Aristotle's theory of universals
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Aristotle's theory of universals is one of the classic solutions to the problem of universals. Universals are types, properties, or relations that are common to their various instances. In Aristotle's view, universals exist only where they are instantiated; they exist only in things (in Latin, it is said they exist in re, which means "in things"), never apart from things. Furthermore, Aristotle said that a universal is identical in each of its instances. So all red things are similar in that there is the same universal, redness, in each thing. There is no Platonic Form of Redness, standing apart from all red things; instead, each red thing has a copy of the same property, redness.
Overview
To flesh out Aristotle's theory of universals, it is useful to consider how the theory might satisfy the constraints on theories of universals (see problem of universals).
First of all, on Aristotle's view, universals can be instantiated multiple times. Aristotle stresses, after all, the one and the same universal, applehood (say), appears in each apple. Common sense might detect a problem here, a problem that can arise for other forms of realism about universals as well, namely: how to make sense of what is exactly the same in all of these different things? That, after all, is what the theory says: to say that different deserts, the Sahara, the Atacama, and the Gobi are all dry places, is just to say that each place is exactly the same (qualitatively) in terms of dryness, or in so far as being a dry place (not that each place is quantitatively dry to exactly the same degree). This may seem troubling if universals are thought to be like physical objects, but Aristotle is talking about a different category of being. So a common defense of realism (and hence of Aristotle's realism) is that we should not expect universals to separately behave as an ordinary physical object itself would do. To say the same universal, dryness, occurs simultaneously in all these places, after all, is nothing more strange than saying each place is dry, ex hypothesi.
Are Aristotelian universals abstract? If so, then for example, how does one abstract the concept of redness from one or more red things?
It will help to explain something about concept formation or generalization, according to Aristotle. Consider what a young child does, who is just on the verge of grasping a generic concept such as human being. The child is marshaling their memories of various encounters with a human specimen in such a way that the universal genus stands in for the essential similarity that stands out, on reflection, in each instance. Today, it might be said that one mentally extracts from each thing the quality that they all have in common. When the child gets the concept of a human being, he or she has learned to ignore the accidental details of their past experiences, (tall or short, male or female, etc.) and pay attention to the relevant quality they all have in common, namely, humanity. On Aristotle's view, the universal humanity is a natural kind defined by the essential properties that all humans have in common.