The problem of universals is an ancient problem in metaphysics about whether universals exist. There are two main positions on the debate: nominalists deny that there are universals, while realists maintain that there are universals.
Universals are general or abstract qualities, characteristics, properties, kinds, or relations, such as being female, blue, an animal, or between, that can be predicated of individuals or particulars or that individuals or particulars can be regarded as sharing or participating in. For example, John, Mary, and Poppy all have the quality of being human—being human or humanity is the universal they have in common. While many standard cases of universals are also typically regarded as abstract objects (such as humanity), abstract objects are not necessarily universals. For example, one might hold that numbers are particular yet abstract objects.
The problem of universals is about their status. Do these universals exist independently of the individuals of whom they can be predicated? Are they merely convenient ways of talking about and finding similarity among particular things that are radically different? If they exist, do they exist in the individuals, or only in people's minds, or in some separate metaphysical domain? These questions arise from attempts to account for the phenomenon of similarity or attribute agreement among things. For example, live grass and Granny Smith apples are similar or agree in attribute, namely in having the attribute of greenness. The issue, however, is how to account for this and related facts.
Realists tend to argue that universals must be posited as distinct entities in order to account for various phenomena. For example, a common realist argument, arguably found in Plato, is that universals are required for certain general words to have meaning and for the sentences in which they occur to be true or false. Take the sentence "Jimmy Page is a musician". The realist may claim that this sentence is only meaningful and expresses a truth because there is an individual, Jimmy Page, who possesses a certain quality, musicianship. Thus, we must posit both the individual and the property he has, and the property is a universal that is distinct from the particular individual who has the property (MacLeod & Rubenstein, 2006, §1b).
Nominalists often argue for their view by claiming that realism has insurmountable problems. Another sort of argument for their view is that nominalism can account for all the relevant phenomena, so—by Ockam's razor or some sort of principle of simplicity—nominalism is a preferable metaphysical theory to realism, since it posits fewer kinds of entities.
Plato, at least during the first part of his life, believed there to be a sharp distinction between the world of sensible objects and the world of universals, or Forms: one can only have mere opinions about the former, but one can have knowledge about the latter. For Plato it was not possible to have knowledge of anything that could change or was particular, since knowledge had to be forever unfailing and general.. For that reason, the world of the Forms is the real world, like sunlight, the sensible world is only imperfectly or partially real, like shadows. Plato, accordingly, took a realist position regarding universals. This Platonic realism, however, in denying full reality to the material world, differs sharply with modern forms of realism, which generally assert the reality of the external, physical world and which in some versions deny the reality of ideals.
One of the first nominalist critiques of Plato's realism was that of Diogenes of Sinope, who said "I've seen Plato's cups and table, but not his cupness and tableness.
Plato's student Aristotle disagreed with Plato. Aristotle transformed Plato's forms into "formal causes," the blueprints or essences of individual things. Whereas Plato idealized geometry, Aristotle emphasized biology and related disciplines, and therefore, so much of his thinking concerns living beings and their properties. The nature of universals in Aristotle's philosophy therefore hinges on his view of natural kinds.
Consider for example a particular oak tree. This is a member of a species, and it has much in common with other oak trees, past, present, and future. Its universal, its oakness, is a part of it. A biologist can study oak trees and learn about oakness and more generally the intelligible order within the sensible world. Accordingly, Aristotle was more confident than Plato about coming to know the sensible world; he is an early empiricist. Aristotle was a new sort of realist about universals; some might call this view moderate realism.
This intrigued medieval philosophers such as Abelard, who wrote an extensive commentary on the Isagoge.
Nominalism was first formulated as a philosophical theory in the Middle Ages. It can be found in Peter Abelard and reached its flowering in William of Ockham, who was the most influential and thorough nominalist. Ockham argued that only individuals existed, and that universals were only mental ways of referring to sets of individuals. "I maintain", he wrote, "that a universal is not something real that exists in a subject ... but that it has a being only as a thought-object in the mind [objectivum in anima]." Hence Ockham's nominalism is also referred to as "conceptualism". As a general rule, Ockham argued against assuming any entities that were not necessary for explanations. Accordingly, he wrote, there is no reason to believe that there is an entity called "humanity" that resides inside Socrates. Nothing further is explained by saying that. This is in accord with the analytical method which has since come to be called Ockham's razor, the principle that the explanation of any phenomenon should make as few assumptions as possible.
A position subsequently identified as conceptualism was formulated by Pierre Abelard. This advertises itself as a middle way between nominalism and realism. There is something in common between like individuals, but it is a concept in the mind, not an objective reality.
Critics argue that conceptualist approaches like Abelard's only answer the psychological question of universals. If the same concept is correctly and non-arbitrarily applied to two individuals, there must be some resemblance or shared property between the two individuals that justifies their falling under the same concept, and that is just the metaphysical problem that universals were brought in to address, the starting-point of the whole problem (MacLeod & Rubenstein, 2006, §3d). If resemblances between individuals are asserted, conceptualism becomes moderate realism; if they are denied, it collapses into nominalism.
George Berkeley, best known for his empiricism, was also an advocate of an extreme nominalism. Indeed, he disbelieved even in the possibility of a general thought as a psychological fact. It is impossible to imagine a man, the argument goes, unless one has in mind a very specific picture of one who is either tall or short, European or Asian, blue-eyed or brown-eyed, etc. When one thinks of a triangle, likewise, it is always obtuse, or right-angled, or acute. There is no mental image of a triangle in general. Not only, then, do general terms fail to correspond to extra-mental realities, they don't correspond to thoughts either.
Berkeleyan nominalism contributed to the same thinker's critique of the possibility of matter. In the climate of English thought in the period following Isaac Newton's great contributions to physics, there was much discussion of a distinction between primary qualities and secondary qualities. The primary qualities were supposed to be true of material objects in themselves (size, position, momentum) whereas the secondary qualities were supposed to be more subjective (color and sound). But on Berkeley's view, just as it is meaningless to speak of triangularity in general aside from specific figures, so it is meaningless to speak of mass in motion without knowing the color. If the color is in the eye of the beholder, so is the mass.
John Stuart Mill discussed the problem of universals in the course of a book that eviscerated the philosophy of Sir William Hamilton. Mill wrote, "The formation of a Concept does not consist in separating the attributes which are said to compose it from all other attributes of the same object, and enabling us to conceive those attributes, disjoined from any others. We neither conceive them, nor think them, nor cognize them in any way, as a thing apart, but solely as forming, in combination with numerous other attributes, the idea of an individual object."
At this point in his discussion he seems to be siding with Berkeley. But he proceeds to concede, under some verbal camouflage, that Berkeley's position is impossible, and that every human mind performs the trick Berkeley thought impossible:
In other words, we may be "temporarily unconscious" of whether an image is white, black, or yellow and concentrate our attention on the fact that it is a man, and on just those attributes necessary to identify it as a man (but not as any particular one). It may, then, have the significance of a universal of manhood.
The 19th century American logician Charles Peirce developed his own views on the problem of universals in the course of a review of an edition of the writings of George Berkeley. Peirce begins with the observation that "Berkeley's metaphysical theories have at first sight an air of paradox and levity very unbecoming to a bishop". He includes among these paradoxical doctrines Berkeley's denial of "the possibility of forming the simplest general conception." Peirce responded to this paradox in the way that one might expect from a man known as the father of pragmatism. He wrote that if there is some mental fact that works in practice the way that a universal would, that fact is a universal. "If I have learned a formula in gibberish which in any way jogs my memory so as to enable me in each single case to act as though I had a general idea, what possible utility is there in distinguishing between such a gibberish ... and an idea?" Peirce also held as a matter of ontology that what he called "thirdness", the more general facts about the world, are extra-mental realities.
William James learned pragmatism, this way of understanding an idea by its practical effects, from his friend Peirce, but he gave it new significance. (Too new for Peirce's taste -- he came to complain that James had "kidnapped" the term, and to call himself a "pragmaticist" instead.) Although James certainly agreed with Peirce and against Berkeley that general ideas exist as a psychological fact, he was a nominalist in his ontology:
There are at least three ways in which a realist might try to answer James' challenge of explaining the reason why universal conceptions are more lofty than those of particulars -- there is the moral/political answer, the mathematical/scientific answer, and the anti-paradoxical answer. Each has contemporary or near contemporary advocates.
In 1948 Richard M. Weaver, a conservative political philosopher, wrote Ideas Have Consequences, a book in which he diagnosed what he believed had gone wrong with the modern world, leading indeed to the two world wars that dominated the first half of the 20th century. The problem was, in his words, "the fateful doctrine of nominalism." Western civilization, Weaver wrote, succumbed to a powerful temptation in the 14th century, the time of William of Ockham, and has paid dearly for it since. "The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence."
Roger Penrose contends that the foundations of mathematics can't be understood absent the Platonic view that "mathematical truth is absolute, external, and eternal, and not based on man-made criteria ... mathematical objects have a timeless existence of their own...."
Nino Cocchiarella (1975), professor emeritus of philosophy at Indiana University, has maintained that conceptual realism is the best response to certain logical paradoxes to which nominalism leads. Note that in a sense Cocchiarella has adopted platonism for anti-platonic reasons. Plato, as one sees in the dialogue Parmenides, was willing to accept a certain amount of paradox with his forms. Cocchiarella adopts the forms to avoid paradox.