ONE SEES two white square patches. Assume for simplicity, first, that we are talking about phenomenal, rather than physical, things, since the phenomenalism-realism question will not concern us, and, second, that the patches have no other non-relational properties. Call them Plato and Socrates. A metaphysician may then ask (1) what are they composed of—what is their ontological analysis? (2) what are the qualities that we attribute to both of them? (3) how are the qualities connected or related to the things? Consider three alternative solutions. One, call it (α), holds that the patches are composed of particulars or substrata and universals (squareness and whiteness) combined in the structural tie of exemplification. In so answering (1), (α) also answers (2) and (3) by asserting that properties are universals and that they are connected to the substrata by the tie of exemplification. A second solution, call it (β), holds that the patches are composites of universal qualities. In so doing it answers (2) and (3) by holding, with (α), that qualities are universals but, unlike (α), that the universals are related to the things in that they are parts of them combined together by a structural tie which we shall call combination. Combination, as opposed to exemplification, combines qualities into things: exemplification combines substrata and qualities into both facts and things. Hence (α) and (β) disagree about the answers to (1) and (3). These disagreements constitute the subject of this paper. What we shall see is, first, that there are radical differences between the arguments that lead to the acceptance of particulars and those that lead to the acceptance of universals. These differences will reveal the former to be specious. Second, we shall consider differences between the ontological ties on (α) and (β). Finally we will discuss relational properties in connection with (α), (β) and a third view, (γ), which considers things to be combinations, not of universals, but of instances of qualities.

Both (α) and (β) agree that there are universals—that

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qualities are universals. To say that the quality white is a universal is to say, in part, that one and the same thing is connected in some way to both Plato and Socrates and accounts for the truth of the sentences "Plato is white" and "Socrates is white." To put it another way, the term "white" in both sentences refers to the same entity. What arguments are there for such a view? Russell elegantly put forth the classic argument in "On the Relations of Universals to Particulars." Reprinted in B. Russell, Logic and Knowledge, ed. by R. Marsh (London, 1956). ¹ To deny universals is to assert that the quality attributed to Socrates is not one and the same with the quality attributed to Plato. The quality "in" each is numerically distinct and, furthermore, no one thing accounts for these distinct qualities being of the same kind. [I mention this latter point since one might, on a version of (γ), hold that there are particular qualities as well as universal qualities. The former account for the whiteness of particular patches; the latter for such particular whitenesses being just that.] One must then hold that such particular qualities are related in some way, since they are the entities in virtue of which we truly assert that both things are white. One must then specify such a relation. The obvious point is that such a relation will either be taken as a universal or a particular instance. If a particular then the original problem recurs when we introduce a third white patch or a pair of black patches. If admitted as a universal then the view finally accepts universals, albeit relational ones. No other alternative can answer the original question—to account for Socrates and Plato having the same color. That is, no alternative acknowledging only individuals—that denies the two patches are connected, in some way, to one and the same entity—can prevent the recurrence of exactly the same kind of question we started out with. Let us consider the case of particulars. One may argue that just as universals account for the sameness of quality, something must account for the difference of two patches which, conceivably, have all their nonrelational qualities in common. This view is held by G. Bergmann in several essays in Meaning and Existence (Madison, 1959) and Logic and Reality (Madison, 1964). However, as the elaboration of this view, and the arguments for it which follow,


are what the present author takes to be involved in it, I do not wish to attribute them to anyone. ² This something, the ground of

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numerical difference, is considered to be a substratum which stands in a unique relation or connection with universals to form or constitute facts and the things we started out with, Plato and Socrates. These ordinary things are thought of as composed of a substratum and universals connected together. Facts about such things may be composed of the substratum and one universal. The facts are about the things since the same substratum is a constituent of both sorts of entities. Such substrata account for the difference of the two patches; for there being two and not one thing. These substrata, in turn, are held to be simply different. At this point one may balk. If substrata are held to be simply different, why bother with them at all? Why not hold that Socrates and Plato are composites, not classes, of universals, and that they are different composites of the same universals? They just simply differ. If substrata can simply differ, why may not composites of universals simply differ? The proponent of substrata must retort that since Plato and Socrates are composite entities they cannot simply differ but must be held to differ in a constituent. Only simple entities can simply differ. Let me call this assertion the axiom of difference. The first point to note is that it is a necessary assumption in the argument to establish the need for substrata in an adequate ontology. We must then inquire why some accept, implicitly or explicitly, such an axiom.

One reason for adhering to the axiom of difference might be the belief that in order to "account" in one's ontology for a certain feature of experience one must introduce an entity of some kind. Thus as universals are said to account for the experience of qualitative identity, substrata account for the experience of numerically different things. Further, an ontological tie like exemplification accounts for the existence of facts and for the experience of one and the same thing having several qualities. Not to so locate or account for features of experience is, on this view, not to engage in ontological analysis. Of course one cannot argue with stipulations. If it is stipulated that the difference of Plato and Socrates must be accounted for by an entity in each that is simply

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different from any other entity of the same kind, and whose difference in turn need not be accounted for, then nothing more can be said. Yet one might point out that considering things like Plato and Socrates to be complexes of universals also locates, in one's ontology, an existent that may be taken to account for the difference of things that we notice. The proponent of substrata might reply that this provides no such account since the thing then accounts for itself. That is, one does not account for the difference of two things by holding that they are simply different combinations of the same universals. This is just to assert that they are different and not "account for" the difference, since one does not hold them to be different in virtue of different constituent entities. Adhering to such a conception of ontological analysis one is naturally led to assert the axiom of difference. Yet why does one hold to such a notion of ontological analysis?

One might argue that to hold that a complex of universals accounts for or grounds difference is to abandon the idea that the existents of one's ontology must be simples, as opposed to composites. Hence, to locate an existent to account for difference must be to locate a simple entity or element. But this is not an argument since it merely restates that a simple existent must account for difference, and we are concerned with why this axiom is adhered to. There is, I believe, a fundamental reason that leads the proponent of substrata to hold that the axiom of difference is necessary for ontological analysis to be significant and meaningful. Providing an ontological analysis, a metaphysician tells us what the "parts" or "constituents" of things are. In so doing he accounts for the "facts" of ordinary experience. Yet there is a problem about his use of terms like "part," "constituent," and "account." Substrata are not "parts" of things either in the sense in which a leg is part of a chair, an atom is part of the leg, a soldier is part of an army, or, for that matter, as a sense datum is held by some to be part of a physical object. How does the metaphysician use the term "part" when he proposes an ontology like (α), (β), or (γ)? Suppose he feels obligated to explain his use by means of ordinary terms and uses. He might point out that we use "part" in various senses, but they all have one thing in common: no two "wholes" can be composed of exactly the same

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"parts." Consider the two ordered pairs [1;3] and [3;1]. The pairs are not composed of the same parts, for, in addition to the numbers, there is the ordering relation which is different. On the view (β) two things are held to be different and yet composed of exactly the same qualities in exactly the same ontological tie or nexus. This points up what is involved in holding that the ordered pairs have different parts. Part of a thing, on an ontological analysis, is the nexus or tie that relates the other constituents. Keeping the feature of the part-whole dichotomy that requires two wholes to differ in a part lets the metaphysician use his special sense of "part" in a way fundamentally like other, ordinary uses. Not keeping this feature might lead him to feel that his use of the dichotomy is meaningless or empty. If so, his whole enterprise is nonsensical. Thus to speak meaningfully of "whole" and "part," two wholes, to be two, must differ in a part. We thus restate the axiom of difference. Using "part" and "whole" in a way fundamentally like all other uses, the metaphysician may then feel he need only further explain how he uses the terms referring to the entities he takes as parts of ordinary things—"substrata," "universal," "nexus," "exemplification," "instance," etc. One may hold that this must be done contextually, within the context of a metaphysical position and by contrast with alternatives. He may further point out that this is legitimate since such terms do not have ordinary uses. Hence no alternative is open. But "part" and "whole," being ordinary concepts, must retain, when used by the metaphysician, the fundamental features that characterize their use. This I take to be the crucial argument for the axiom of difference. But it neither does what it purports to, nor need what it purports to do be done. It does not do what it purports to in view of the very special sort of thing the nexus of exemplification is which combines "parts" into "wholes." Such a nexus enables a universal to combine with two distinct substrata into two distinct facts and to be a common part of two spatially distinct things. No ordinary thing is a part of two other spatially separate ordinary things. On (β) one complex of universals is enabled to be different from another complex of the same universals since universals and the nexus of combination are the special "things" they are. Exemplification, on (α), permits

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two substrata to combine with one and the same universal into two things and one substratum to combine with two universals into one thing. The point is that a nexus and ontological elements play quite special roles in each case. It is misleading to speak as if one metaphysician's use of "part" and "whole" is more ordinary, since he does not acknowledge that two complexes may share all constituents. Ordinary analogies do not help to explicate the sense in which a substratum, a universal, and a nexus are "parts" of a white patch. Moreover, one may point out that the metaphysician's use, without the axiom of difference, still corresponds in certain ways to ordinary uses of "part" and "whole." The relation of whole to part is (a) one-many; (b) so used with terms like "simple" and "complex" that the whole, relative to its parts, is complex and, they, relative to it, are simple; (c) such that the parts are combined by a relation (the nexus) to form the whole; (d) the simples of the system can only be parts and not wholes. In short, "constituent," "element," "complex," "simple," and "nexus" are such special notions in metaphysical analysis and so intimately connected to the part-whole dichotomy that the latter can hardly masquerade as an ordinary distinction. An additional correspondence with ordinary uses that is provided by the axiom of difference does not really add anything, and, in view of (a), (b), (c), and (d), is not needed.

Adherence to the axiom of difference might indicate that the "class-member" distinction dominates one's conception of partwhole. On the one hand, two classes to be two must differ in a constituent or member, and, on the other hand, several classes can have a common member as several things can exemplify one universal. Perhaps one who thinks in terms of the axiom of difference implicitly thinks of things as collections of substrata, universals and a nexus. This is suggestive if we consider that many philosophers nowadays get at ontology through language, improved or otherwise. Hence in considering complex entities and their parts one might insist that simple signs in language must correspond to simple things in ontology and complex things must be indicated by complex signs. Moreover, the simple signs in a complex sign should indicate the simple things in the complex entity. If one holds that language should "picture" entities in

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this way, then one will be able to consider the constituents of two complex entities by noting the constituent signs in the complex signs that indicate them. A complex sign would provide a list of its referent's parts. But if two complex entities had all parts in common, we would have one list and not two. Hence the complex sign could not be coherently used to indicate two things. Language would not picture reality. Insisting that it must can lead one to the axiom of difference. In any case, we have seen that the argument holding substrata to be necessary for individuation requires the axiom of difference. The argument for universals needs no corresponding assumption. One does not assume that something common must be referred to by the term "white" when one says "Plato is white" and "Socrates is white": one argues that this must be so for the two sentences to ascribe the same quality to both subjects. Of course this means that one must refute all nominalistic gambits. But this is not done by assuming a correlate to the axiom of difference. If the term "white" in each sentence does not refer to the same thing, then one does not say the same thing of each particular, unless some further connection and entity is introduced. This is the basic theme in Russell's argument for universals. In view of this an objector might insist that there is a correlate to the axiom of difference, for one is assuming that to be used to say the same thing in two sentences a predicate must refer to one thing. But this, if it be an assumption, is not at all like the axiom of difference. It simply states, first, that terms must be connected or refer to entities in order for sentences to be about or true of things, This does not preclude, by stipulation, attempts to link sentences as wholes to entities. One would have to argue that such a gambit must also ultimately recognize universals, since propositions or facts will have to be complexes containing other entities. But this involves arguments removed from the issues of this paper. ³ and second, that reference must be consistent if what is said, by two uses of a term, is to be the same. The terms "Plato" and "Socrates" can refer to different things and, consequently, the sentences "Plato is white" and "Socrates is white" can be about such different things if and only if there are two things. What, if anything, makes them different is a further question. The axiom of difference is relevant to this

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further issue. The term "white" can be used to say one and the same thing, in two sentences about two things, if and only if there is a common thing that it refers to (or is connected to in some way) in both occurrences. This corresponds not to the axiom of difference but to the trivial point about two things being required for the two sentences to be about two things. What would correspond to the axiom of difference would be an assumption about the need for some additional thing to account for the quality's being the same in both cases. But no additional thing accounts for that; to say that it is the same in both cases is to say that it is a universal.

Perhaps the point we are concerned with can be made in another way. Since there are two distinguishable white patches, we have no problem connecting the names "Plato" and "Socrates" to their referents. The term "white" is connected to a quality of each. We may then ask if the quality attributed to Plato is the same as that attributed to Socrates. If we say "no" we are faced with the problem of using the same term (to say the same thing) to refer to (or be connected with) different entities. As Plato and Socrates are distinguishable, there is, to repeat, no corresponding problem. One might believe there is if he thinks that we are led to acknowledge substrata by asking "what makes things different" just as we are led to universals by asking "what makes things the same in a respect." This way of putting the question leads us to assume that something must make them different. However, if we ask why we can truly predicate the term "white" of two distinct things, we are led to universals. But, if we ask why two names can name distinct things we are led to assert, trivially, that there are two distinct things— not two distinct substrata. In effect the same point comes up in another way when the proponent of the axiom of difference insists that the difference of substrata is not to be accounted for since such entities are simples. Such simples account for the difference of complex entities, the patches, but their difference need not be accounted for in turn. The case of universals is quite different. These entities account for the sameness of respect of the two patches. But to ask about a universal, what accounts for its being one, would be either to ask, nonsensically, why it is the same as itself or to inquire, legitimately, about the

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connection between universals and particular things. Part of what is involved is that while substrata are held to be "parts" of "complex" ordinary things, universals are not "parts" of qualities. ⁴ While this raises a question about the nature of the nexus, One may, as Bradley did, feel that a nexus is incomprehensible. The point is that if there are problems about a nexus they weigh equally for (α) and (β), and such problems do not serve to put universals and substrata on a par with respect to a stipulation like the axiom of difference. ⁵ one need not introduce a stipulation, like the axiom of difference, to avoid a question. For while the question substrata were introduced to answer may be re-raised about them, this is not so for universals. To avoid this one can only stipulate that the question is inadmissible. This suggests not only that there is a significant difference between arguments for universals and those for substrata, but also that the problem of individuation is specious.

The second issue I wish to discuss concerns ontological ties like exemplification and combination. On view (β) we may consider a white square patch to be pictured linguistically by

C1 (W, S)

(1)

where "C¹" stands for the nexus "combination." The linguistic picture is misleading since it appears to turn the nexus into something like an ordinary relation, but this can be ignored for the sake of simplifying the presentation. On (α) the picture would be

E1 (s, W, S)

(2)

with "E¹" for the nexus uniting the substratum s to its universal qualities, W and S. For the proponent of (α) there are facts as well as things. The relevant ones here would be those referred to by the sentences "Ws" and "Ss." One might then think of an alternative "picture" of a white patch like Socrates as

Ws & Ss.

(2')

This shows that E¹ combines the two-fold function of exemplifying, as a relation between a substratum and a universal, and combining, as a relation that connects several facts into one thing. This may lead one to speak of a thing like Socrates as a conjunction of facts or as a complex fact, as opposed to constituent simple or atomic facts. ⁶

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Of course the combining role is shared by the substratum s, which is the sort of thing that can exemplify several qualities. Thus we might think of two relations or ontological ties being involved. We would have E¹ which connects elements into a thing and, say, E² which connects a substratum and a quality into a fact. Thus we would have, in addition to (2)

E2 (s, W)

(3)

and

E2 (s, S)

(4)

However, one might point out that given (2), E¹, and the categorical difference between s, on the one hand, and W and S, on the other, we can generate both (3) and (4) and, hence, E². E² would hold between any two elements combined by E¹, where the elements are of different ontological kinds—particulars and universals. Given this "construction" of E² we can derive (3) and (4) from (2). Thus one might insist that only one nexus is involved. Alternatively, one may feel that to claim that only one nexus is required due to such logical connections between the two is to think of ontological ties as being too much like ordinary relations or mathematical functions. For, even granting that to hold that only E¹ is required is to think of things like Plato and Socrates as complex facts, there are still facts, like Ws, and complex facts, like Socrates, which are things. Having two sorts of complex entities, even though they both are complexes constructed from universals and particulars, may well be considered to require two ontological ties. Be that as it may, (α) at least requires both an additional entity, s, and a nexus that has a twofold function.

The need for a nexus with such a complex function simply reflects that (α) acknowledges facts as entities as well as things. On (β) there are no facts. When one says (5) "Socrates is white," where "Socrates" refers to the complex "pictured" by (1), one claims that the universal white is part of the complex. The complex thing is what makes the sentence true, not a fact composed of two simple entities in a structural relation. Facts are no longer needed. But in the sentence, predication no longer neatly reflects a nexus as it appears to do on (α). On this latter view we have,

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in (3) for example, the sign "s" corresponding to the substratum, the sign "W" to the universal and "E²" (or juxtaposition of "W" and "s") reflecting the nexus. Three linguistic aspects correspond to three ontological entities. In virtue of this correspondence the sentence, as a whole, corresponds to the fact made up of the three ontological entities. By contrast, if we transcribed (5) on view (β), with "C²" for "contains," as

C2 (Socrates, W)

(5')

the sign "C²" would not correspond to any ontological entity or feature. Predication in language truly holds between the sign "Socrates" and the sign "W," since "Socrates" refers to a composite of qualities that are combined by C¹ and that composite includes W. The sign "C²" would be no more than a linguistic shadow of the nexus C¹. C¹ only has the function of combining elements into things, not elements into facts. Hence its sole function corresponds only to one of the functions exemplification performs in (α). But it is in virtue of this single function that some sentences are true and others false. On (β), however, language no longer neatly pictures what that view holds to be "reality," but then the ontology has not been constructed on the linguistic model of subject, predicate, and predication. Furthermore, the ontology of (β) is not so complex in that the ontological tie only has a single function. Questions may be raised about the naming of complex entities on (β) and as to whether sentences like "Socrates is white" become analytic on that view. I have attempted to deal with such issues in "Things and Qualities" to appear in the annual proceedings of the Oberlin philosophical meetings for 1964. ⁷

We may complicate the issue by acknowledging universals of the higher types, color for example. With "col²" for "color," consider the true sentence

Col2 (W).

(6)

Clearly, since W is held to be a simple entity we do not then mean that color is a constituent of W as W is a constituent of Socrates. Hence must not (β) introduce a further ontological nexus for such a case, corresponding to exemplification in (α), and thus also

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introduce facts? Before discussing this let us see how (6) would be analyzed on (α). Recall that to avoid having both E¹ and E² on (α), we considered the possibility of constructing the latter from the former, of deriving (3) and (4) from (2). But clearly such derivation is possible from something like (2) to something no like

E2 (Col2, W)

(6')

Hence, one must acknowledge E¹, which ties first level qualities and substrata into things like Socrates, and E², which ties things and qualities of different levels into facts. Further, only some of the latter facts may then be constructed from E¹. One could introduce a further connection, E³, to unite universals of different types into facts. Then we could hold that all E² connections were constructable from E¹, but no E³ connections. In either case two basic connections would be involved, since not all cases of the one would be derivable from the other. This reflects a point many philosophers have expressed, though in quite different ways: predication in "F(x)" is different from that in "F² (f)." The issue can perhaps be clarified in the following way. Suppose, on (α), one decided to include second level universals, say color and shape ("Sh²") in the composition of Socrates. Then, instead of (2) we would have

E¹ (s, W, S, Col², Sh²)(2')

picturing Socrates. One could not then specify, simply in terms of kinds of elements, which entities went to make up facts, for this would not serve to differentiate between "Col²(W)" and "Col²(S)." One could of course differentiate between kinds (not types) of universals and reflect this difference syntactically, just as the differences among "s," "W," and "Col²" syntactically express the differences among particulars and universals of different types. But this would simply provide a linguistic smokescreen to cover up the fact that something other than E¹ is needed to generate "E²(Col², W)" from (2'). Besides, considering Col² as a constituent of Socrates is already a bit strange, since color is not a property of Socrates (or of s).

If there are universals of the higher types a proponent of (β) must also acknowledge a nexus in addition to C¹. This second

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nexus will connect universals of different types into facts. But this does not mean that (α) is a simpler ontology than (β). For not only does (α) have a nexus with a two-fold function, E¹, and bare substrata, but (α) must, to deal with universals of the higher types, introduce a further nexus and, hence, recognize two kinds of facts. If, in attempting to avoid this, the proponent of (α) considers properties like color and shape as constituents of Socrates in order to generate

E²(Col², W) and E²(Sh², S)

from (2') then clearly the proponent of (β) can do something similar by considering something like "C¹(W, S, Col², Sh²)" to replace (1). We must not be misled by an apparent difference between (α) and (β). The adherent of (β) acknowledges that the sentence "Socrates is white" is true since one is a constituent of the other, but that "White is a color" is true, not since one is a constituent of the other, but since one exemplifies the other. The proponent of (α) holds that both are true in view of an exemplification connection that gives rise to facts. But speaking of exemplification in both cases covers up the fact that two ontological connections are needed. Nor will it do to hold that at least on (α) they are of the same "sort," exemplification, while on (β) one is a part-whole relation and the other exemplification. This, again, is to be misled by linguistic and not ontological differences between the two views. On (β) a nexus holds between the constituent qualities of things, it does not connect a part with a whole, but several parts into a whole. It holds only between universals as (1) shows. The second nexus also holds among universals, but between universals of different types such as Col² and W. Hence one nexus combines universals of the same type into individual things, the other combines universals of different types into, say, facts. Speaking of part and whole enters only when we consider the linguistic relation of predication between the subject and predicate signs of the sentence "Socrates is white." The predicate refers to a part of the complex entity named by the subject term. On (α) both sentences, "W(s)" and "Col²(W)," are true because of connections between the simple referents of the subject and predicate signs. But the connections are different, as we have

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seen. Hence (α) has two kinds of facts, one kind corresponding to each kind of sentence. We may conclude that the existence of higher level qualities does not provide an argument for (α) on the ground that fewer ontological ties are needed.

The proponent of (γ) is forced, even without higher level qualities, to recognize an additional nexus. On the basis of the argument for universals (γ) must acknowledge relational universals to account for instances of whiteness all being whitenesses. Not being related to one universal entity, they simply relate to themselves by a relation of similarity, or some such thing. Socrates is then a construction from an instance of whiteness combined with an instance of squareness. Call these entities "w₁" and "s₁," respectively, and the corresponding, but distinct, instances in Plato "w₂" and "s₂." Let "C*" stand for the nexus that combines such entities into the complex things—the patches. We may then picture Socrates and Plato respectively by

C*(w₁, s₁)

and

C*(W₂, s₂).

Since w₁ is related to w₂ in some way, but not to either s₁ or s₂, and as s_l has that relation to s₂, we must acknowledge not only the relation but the exemplification of it by the pairs of instances. Thus in addition to the instances and the relational universal, R, we must introduce a further nexus, E*, and facts pictured by

E*(R, w₁, w₁)

and

E*(R, s₁, s₂).

Just as C* may be said to be a "combining" relation, E* may be spoken of as an "exemplifying" one. It would make no difference if one sought to identify R, the similarity relation, with the nexus E*. The point is, an ontological tie is needed in addition to C*. This complicates (γ) beyond that of (β). With respect to (α), however, the proponent of (γ) might point out that E¹ is an ontological nexus with a two-fold function, exemplifying and combining, so to speak. For on the one hand it permits a substratum to connect with one universal to form a fact, and together with the substratum it enables several facts to be about the same thing.

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Alternatively, a proponent of (α) may insist that on (β) the nexus C¹ not only combines but serves to individuate and, hence, has a two-fold function as well. This returns us to the argument about the axiom of difference. But even if C¹ be a nexus with a two-fold function, E¹ is also. Moreover, (α) involves a further ontological kind, substrata, and the two-fold function of E¹ gives rise to two types of entities, simple facts and complex facts (things). C¹, by contrast, only combines qualities into complex things.

Thus far we have confined the contrast of (α) and (β) to non-relational qualities. Suppose the sentence "Socrates is to the left of Plato" is true and that proponents of both (α) and (β) hold that "left of" is a simple relational universal. A proponent of (α) might then argue that on (β) one must either introduce a further nexus to account for the truth of relational sentences or include relational qualities as constituents of things like Plato and Socrates. Assume the second alternative will not do. For a discussion of some issues surrounding this assumption and of the use of relational qualities to differentiate objects see my "Things and Descriptions" to appear in the American Philosophical Quarterly. ⁸ On (β) one must then hold that a relation like "left of" (hereafter L) is exemplified by two complexes of non-relational universals, Socrates and Plato. There must then be, in addition to C¹, a tie, say Ex, that connects L, Socrates and Plato into a fact (or whole other than a "thing"). This fact may be pictured by

Ex (L, Plato, Socrates).

On (β) we then have two ties and relational facts as well as complex things. But the proponent of (α) must do something similar. For if he omits L from the analysis of Socrates and Plato, from (2), he must introduce a tie in addition to E¹ to combine substrata and relational universals into relational facts. Again, (α) has no advantage over (β), and relational universals, no more than universals of the higher types, need lead us to bare substrata. The proponent of (α) gains nothing by holding that the nexus which gives rise to relational facts may be identified with the one which connects universals of different types. For the adherent of (β) may make a corresponding claim.

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The handling of relations on (β) suggests some points in connection with classical arguments about the "reality" of relations and the distinction between essential and accidental properties. In that relations are not included as constituents of things one might take this to be a significant difference between relational and non-relational qualities. This may be taken to explicate why some hold that relational qualities are not existents. It is interesting to note that Moore held that properties of complexes of qualities were non-existent (non-natural) "adjectives." See my "Moore's Ontology and Non-natural Properties," Review of Metaphysics, XV, 3 (March 1962), pp. 365-95. For a consideration and defense of Moore's and Russell's early arguments for universals see A. Donagan, "Universals and Metaphysical Realism," The Monist, 47, 2 (Winter 1963), pp. 211-246. ⁹ But as some relational qualities are held to be simple elements in one's ontology they are, in that basic sense, existents. Not including relations as constituents of things one holds them to be "external" in one clear sense of that term. Taking them to be external in that sense, we note a further difference between relational and non-relational qualities. It follows from a thing's being a composite of qualities that it cannot change in one of its constituent qualities and be one and the same thing. This is involved in the notion of "thing" on (β). But it does not follow that a thing cannot change relations and still be one and the same. All relations are in this sense "accidental" as opposed to "essential." This connects "accidental" with "external" and "essential" with "internal." Extending this distinction one might hold that not all non-relational qualities of a thing need be constituents of it. Hence some might be held to be exemplified by one thing as the relation L is exemplified by two things. Such properties would, like all relations, be accidental as opposed to essential. Again, in a clear sense, a quality that was a constituent of a thing might be held to be substantial as opposed to adjectival, though not substantial in the sense in which a complex of qualities—a particular thing—would be said to be substantial. (β) thus offers the possibility of incorporating and explicating several classical themes in the history of metaphysics.

Indiana University.