In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being, or simply categories, is to determine the most fundamental and the broadest classes of entities. A distinction between such categories, in making the categories or applying them, is called an ontological distinction. Various systems of classification have been proposed; these often include categories for substances, properties, relations, states of affairs, or events. A representative question within the theory of categories might be, for example, that which asks: "Are universals prior to particulars?"
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👉 Relation (metaphysics) in the context of Universal (metaphysics)
In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs share the quality of "chairness", as well as "greenness" or the quality of being green; in other words, they share two "universals". There are three major kinds of qualities or characteristics: types or kinds (e.g. mammal), properties (e.g. short, strong), and relations (e.g. father of, next to). These are all different types of universals.
Paradigmatically, universals are abstract (e.g. humanity), whereas particulars are concrete (e.g. the personhood of Socrates). However, universals are not necessarily abstract and particulars are not necessarily concrete. For example, one might hold that numbers are particular yet abstract objects. Likewise, some philosophers, such as D. M. Armstrong, consider universals to be concrete.
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Relation (metaphysics) in the context of Aristotle's theory of universals
Aristotle's theory of universals is Aristotle's classical solution to the problem of universals, sometimes known as the hylomorphic theory of immanent realism. Universals are the characteristics or qualities that ordinary objects or things have in common. They can be identified in the types, properties, or relations observed in the world. For example, imagine there is a bowl of red apples resting on a table. Each apple in that bowl will have many similar qualities, such as their red coloring or "redness". They will share some degree of the quality of "ripeness" depending on their age. They may also be at varying degrees of age, which will affect their color, but they will all share a universal "appleness". These qualities are the universals that the apples hold in common.
The problem of universals asks three questions. Do universals exist? If they exist, where do they exist? Also, if they exist, how do we obtain knowledge of them? In Aristotle's view, universals are incorporeal and universal, but only exist only where they are instantiated; they exist only in things. Aristotle said that a universal is identical in each of its instances. 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. For the Aristotelian, knowledge of the universals is not obtained from a supernatural source. It is obtained from experience by means of active intellect.