Abstract and concrete are classifications that denote whether the object that a term describes has physical referents. Abstract objects have no physical referents, whereas concrete objects do. They are most commonly used in philosophy and semantics. Abstract objects are sometimes called abstracta (sing. abstractum) and concrete objects are sometimes called concreta (sing. concretum). An abstract object is an object that does not exist at any particular time or place, but rather exists as a type of thing—i.e., an idea, or abstraction. The term abstract object is said to have been coined by Willard Van Orman Quine. The study of abstract objects is called abstract object theory.
The type–token distinction identifies physical objects that are tokens of a particular type of thing. The "type" of which it is a part is in itself an abstract object. The abstract-concrete distinction is often introduced and initially understood in terms of paradigmatic examples of objects of each kind:
Abstract objects have often garnered the interest of philosophers because they raise problems for popular theories.
Some, such as Edward Zalta and arguably, Plato in his Theory of Forms, have held that abstract objects constitute the defining subject matter of metaphysics or philosophical inquiry more broadly. To the extent that philosophy is independent of empirical research, and to the extent that empirical questions do not inform questions about abstracta, philosophy would seem especially suited to answering these latter questions.
Another popular proposal for drawing the abstract-concrete distinction contends that an object is abstract if it lacks any causal powers. A causal power has the ability to affect something causally. Thus, the empty set is abstract because it cannot act on other objects. One problem for this view is that it is not clear exactly what it is to have a causal power. For a more detailed exploration of the abstract-concrete distinction, follow the link below to the Stanford Encyclopedia article.
Recently, there has been some philosophical interest in the development of a third category of objects known as the quasi-abstract.
Concrete and abstract thought in psychology
Jean Piaget uses the terms "concrete" and "formal" to describe two different types of learning. Concrete thinking involves facts and descriptions about everyday, tangible objects, while abstract (formal operational) thinking involves a mental process.