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. Aristotle thought—to put it in a not-very-enlightening way—that universals are simply 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 (he said they exist in re, which means simply "in things"), never apart from things. Beyond this Aristotle said that a universal is something 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, in each red thing there is the same universal, redness.
To further flesh out Aristotle's theory of universals, it is useful to consider how the theory might satisfy the constraints on theories of universals listed in the problem of universals article.
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), that appears in each apple. Common sense might detect a problem here. (The problem can arise for other forms of realism about universals, however.) Namely, how can we make sense of exactly the same thing being in all of these different objects? 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 the exact same being, the universal dryness, occurs at each place. Universals must be awfully strange entities if exactly the same universal can exist in many places and times at once, or so one might think. But maybe that's not so troubling; it seems troubling if we expect universals to be like physical objects, but remember, we are talking about a totally different category of being. So a common defense of realism (and hence of Aristotle's realism) is that we should not expect universals to behave as ordinary physical objects do. Maybe then it is not so strange, then, to say that the exact same universal, dryness, occurs all over the earth at once; after all, there is nothing strange about saying that different deserts can be dry at the same time. The question is whether this could still be said if the earth had only one biosphere.
Are Aristotelian universals abstract? And are they, then, what we conceive of when we conceive of abstract objects such as redness? Perhaps. It will help to explain something about how we form concepts, according to Aristotle. We might think of a little girl just forming the concept of human beings. How does she do it? When we form the concept of a universal on Aristotle's theory, we abstract from a lot of the instances we come across. We as it were mentally extract from each thing the quality that they all have in common. So how does the little girl get the concept of a human being? She learns to ignore the details, tall and short, black and white, long hair and short hair, male and female, etc.; and she pays attention to the thing that they all have in common, namely, humanity. On Aristotle's view, the universal humanity is the same in all humans (i.e., all humans have that exact same type in common); and this allows us to form a concept of humanity that applies to all humans.
Are Aristotelian universals the sorts of things we refer to when we use general terms, like 'redness' and 'humanity'? Again, perhaps. The idea is that when we refer to humanity, we refer to the type, human being, that appears identically in each human. We do not refer simply to all the humans, but instead the type, human being, which is the same in each human.
