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A universal may have instances, known as its particulars. For example, the type dog (or doghood) is a universal, as are the property red (or redness) and the relation betweenness (or being between). Any particular dog, red thing, or object that is between other things is not a universal, however, but is an instance of a universal.
Redness, by contrast, is not a particular, because it is abstract and multiply instantiated (for example a bicycle, an apple, and a particular woman's hair can all be red). In the nominalist view, everything is particular. A universal at each moment in time, from the point of view of an observer, is a set of particulars.
In Aristotle's view, universals are incorporeal and universal, but only exist only where they are instantiated; they exist only in things. [1] 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.
A central distinction in ontology is between particular and universal entities. Particulars, also called individuals, are unique, non-repeatable entities, like Socrates, the Taj Mahal, and Mars. [29] Universals are general, repeatable entities, like the color green, the form circularity, and the virtue courage. Universals express aspects or ...
Nyāya postulates the existence of universals based on our experience of a common characteristic among particulars. Thus, the meaning of a word is understood as a particular further characterized by a universal. [28] For example, the meaning of the term 'cow' refers to a particular cow characterized by the universal of 'cowness'.
In particular, the concept of universal property allows a simple proof that all constructions of real numbers are equivalent: it suffices to prove that they satisfy the same universal property. Technically, a universal property is defined in terms of categories and functors by means of a universal morphism (see § Formal definition , below).
A trope is a particular instance of a property, like the specific greenness of a shirt. One might argue that there is a primitive, objective resemblance relation that holds among like tropes. Another route is to argue that all apparent tropes are constructed out of more primitive tropes and that the most primitive tropes are the entities of ...
In predicate logic, universal instantiation [1] [2] [3] (UI; also called universal specification or universal elimination, [citation needed] and sometimes confused with dictum de omni) [citation needed] is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class.