Abstract and concrete

In philosophy and the arts, a fundamental distinction is between things that are abstract and things that are concrete. While there is no general consensus as to how to precisely define the two, examples include that things like numbers, sets, and ideas are abstract objects, while plants, dogs, and planets are concrete objects.^[1] Popular suggestions for a definition include that the distinction between concreteness versus abstractness is, respectively: between (1) existence inside versus outside space-time; (2) having causes and effects versus not; 3) being related, in metaphysics, to particulars versus universals; and (4) belonging to either the physical versus the mental realm (or the mental-and-physical realm versus neither).^[2][3][4] Another view is that it is the distinction between contingent existence versus necessary existence; however, philosophers differ on which type of existence here defines abstractness, as opposed to concreteness. Despite this diversity of views, there is broad agreement concerning most objects as to whether they are abstract or concrete,^[1] such that most interpretations agree, for example, that rocks are concrete objects while numbers are abstract objects.

Abstract objects are most commonly used in philosophy, particularly metaphysics, and semantics. They are sometimes called abstracta in contrast to concreta. The term abstract object is said to have been coined by Willard Van Orman Quine.^[5] Abstract object theory is a discipline that studies the nature and role of abstract objects. It holds that properties can be related to objects in two ways: through exemplification and through encoding. Concrete objects exemplify their properties while abstract objects merely encode them. This approach is also known as the dual copula strategy.^[6]

The type–token distinction identifies physical objects that are tokens of a particular type of thing.^[7] 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. 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 and 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,^[8] Edward Zalta^[9] and arguably, Plato in his Theory of Forms,^[9] 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^[10] and G. W. F. Hegel.^[11]

Gottlob Frege said that abstract objects, such as propositions, were members of a third realm,^[12] different from the external world or from internal consciousness.^[1] (See Popper's three worlds.)

Another popular proposal for drawing the abstract–concrete distinction contends that an object is abstract if it lacks causal power. 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 with this view is that it is not clear exactly what it is to have causal power. For a more detailed exploration of the abstract–concrete distinction, see the relevant Stanford Encyclopedia of Philosophy article.^[9]

Recently^[when?], there has been some philosophical interest in the development of a third category of objects known as the quasi-abstract. ^{[citation needed]} 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.^[13] Specifically, the ability to have temporal location, but not spatial location, and have causal agency (if only by acting through representatives).^[14] These characteristics are exhibited by a number of social objects, including states of the international legal system.^[15]

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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.

• Zalta, Edward N. (1983). Abstract Objects: An Introduction to Axiomatic Metaphysics. Synthese Library. Vol. 160. Dordrecht, Netherlands: D. Reidel Publishing Company. ISBN 978-90-277-1474-9.

• Abstract and concrete at PhilPapers
• Nominalism, Realism, Conceptualism, from The Catholic Encyclopedia
• Abstract vs. Concrete in Writing, from Writing for Results