abstract entity an object lacking spatiotemporal properties, but supposed to have being, to exist, or (in medieval Scholastic terminology) to subsist. Abstracta, sometimes collected under the category of universals, include mathematical objects, such as numbers, sets, and geometrical figures, propositions, properties, and relations. Abstract entities are said to be abstracted from particulars. The abstract triangle has only the properties common to all triangles, and none peculiar to any particular triangles; it has no definite color, size, or specific type, such as isosceles or scalene. Abstracta are admitted to an ontology by Quine’s criterion if they must be supposed to exist (or subsist) in order to make the propositions of an accepted theory true. Properties and relations may be needed to account for resemblances among particulars, such as the redness shared by all red things. Propositions as the abstract contents or meanings of thoughts and expressions of thought are sometimes said to be necessary to explain translation between languages, and other semantic properties and relations. Historically, abstract entities are associated with Plato’s realist ontology of Ideas or Forms. For Plato, these are the abstract and only real entities, instantiated or participated in by spatiotemporal objects in the world of appearance or empirical phenomena. Aristotle denied the independent existence of abstract entities, and redefined a diluted sense of Plato’s Forms as the secondary substances that inhere in primary substances or spatiotemporal particulars as the only genuine existents. The dispute persisted in medieval philosophy between realist metaphysicians, including Augustine and Aquinas, who accepted the existence of abstracta, and nominalists, such as Ockham, who maintained that similar objects may simply be referred to by the same name without participating in an abstract form. In modern philosophy, the problem of abstracta has been a point of contention between rationalism, which is generally committed to the existence of abstract entities, and empiricism, which rejects abstracta because they cannot be experienced by the senses. Berkeley and Hume argued against Locke’s theory of abstract ideas by observing that introspection shows all ideas to be particular, from which they concluded that we can have no adequate concept of an abstract entity; instead, when we reason about what we call abstracta we are actually thinking about particular ideas delegated by the mind to represent an entire class of resemblant particulars, from which we may freely substitute others if we mistakenly draw conclusions peculiar to the example chosen. Abstract propositions were defended by Bolzano and Frege in the nineteenth century as the meanings of thought in language and logic. Dispute persists about the need for and nature of abstract entities, but many philosophers believe they are indispensable in metaphysics.
See also ARISTOTLE , BERKELEY , FREGE, METAPHYSICAL REALISM , OCKHAM , PLATO , PROPERT. D.J.