I believe that the motivation behind accepting universals, both uninstantiated and instantiated, need not lead one to accept universals. To illustrate this claim, I will explore the problem of uninstantiated universals. I hope to show that neither uninstantiated nor instantiated universals, as commonly understood, are needed, and that a universal-free theory of nominalism can adequately perform the work often done by universals. Such an account will have no problems with uninstantiated universals.
First, I will describe three theories about universals: Platonic realism, Aristotelian realism, and nominalism. I will focus on the implications that these theories have for uninstantiated universals and their ontological status. I will then address some reasons why uninstantiated universals may be desired as well as reasons why they may be problematic for certain realists. I believe that if, as the Aristotelian realist believes, uninstantiated universals are problematic, instantiated universals may very well also be problematic, and that the solution then is to abandon universals entirely.
Unlike particulars, universals are abstract objects or terms. Whereas a specific white horse is a particular, the ``whiteness'' of the horse is a universal. Universals may be thought of as corresponding to properties. Whiteness, for example, is the property of being white. White horses, white flowers, and white shoes all have the property of being white. That is to say, they exemplify whiteness (IEP).
Some philosophers, known as nominalists, deny the existence of universals, but many others accept that there are such abstract properties and types as whiteness, horseness, and triangularity. These philosophers are known as realists (IEP). Realists are split into two camps on the issue of where universals exist. Some realists say that universals exist in a special realm, a ``Platonic heaven'', separate from our spatiotemporal world. Others posit that universals exist in the world of particulars; in fact, they exist in particulars. I will refer to this first group of realists as Platonic realists and the second group as Aristotelian realists (Loux, 47-48).
Platonic realists believe in a theory of universalia antes res or ``universals before things''. Such realists believe that universals are prior to particulars. For the Platonist, universals exist in the realm of universals independent of our world of particulars (Loux, 47). Universals may instantiate particulars, or they may not. That is, a Platonic realist theory admits for the possibility of uninstantiated universals. There may be universals for which there are no corresponding particulars (Armstrong, 198).
Aristotelian realists object to the idea of having a separate realm for universals. The Aristotelian theory can be seen as a response to the Platonic theory, an attempt to simplify realism by abolishing the otherworldly realm of universals. Aristotelian realists locate universals in our world, the world of particulars (IEP). In fact, Aristotelian realism can be described as a view of universalia in rebus or ``universals in things''. For the Aristotelian, universals are inseparable from particulars; they are found in particulars. The Aristotelian believes that every universal has at least one instance at some point in time (Armstrong, 199). That is, they deny that there can be such things as uninstantiated universals. Aristotelian realists believe that properties ``need to be anchored in the spatiotemporal world'' (Loux, 47-48). There is no way to reconcile uninstantiated universals with Aristotelian realism. Thus, the Aristotelian cannot accept uninstantiated universals in his ontology.
A third position is that of universalia post res or ``universals after things''. This position, associated with nominalism, asserts that universals are really just names that are given to describe and categorize particulars. Abstract universals, say nominalists, do not really exist; they are simply words that are applied to collections of particulars (IEP).
These three theories clearly differ with respect to their positions on uninstantiated universals. According to nominalism, there are no universals, instantiated or otherwise. Under realism, uninstantiated universals need not be a problem. According to Platonic realism, there are universals in a realm of universals, and these universals may or may not be instantiated in particulars. According to Aristotelian realism, however, instantiated universals exist in particulars, but no uninstantiated universals are allowed.
I will now take a closer look at uninstantiated universals and discuss what uninstantiated universals might be. I think potential uninstantiated universals can be approached by turning to uninstantiated properties. Uninstantiated properties include such things as ``being round and square'', ``being a unicorn'', ``being the second even prime'', and ``being perfectly just''. If there are universals corresponding to these predicates, they are ``roundnsquare-ness'', ``unicorn-ness'', et cetera.
One argument for the existence of uninstantiated universals is known as the argument from meaning. The argument goes roughly as follows: Just as the predicate ``being a horse'' is meaningful, both the word ``unicorn'' and the predicate ``being a unicorn'' are meaningful. For ``unicorn'' to be a meaningful word, there must be something that corresponds to the word ``unicorn'' - that is, the universal unicorn or the essence ``unicorn-ness'' (Armstrong, 199).
While there seems to be nothing immediately problematic about the Aristotelian giving up the universal ``unicorn-ness'', what about ``perfect justness''? If there is nothing which is perfectly just, as I assume is the case, the Aristotelian realist is committed to the believe that there is no universal of ``perfect justness''. The Platonist, on the other hand, believes there is such a universal, and it is this universals that particulars we say are just (or partially just) ``participate in''. In this case it seems clear that an uninstantiated universal can be useful for describing particulars. Unlike Platonic realism, Aristotelian realism, unfortunately, leaves no room for such universals.
If uninstantiated universals are so useful, why is the Aristotelian unwilling to accept them? The primary reason is that there seems to be no way to have uninstantiated universals in a one-realm spatiotemporal world. But the only alternative to Platonic realism is not Aristotelian realism: another option is nominalism. I believe this theory deserves the careful consider of anyone who is unwilling to accept uninstantiated universals. If uninstantiated universals are so problematic, perhaps there is an even greater problem of which the problem of uninstantiated universals is only symptomatic.
D. M. Armstrong and other Aristotelian realists ask why we should attribute metaphysical reality to such standards to ideal standards such as prefect circularity? (Armstrong, 200) I applaud his question, but wonder why, if we can use notions like perfect circularity without having a corresponding universals, we need to attribute metaphysical reality to any standards. That is, I would like to question why we need universals at all. Perhaps we should abandon realism entirely in favor of nominalism.
Why is it that we want uninstantiated universals? I believe that uninstantiated universals can be useful constructs. They allow us to categorize such nonexistent objects as prefect ideals, imaginary unicorns, impossible round and square shapes, and the formal concepts of mathematics. But do we need universals for this? The Aristotelian doesn't seem to think so. If this can be accomplished without universals as such, why can't the work of instantiated universals be done by uninstantiated predicates alone without appeal to universals?
I believe that universals, or at least universals as understood by realists, are unnecessary. Instead, I consider myself to be a nominalist and believe that universals are just names. They are labels for ideas, a way of defining categories. ``Whiteness'', for example, is not some real existing thing; it is the name we use to discuss the set of white things. Similarly, there is no such thing as ``horseness'' that is exemplified by horses; ``horseness'' is a label applied to the set of horses.
The notion of universals as mere labels applies to uninstantiated universals as well. If it makes sense to talk about ``squareness'' and ``roundness'', the idea of ``roundnsquare-ness'' is just as meaningful. ``Roundnsquare-ness'' need not have some special ontological status. We do not need the realist's universal of perfect justness to discuss justice; we need only the idea of perfect justness. Universals, while useful tools for thinking about particulars, seem unnecessary. What we really need are categories, including empty categories, for classifying particulars.
Just as it can be meaningful to speak of the predicate ``is a unicorn'', it may be useful to have the label ``unicorn-ness'' to describe unicorns. So what if unicorns are imaginary? The fact that no particular unicorns exist does not mean that the category unicorn also fails to exist under this account. The category unicorn is simply a description of the essential properties that an object must have to be a unicorn. Uninstantiated universals, if universals are to be understood as classes, seem to present no problem.
There is, then, no problem with uninstantiated universals, but rather a problem with all universals, at least as they are understood by the Aristotelian realist. Universals need not be such a problem. I believe that the nominalist account of universals - that universals have no ontological status but are merely names for categories - is a compelling theory that offers relief from such problems.