that obtain independently of the number of instances of those or other universals (such as red-orange or pink). It is not so with sets. Sets do depend on the number of their members. Third, the resemblance among universals expressed in (1) are resemblances in one respect, viz., color. But tropes resemble in more than one respect (each has a “nature” and a “location” in some sense, and can resemble other tropes in either way). Thus, they can be grouped into resemblance sets in more than one way.

Perhaps a Nominalist could try a second approach, namely, a reductive approach. Here the Nominalist could argue that “red,” “orange,” and “blue” in (1) are not singular terms, but rather, abbreviations for discourse about a plurality of tropes. I will discuss this strategy as it applies to sentences like (2) Red is a color.

This is merely for convenience, because most discussions of the reductive approach in the literature focus on sentences like (2).


III. Abstract Singular Terms and Reductive Paraphrases

Extreme Nominalism

How might an Extreme Nominalist paraphrase (2). He might try the following: (2b) Everything red is colored.

This will not work. Consider the scattered location, L, of all red things. Everything L-located is colored, but L-location is not a color. Similarly, everything red might have been triangular so that everything triangular was colored. But triangularity would not be a color. The Extreme Nominalist could try, instead, (2c) Necessarily, everything red is colored.

This could avoid the objections raised against (2b). But it is still inadequate, for everything red is also extended, shaped, and located and, arguably, this is true necessarily. But redness is not extension, shape, or location.


Philosophers like Wolterstorff, Armstrong, and Loux believe that Nominalists can adequately handle sentences like (2) by employing a reductive strategy. Again, I disagree. The Nominalist paraphrase that is usually offered as being a successful treatment of (2) is something like this: (2d) Reds are colors.

Sometimes (2d) is expressed by saying, “Everything which is a red is a color.” Armstrong paraphrases (2) like this: “For all (ordinary) particulars, x, if x has a (particular) coloredness and the class of particular rednesses is a sub-class of the class of the particular colourednesses.”~6 There are three categories of arguments I want to raise against (2d).

I. Arguments Against Extreme Nominalists Applied to Nominalism

Recall the objection raised against the Extreme Nominalist paraphrase (2b). There it was pointed out that the scattered location, L, of all red things is not itself a color even though everything L-located is a color. Now, this same objection applies to (2d). Tropes are necessarily located at the place where they exist (and they are extended and shaped as well). Consider the scattered location, L’, of all red tropes. Everything L’-located would be a color, but L’-location is not a color. Since the location (which Campbell identifies with formed-volume) and nature of a trope are identical—they differ only by a distinction of reason—then we can put this as follows: L’-locations are colors.

One could object that there may be other tropes at some of the same locations as some red tropes and, therefore, it is false that everything L’-located is a color. But two things can be said against this idea. First, even if it were true, this would merely be a contingent fact. [lopes are independent entities — the very alphabet of being is what D. C. Williams called them—and all red tropes could have existed at locations where no other tropes were present. Second, since all tropes have natures which differ from their locations by a distinction of reason, shell their natures are identical to their location. It follows that all tropes at the same location are actually identical. In fact, tropes can arguably be treated as bare particulars identical to places. It would seem, then, that the Nominalist doctrine of the simplicity of tropes leads to inconsistencies when it comes to permitting the compresence of tropes.

What about a Nominalist paraphrase of (2d)? A Nominalist might try (2e) Necessarily, reds are colors.

The problem is that it is also necessary that reds are extended (as well as shaped and located), so one could say (2f) Necessarily, reds are extensions.

But the universal, redness, is not an extension (or a shape or location). In response, a Nominalist might appeal to Armstrong’s version of (2f)17

(2f’) For all (ordinary) particulars, x, if x has a (particular) redness, then x has a (particular) extendedness and it is not the case that the class of the particular rednesses is a sub-class of the class of the particular extendednesses.

But this is not true. The red tropes are necessarily at their location, i.e., have their particular extendedness (extension and location are identical). Indeed, red tropes are identical to their locations. So the class of particular rednesses is identical to the class of their particular extendednesses (they have the same members), and, therefore, the class of particular rednesses is a sub-class of the class of particular extendednesses. So it seems that some of the objections raised against Extreme Nominalism are equally effective against Nominalism.

2. Arguments Based On a Realist Account of Higher Order Predication

There is a further problem which can be raised against (2d). This can be brought out by thinking about what it means to say: (2) Red is a color. Most Realists are agreed that (2) is an example of predication, specifically, the predication of a second order universal of a first order universal. But Realists have differed as to how to analyze (2) 18

For the moment, let us assume that the following account of (2) is the best one among Realist alternatives. In this account, (2) expresses a genus/species relation in the category of quality. This relation is one of essential predication. In other words, (2) says that color (a second order universal), an identical constituent of all first order colors, is an essential constituent of redness. If one affirmed that blue is a color, one would be saying that color is a constituent of blueness. Thus, in cases of inexact resemblance, say when red resembles blue, you have a generic identity (the second order universal, color, is a literal, essential constituent in redness and blueness) and a specific diversity (red is this-color, blue is that-color).

If this account is correct, then (2) would be better expressed as (2′) Red is color. (2′) asserts that color is an essential constituent in red and it is predicated of some other constituent in red (a bare particular, perhaps), and red is identical to this-color. (2′) be-comes the ontological ground for (2). (2) contains an “is” of classification.19 As it stands, (2) says that red is a color. It places red in the class of colors and (2′) grounds this classification by saying that red has a constituent in it, color, which is that entity which all members of the class of colors share in common.20

From what has just been said, it follows that a proper account of (2) involves three things: 1) seeing that (2) expresses (or presupposes) essential predication, 2) grounding the membership of red in the class of colors, and 3) assaying redness as a complex entity, viz., this-color, where color is the genus (nature, essence) of redness. If this is what a proper account of (2) involves, then neither (2d) nor any other Nominalist paraphrase of (2) will succeed, for they all must treat red as a simple entity.

This point was brought out long ago by J. R. Jones against the Nominalists of his day like G. F. Stout.21 Jones argued that if x is a trope, then since x is simple, any attempt to assay the constituents of x that involves a predication such as Fx & Gx cannot be true. FX & GX says that F and G are constituents of x. Now let x be a red trope, say red1. It would seem that (2d) says of each red trope that it has color as a constituent In other words, if F is red and G is color, then (2d) appears to say that red1 has color as a constituent. Red1 has redness and it has color. So red1 is not simple.

To avoid this conclusion, the Nominalist must hold that (2d) does not state that a trope has its redness or its color. (2d) becomes a way of stating the brute, unanalyzable fact that red tropes are in a set that is itself in the set of colors. But this is not a paraphrase of a Realist account of (2). It is a replacement because it denies the three key features of (2) that a Realist believes any alternative to (2) must explain.

For one thing, the Nominalist account denies that (2) is an example of essential predication. this is because color is no longer a constituent in redness. Furthermore, if A is the essence of B, then if B loses A, B ceases to exist.22 If Campbell loses humanity, then Campbell ceases to exist. Similarly, if redness loses color, redness would cease to exist. But if the Nominalist account of (2d) is correct, (2d) expresses set membership, and the elements of a set do not change when the set changes. If one has a set of the natural numbers from 1 to 10, and then forms a set of natural numbers from 1 to 9, nothing happens to 1. Likewise, if there were no green tropes in the world, then the color set of all sets whose members are color tropes would be different than it is now. But the set of red tropes would not change, nor would each member of that set. Red tropes remain intact regardless of what happens to other tropes.

So the existence of a red trope and its “nature” do not depend on alterations in the set of all sets whose members are color tropes. Thus, the latter is not the essence of the former. Sets are of the essences of their members.

This can be seen in another way. Consider a world where there were no colors other than red. The only color tropes would be red tropes. In this case, redness would be identical to color because two sets are identical just in case their members are identical. “Color” would be just another way of saying “redness.” In this world, a red apple would have a red trope but it would not have a color trope as a distinct entity from the red trope. On the other hand, a Realist could argue that when a red apple instances redness in this world, it does instance the universal, color, as a different (though inseparable) entity. If x instances a determinate universal, F, it also instances every determinable universal that is a constituent of F. But these universals are not identical. Sentences (2d) and (2e), especially as Armstrong states them, do not capture this fact. So they are inadequate from a Realist point of view.

Second, the Nominalist account does not ground the membership of the set of red tropes in the set of colors. If it did, then it would make an implicit appeal to a universal that is in each member of that set. And, third, reds are not complex entities but simples in a Nominalist ontology. So, if these three features are part of a correct Realist account of (2), then Nominalist paraphrases are really replacements that fail to do justice to a range of phenomena which motivates Realism in the first place.

It is always open to a Nominalist to argue that this Realist account of (2) is not what is involved in holding that “Red is a color” is true. So, the force of this objection comes down to whether or not the three issues described above are what are really involved in red being a color and whether Nominalist alternatives can really say all that needs to he said about (2).

Even if the Realist uses some model to explain sentences like (2) other than the one I have been employing, I believe he still can argue against a Nominalist paraphrase of (2). Suppose a Realist adopts what some call a determinable/determinate view of (2). According to this view, color is a determinable that covers the nature of and is particularized in the determinate, redness. The first order universal, redness, is color particularized at the level of the first order universal. The generic universal, color, is in some sense identical to the specific Universal red, and in some sense different from it. As Brand Blanshard put it: “The universal is thus in it differentiations; it is identical to them; it is distinct from them.”23 The genus is realized in the species and the species is a realization of the genus. The species contains no entity outside the nature of the genus. Rather, the species comes from within it. To be red is to be color, and to be color is to be red or orange or some other determinate shade of color. So according to this view, red is a simple entity and as such, it is a way of being color

The determinable/determinate view is not my view. But I still believe it or other Realist accounts of higher order predication can raise an objection to a Nominalist account of (2). The Realist could argue that the determinable/determinate relation is one that obtains between universals of different orders but not between a universal and a particular, i.e. a trope. A trope is not a way of being red like redness is a way of being color. Redness is a modification of color, but it is still something general. On the other hand, the subjects of predication in (2d) or (2e), when we say a red is a color, are not a way of being anything, much less color. The connection between a higher and lower order universal is a necessary connection, but the relation between color and a particular red trope is a contingent connection. A red trope is a particular-entity-here, and it is not sufficiently general to be a way of being color.

This point can be seen in another way. A red trope, in some sense, is a-nature-and-a-location. But location is outside the nature of redness. It does not come from within it as a particularization or realization of that nature. There does not seem to be an intimate connection between this location here (where red’ is located) and the redness of red ~. However, it is easier to see how one could construe redness as somehow “in’ color and as the realization of color. Redness seems to be more closely related to color than location is to redness. So it is easier to see how redness is a way of being color than it is to see how this location is a way of being red.

In short, the determinable/determinate structure is neither extendable to the relation between red’ and its nature nor to the relation between a red and a color. In neither case do we have the subject as a way of being the predicate. So a Nominalist account of predication in general, and (2) in particular, cannot utilize the determinable/determinate relation. But if this relation is required to make sense of (2), then the Nominalist paraphrase in (2d) or (2e) is an inadequate replacement for (2). They do not express the same thing.

The Nominalist could respond by saying that the Realist has begged the question here by already assuming that there is a categorical distinction between universality and particularity in order to make her case that the determinable/determinate relation is a relevant feature of predication between orders of universals. But since there are no universals, this relation is irrelevant and it is a virtue that (2d) or (2e) does not capture it.

An Argument from Husserl

I wish to raise one final objection against (2d) and (2e). These sentences are general and make claims about a totality of individual reds. On the other hand, the Realist holds that (2) is a singular proposition making a claim about a particular entity, the universal redness. The Realist expresses this conviction in (2a). Thus, the Realist believes that (2d) and (2e) are not adequate paraphrases of (2) and this can be pointed out by focusing on the differences between (2d) and (2e) vis-Ã -vis (2) and by mentioning some problems with the former.

This line of argument is essentially the one used by Husserl in Sections 1-4 of Chapter 1 of Logical Investigations 11. Husserl’s main point is that we are conscious of universal objects in acts that are different from those in which we are conscious of individual objects, even when those objects are particularized attributes. Thus, the ideal unity of the former cannot be reduced to the dispersed multiplicity of the latter. These acts have different intentional objects. This can be illustrated by three features that highlight the difference.24

First, when one intends a group of reds, either at a single glance or in single acts of comparing each red trope to another, there is an implicit recognition of multiplicity and an act of comparison. One notices exact similarities. When one intends the universal redness, no such multiplicity is involved nor is there a need for comparison. We intend the single entity, redness, in its unity. Thus, the two acts are essentially different because their objects are different. It should be noted, as well, that in the second intention the object is redness, a color, and so forth. It is not a set.

Second, I never have before me all the red tropes there are. So if redness is the totality of all reds, then there is more I can learn about redness. If there is a red trope on the surface of Mars, then my knowledge of redness is incomplete until I know about this red trope.25 On the other hand, when I attend to the universal redness, I know all of it because it is here before me. There is nothing essential to it that is left out for me to know about redness which can be known merely by seeing other reds in the same way I see this one.

Third, when redness is construed as a totality of reds as in (2d) and (2e), the question arises as to what unifies this totality. This question does not even arise, however, when one’s intentional object is the universal redness. For it is not a totality.

These three features illustrate that the two acts (or, to put the point linguistically, the sentences (2d) and (2e) vis a vis (2)) are different because their intentional objects (referents) are different. So, talk about universal objects cannot be accurately reduced to or paraphrased in terms of talk about a dispersed multiplicity of tropes. Husserl provides a fitting summary to this argument: “These distinctions and others like them are quite irremovable. We are not merely dealing with abbreviated expressions: we cannot eliminate such differences through any elaboration or circumscription.”26


The debate among Extreme Nominalists, Nominalists, and Realists regarding the existence and nature of universals involves the phenomenon of abstract reference and sentences like (1)-(3). Most philosophers agree that these sentences provide serious problems for the Extreme Nominalist but not for the Nominalist. The Nominalist can employ two basic strategies in treating these sentences. He can hold that they contain abstract singular terms referring to sets of tropes. And he can paraphrase these sentences in such a way that they become general claims about a totality of individual tropes. I have argued that both strategies fail. If I am right, then sentences like (1)-(3) provide good reasons for rejecting Nominalism as well as Extreme Nominalism. Opinions to the contrary are simply mistaken.

Received September 5, 1989


1 Realists differ over the account they give of higher order predication. Some would hold, for example, that (2) places red. Other that it expresses some sort of determinable/determinate relation. These differences will be discussed later, but for now, they do not matter. All these Realist views agree that (1)-(3) involve reference to universals, and that is the main issue in the debate with Extreme Nominalists and Nominalists.

2 Not all Realists agree with me on this point. In general, Realists often differ over what set of phenomenon should provide the major support for Realism, e.g. resemblance for Panayot Butchvarov, predication for Nicholas Wolterstorff, and abstract reference for Michael Loux. I see no reason to emphasize any of these at the expense of the others. For more on this, see JP Moreland, Universals, Qualities, and Quality-Instances (Lanham: University Press of America, 1985).

3 See D. C. Williams, “On the Elements of Being: I,” The Review of Metaphysics, vol. 7 (1953), pp. 03-18; “The Elements of Being: II,” The Review of Metaphysics, vol. 7 (1953), pp. 171-92; G. F. Stout, “The Nature of Universals and Propositions,” reprinted in The Problem of Universals, ed. by Charles Landesman (New York: Basic Books, 1971), pp. 153-66; Keith Campbell, “Abstract Particulars and the Philosophy of Mind, “Australasian Journal of Philosophy, vol.61 (1983), pp. 129-41; ‘The Metaphysics of Abstract Particulars,” h1 Midwest Studies in Philosophy) Volume Vl: The Foundations of Analytic Philosophy, ed. by Peter A. French, Theodore E. Uehling, and Howard K. Wettstein (Minneapolis: University of Minnesota Press, 1981), pp. 477-88; Metaphysics: An Introduction (Encino: Dickenson Publishing Co., 1976). Some classify Husserl as a Nominalist, but I have argued against this elsewhere. See J. P Moreland, “Was Husserl a Nominalist?” Philosophy and Phenomenological Research, vol. 49 (1989), pp. 661-74.

4 For a criticism of Campbell’s version of Nominalism, see JP Moreland’ “Keith Campbell and the Trope View of Predication,’ Australasian Journal of Philosophy (forthcoming).

5 D. M. Armstrong, Universals and Scientific Realism, 2 vols. (Cambridge: Cambridge University Press, 1978); Edwin B. Allaire, “Existence, Independence, and Universals,” in Iowa Publications in Philosophy, Vol. 1: Essays in Ontology, ed. by Edwin B. Allaire (The Hague: Martinus Nijhoff, 1963), pp. 03-13; Gustav Bergmann, Realism: A Critique of Brentano and Meinong (Madison: The University of Wisconsin Press, 1967).

6 D. C. Williams, “On the Elements of Being: 1,” p. 10.

7 Nicholas Wolterstorff, On Universals (Chicago: University of Chicago Press, 1970), p. 199.

8 Cf. D. M. Armstrong, Universals and Scientific Realism, Vol. I, pp. 58-63; Michael Loux, Substance and Attribute (London: D. Reidel, 1978), p. 75. Loux’ treatment of sentences like (3) is, in my opinion, inconsistent with Realism. For a defense of this claim, see Moreland, Universals, Qualities, and Quality Instances, pp. 144-58.

9 Cf. Frank Jackson, “Statements About Universals,” Mind, vol. 86 (1977), pp. 427-29; Armstrong, Universals and Scientific Realism, Vol. I, pp. 58-60; Arthur Pap, Nominalism, Empiricism, and Universals: I,” The Philosophical Quarterly, vol.9 (1959), pp.330-40.

10 I am not assuming that redness is a simple entity for Realists. For a helpful Realist treatment of the simplicity of colors, see Panayot Butchvarov, Resemblance and Identity (Bloomington: Indiana University Press, 1966), pp.36-47.

11 Armstrong, Universals and Scientific Realism, Vol. I, pp.59-60. |

12 Ibid.

13 Cf. D. C. Williams, “On the Elements of Being: 1,” pp.9-12, for an example of this.

14 Indeed, the very idea of a natural set of resembling tropes is troublesome. For if a trope’s nature is identical to its location, then it is difficult to avoid the conclusion that tropes are, after all, bare particulars identical to places. See Moreland, “Keith Campbell and the Trope View of Predication.”

15 (1e) also fails because it spells out resemblance in terms of set membership. But the Trope Nominalist wants to explain set membership in natural sets in terms of resemblance. So (1e) would clearly be circular in this case.

16 Armstrong, Universals and Scientific Realism, Vol. l, p. 61.

17 Ibid.

18 For a very helpful discussion of different Realist views of resemblance between universals and higher order predication as expressed in (2), see Armstrong, Universals and Scientific Realism, Vol. II, pp. 101-31.

19 Cf. Michael Loux, “Form Species, and Predication in Metaphysics Z, H, and O,” Mind, vol. 88 (1979), pp. 01-23.

20 For a fuller statement and defense of the view I am presenting here, see Evan Fales, “Generic Universals,” Australasian Journal of Philosophy, vol. 60 (1982), pp.29-39.

21 J. R. Jones, What Do We Mean by An ‘Instance’? Analysis, vol. 11 (1950), pp. 11-18.

22 By viewing the relation between higher and lower orders of universals as a relation of essential predication, we have an explanation for why higher order universals transcend lower ones. Color can exist without redness but not vice versa because color is an essential constituent in redness, but redness is not an essential constituent in color.

23 Brand Blanshard, The Nature of Thought, 2 vols. (London: George Allen and Utlwil1 Ltd., 1939), Vol. l, p.611.

24. Husserl’s argument focuses on mental acts, their character, and their intentional objects. He does not focus on words or sentences. But this does not affect the application of his points to (2), (2d), and (2e), since it is primarily the use and not the mention of these sentences that is important here.

25 This point was suggested to me by Dallas Willard.

26 Edmund Husserl, Logical Investigations, 2 vole., tr. by J. N. Findlay (London: Routledge & Kegan Paul, 1970), Vol. I, p. 341. It could be argued that Husserl’s points about having an object like redness directly before me and attending to it immediately is hopelessly old-fashioned, given that Wittgenstein, Kripke, Goodmalt and others have shown that thought it is rule governed activity. Thus, we have no idea of what having an object “here directly before me” would mean. The issues involved in this objection are too complex to be dealt with here (Is there a private language? Do we need to think by means of language at all? Is perceptual realism true? and so on). If one sides with the early Husserl on these questions, then this objection loses its force. Further, Husserl’s arguments could be recast in terms of linguistic rules and sentences. Thus, the rules involved in understanding and applying sentences like (2) utilize subject terms wl1icil prima facie behave like abstract singular teens. On the other hand, sentences like (2d) and (2e) involve rules which make reference to the notions of multiplicity and totalities (e.g., classes and sub-classes), diversity/similarity in respects of resemblances between or among objects, and the dispersal of the objects referred to by the terms used in those sentences (e.g., “particular colorednesses”). Thus, Husserl’s point can be made in terms of linguistic entities and rules.

15 Cf. Robert N. Wennberg, Terminal Choices: Euthanasia, Suicide, and the Right To Die (Grand Rapids: Eerdmans. 1989); Life in the Balance