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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]

In philosophy

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:

Examples of abstract and concrete objects
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 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.)

Abstract objects and causality

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]

Quasi-abstract entities

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]

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.

Abstract idea	Concrete 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.

References

^ ^a ^b ^c Rosen, Gideon (2020). "Abstract Objects". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 4 January 2021.
^ Honderich, Ted (2005). "abstract entities". The Oxford Companion to Philosophy. Oxford University Press.
^ Craig, Edward (1996). "Abstract objects". Routledge Encyclopedia of Philosophy. Routledge.
^ Abrams, Meyer Howard; Harpham, Geoffrey Galt (2011). A Glossary of Literary Terms. Cengage Learning. ISBN 978-0495898023. Retrieved 18 September 2012.
^ Armstrong, D. M. (2010). Sketch for a systematic metaphysics. Oxford: Oxford University Press. p. 2. ISBN 9780199655915.
^ Zalta 1983, p. 33.
^ Carr, Philip (2012) "The Philosophy of Phonology" in Philosophy of Linguistics (ed. Kemp, Fernando, Asher), Elsevier, p. 404
^ Ernst Mally – The Metaphysics Research Lab
^ ^a ^b ^c Rosen, Gideon. "Abstract Objects". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ KrV A51/B75–6. See also: Edward Willatt, Kant, Deleuze and Architectonics, Continuum, 2010 p. 17: "Kant argues that cognition can only come about as a result of the union of the abstract work of the understanding and the concrete input of sensation."
^ Georg Wilhelm Friedrich Hegel: The Science of Logic, Cambridge University Press, 2010, p. 609. See also: Richard Dien Winfield, Hegel's Science of Logic: A Critical Rethinking in Thirty Lectures, Rowman & Littlefield Publishers, 2012, p. 265.
^ Gottlob Frege, "Der Gedanke. Eine logische Untersuchung", in: Beiträge zur Philosophie des deutschen Idealismus 1 (1918/19), pp. 58–77; esp. p. 69.
^ B. Smith (2008), "Searle and De Soto: The New Ontology of the Social World". In The Mystery of Capital and the Construction of Social Reality. Open Court.
^ Robinson, E. H. (2011). "A Theory of Social Agentivity and Its Integration into the Descriptive Ontology for Linguistic and Cognitive Engineering" (PDF). International Journal on Semantic Web and Information Systems. 7 (4): 62–86. doi:10.4018/ijswis.2011100103. Archived from the original (PDF) on Aug 10, 2017.
^ E. H. Robinson (2014), "A Documentary Theory of States and Their Existence as Quasi-Abstract Entities", Geopolitics 19 (3), pp. 1–29.

Sources

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.