Since the ancient Greek philosophers (esp. Plato and Aristotle), the question what a universal is, whether it exists ontologically or only epistemologically, and what its relation is to particulars, has occupied the mind of philosophers. Below, I summarize the main theories.

Platonism

In Plato, the universal as an abstract entity has its own independent spiritual being. The ideas are the actual being and constitute the reason for being and knowledge for the material single things. For Plato true knowledge is only possible of something immutable. The things perceptible by the senses are in constant change and therefore unsuitable for true knowledge. That Unchangeable are the general ideas that exist prior to the particular things, and in which the individual things participate as inauthentic being.

A problem with this excessive realism is the relationship between the ideas as the general and the particulars. Plato's self-proposed solutions (methexis, parousia, koinonia) are not satisfying. Furthermore, there is the problem of self-application of the general to itself (see tritos anthropos).

Moderate Realism

Aristotle criticized Plato's theory of ideas: Plato, because he defined the ideas as perfect separate substances, has made an unnecessary duplication. Therefore, for Aristotle, the universal belongs to the individual substances and is realized in the individual things (second substances). The general therefore has not its own reality (chorismo problem in Plato). The general (to katholou) exists in things and is obtained through experience and produced by thought. With Plato, the general could can only be recognized through anamnesis (recollection), whereas Aristotle started from experience. Recollections of similar experiences form a general conception of the similar and identical in things.

The Scholastic Thomas Aquinas then defined the general as a category of thinking, which, however, is a structure realized in the individual things, which is created by the intellect through abstraction.

The fundamental problem of realism is the question of how the universal is present in individual, that is, where it is located (in rebus). But if this is only meant metaphorically, then nothing is yet explained by it, but indicates only an analogy. Platonism and the moderate realism of Aristotle both take the general as an abstract reality, with Plato giving it its own and independent reality, and Aristotle considering the general realized in the individual substances.

Conceptualism

Precisely this reality of the general beyond our mind, whether separate from or inherent in things themselves, is criticized by conceptualism. The general is here nothing other than a concept. Especially the English empiricists represented this view. For example, John Locke defined the general as one idea ("general idea") obtained by means of abstraction. The general is a generalization of the particular ideas obtained through experience. It does not represent reality but is a product of the mind. Thinking forms a general idea based on the similarity between individual things.

Kant considers the general as a transcendental concept of the understanding which makes experience possible in the first place. The general therefore does not have its own being, but there are rules of combination of the manifold of experience into a whole. Therefore, the general is an act of the mind.

However, the question remains as to what the basis is in reality for the universal, which is obtained from experience, thinking and language. The conceptualists and nominalists start from language (names, concepts) in order to explain how words can take on general meaning. But that does not yet sufficiently explain the relation to reality of the sensible world.

Nominalism

Nominalism also criticizes the assumption that the universal has a reality in things. Extreme nominalism regarded the general as an arbitrary name for a class of single things, or even just as a breath of voice (flatus vocis). This arbitrariness gives rise to problems of communication, since meaning can be set arbitrarily.

Ockham then introduced his so-called fictum theory, which considers the general as an intention of thinking only (intentio animae), defined as a sign-like relationship formed in thought. The general has a reality of its own kind, but only in our mind. As a predicate it can be predicated of a majority of things (logical level). The general is a natural sign as opposed to conventional signs (semantic level). And finally, one can designate the universal as a quality created by thought and existing in it (ontological level).

Nominalism makes scientific universal judgments possible, which, precisely because of the reduction of ontological assumptions, lead to a judgment that can be logically valid without having to assume the existence of terms. That way, hypothetical judgments are possible without difficulty.

Theory of Resemblance

Hobbes already pointed out that the general is based on similar qualities of things. There are similarities between the elements of a class of particulars. When these properties are in the individual things themselves, nominalism cancels itself out. When the similarities are posited by the mind in the particulars, there is again the problem of subjectivity, as with the extreme nominalism. In each case, at least one universal must be assumed, namely that of resemblance (infinite regress).

Wittgenstein's theory of family resemblance assumes that Individual things form a family because of their similarity. However, there is not only one relationship of similarity, but a series of familiar similarities. For example, all games do not have a universal "game" in common, but there are only similarities of different kinds between the individual games. In this theory, too, there is the problem that at least one universal must be assumed, i.e. "family resemblance".

Russell also claims that it is not possible to eliminate universals, because without them the world is not intelligible in its own structure. However, it is possible to reduce universals, but the one universal of "resemblance" cannot be eliminated.