(The following is taken from Michael Devitt and Kim Sterelny’s Language and Reality: An Introduction to the Philosophy of Language.)

What we will discuss is another central problem of traditional first philosophy: the one-over-many problem. It is obvious that the world is full  of individual things; stones, trees, cats and so on. But in addition to these  “Particulars”, are there “universals” shared by many particulars? Recently, a number of philosophers have argued that there are theoretical advantages in positing the existence of universals. But historically they were posited because of the one-over-many problem. That leads to universals as follows. Here is a red rose. There is a red house. That is a red sunset. Now surely, it is claimed, there must be something that all these things have in common that makes them red. That something is the “attribute” redness. So argued Quine’s adversary, McX, in Quine’s classic paper “On What There is” (1953: 9-10). Each thing must partake of the “form” redness. So argued Plato two millennia ago. These things have the same nature, the “property” redness. So argues David Armstrong to this very day (1978). This attribute, or form, or property, is “the one” that spreads itself over, or runs through, “the many”. It is a universal shared by many particulars. In this way first philosophers through the ages have convinced themselves of the existence of universals.

The conviction has generated a host of bizarre metaphysical problems. What is a universal? Where does it exist? Is there a universal for every predicate, even empty ones? What is a particular? How is a universal related to particulars? Universals are said to “inhere in” particulars and the particulars to “partake of” the universals, but how is that achieved? By metaphysical glue (“Plato’s grip”)? Even particulars begin to look mysterious, for what are they when stripped of their clothing of universals? Philosophers have been driven to think of them as “bare particulars”, “mere thisnesses”, or propertyless “substrata”. Struggles with these problems have led some to say that there are, instead of, or as well as, properties, property-instances: “abstract particulars” or “tropes”.

Controversy has raged over these problems for centuries. If we can dissolve them, we should. In particular, we should not believe in the existence of universals unless we really have to. We should favor here, as in science, simple and economical theories. In ontology, the less the better.

Does the one-over-many argument really require us to posit universals? We think not. Certainly there are red roses, houses and sunsets. We are tempted to say that there is something, redness, that they all share, but we need not say that. We do just as well saying that they are all red. What we are tempted to say is a mere manner of speaking, to be avoided when the ontological chips are down. There is nothing about the situation that requires us to talk of redness. To suppose that there is redness as well as red things clutters the landscape without explanatory or descriptive gain.

The friend of universals will object. “You have failed to say in virtue of what all these things are red.” Our failure here could be a scientific one: we have not said what it is, physically, about a thing that makes it red. However, this is not the failure the friend of universals has in mind. Suppose we removed the failure, pointing out that it is in virtue of being P that things are red, where ‘P’ is the appropriate physical predicate. The friend would still not be satisfied. “ In virtue of what are the things P?” He does not want a scientific explanation, he wants a metaphysical explanation.

At this point, the naturalistic philosopher demurs: there is nothing further to explain. “Things just are P. What more could you want to know?”  The first philosopher will insist that a metaphysical explanation is needed. We seem to be at an impasse. However, the naturalistic philosopher has one more card to play. If there really were something requiring a metaphysical explanation here, we would expect to find some sign of progress in the two thousand years that philosophers have struggled to provide that explanation. Yet there is no sign of progress: Armstrong is no closer to a solution than Plato. This is strong evidence that there is no problem: the one-over-many is a pseudo problem; the explanations prompted by it are pseudo explanations.

We have chosen to discuss the one-over-many not only because it is a major example of first philosophy, and one of its most conspicuous failures, but also because we suspect that the reason philosophers are beguiled by this pseudo problem is to be found in their theory of language. We suspect that underlying their response to the one-over-many is an implicit commitment to the ‘“Fido’-Fido” theory of meaning.

This theory has had a persistent hold over the minds of philosophers and many others. According to the theory, the meaning of a term is its role of naming something. It will be remembered that on the Millian view (2.5) the meaning of the name, ‘Fido’, is its role of naming Fido. The  ‘Fido’-Fido theory generalizes this view of meaning to all terms.

Consider:

That rose is red.

This sentence, like all others, has a certain complexity. It has two terms, the singular term ‘that rose’ and the general term ‘red’, of different grammatical categories and playing quite different roles (2.2, 2.4). How can  the ‘Fido’-Fido theory cope with this complexity? It has to see the two  types of term naming two types of entities: the different roles of the terms require  different types of entities. The entity named by ‘that rose’ is a  particular rose; that named by ‘red’ is the universal, redness, which can be shared by many particulars. The one-over~many begins to look like a real problem.

The ‘Fido’—Fido theory is false. Our PartII discussion exemplifies a quite different way of coping with the complexity of sentences. It is not that  each term stands in the one semantic relation of naming to different  kinds of entities. Rather, the terms stand in different semantic relations to  the same kinds of entities, neither “particulars” nor “universals” but just plain objects. Thus ‘that rose’ designates a certain object, a rose, while ‘red’ applies to many objects, including many roses. Where the ‘Fido’- Fido theory catches the complexity with different sorts of entity, we catch it with different sorts of relation. The only entities we need are objects of the familiar sort.  If we are right in these speculations, the one—over-many is not only an example of the failure of traditional first philosophy, but also another example of a bad theory of language leading to a bad theory of the world (Part IV).