In metaphysics, 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 (AOT). According to AOT, some objects (the ordinary concrete ones around us, like tables and chairs) exemplify properties, while others (abstract objects like numbers, and what others would call "non-existent objects", like the round square, and the mountain made entirely of gold) merely encode them (this is also known as the dual copula strategy).
In philosophy
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 | Concrete |
|---|---|
| Tennis | A tennis match |
| Redness | Red light reflected off of an apple and hitting one's eyes |
| Five | Five cars |
| Justice | A just action |
| Humanity (the property of being human) | Human population (the set of all humans) |
Abstract objects have often garnered the interest of philosophers because they raise problems for popular theories. In ontology, abstract objects are considered problematic for physicalism and some forms of naturalism. Historically, the most important ontological dispute about abstract objects has been the problem of universals. In epistemology, abstract objects are considered problematic for empiricism. If abstracta lack causal powers or spatial location, how do we know about them? It is hard to say how they can affect our sensory experiences, and yet we seem to agree on a wide range of claims about them.
Some, such as Ernst Mally, 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.
In modern philosophy, the distinction between abstract and concrete was explored by Immanuel Kant and G. W. F. Hegel.
Gottlob Frege said that abstract objects, such as numbers, were members of a third realm, different from the external world or from internal consciousness.
Abstract objects and causality
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, see the relevant Stanford Encyclopedia of Philosophy article.
Quasi-abstract entities
Recently, there has been some philosophical interest in the development of a third category of objects known as the quasi-abstract. Quasi-abstract objects have drawn particular attention in the area of social ontology and documentality. Some argue that the over-adherence to the platonist duality of the concrete and the abstract has led to a large category of social objects having been overlooked or rejected as nonexistent because they exhibit characteristics that the traditional duality between concrete and abstract regards as incompatible. Specially, the ability to have temporal location, but not spatial location, and have causal agency (if only by acting through representatives). These characteristics are exhibited by a number of social objects, including states of the international legal system.
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.
| Concrete idea | Abstract idea |
|---|---|
| Dense things sink. | It will sink if its density is greater than the density of the fluid. |
| You breathe in oxygen and breathe out carbon dioxide. |
Gas exchange takes place between the air in the alveoli and the blood. |
| Plants get water through their roots. | Water diffuses through the cell membrane of the root hair cells. |
