Inphilosophy andthe arts, a fundamental distinction exists betweenabstract andconcrete entities. While there is nouniversally accepted definition, common examples illustrate the difference:numbers,sets, andideas are typically classified as abstract objects, whereasplants,dogs, andplanets are considered concrete objects.^[1]

Philosophers have proposed several criteria to define this distinction:

1. Spatiotemporal existence – Abstract objects exist outsidespace-time, while concrete objects exist within space-time.
2. Causal influence – Concrete objects can cause and be affected by other entities (e.g., a rock breaking a window), whereas abstract objects (e.g., the number 2) lack causal powers and do not cause anything to happen in the physical world.
3. Metaphysical relation – Inmetaphysics, concrete objects are specific, individual things (particulars), while abstract objects represent general concepts or categories (universals).
4. Ontological domain – Concrete objects belong to the physical realm (or both the physical and mental realms), whereas abstract objects belong to 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 inphilosophy, particularly metaphysics, andsemantics. They are sometimes calledabstracta in contrast toconcreta. The termabstract object is said to have been coined byWillard 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 thedual copula strategy.^[6]

Thetype–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 ofparadigmatic examples of objects of each kind:

Abstract objects have often garnered the interest of philosophers because they raise problems for popular theories. Inontology, abstract objects are considered problematic forphysicalism and some forms ofnaturalism. Historically, the most important ontological dispute about abstract objects has been theproblem of universals. Inepistemology, abstract objects are considered problematic forempiricism. 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 asErnst Mally,^[8]Edward Zalta^[9] and arguably,Plato in hisTheory of Forms,^[9] have held that abstract objects constitute the defining subject matter ofmetaphysics 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.

Inmodern philosophy, the distinction between abstract and concrete was explored byImmanuel Kant^[10] andG. 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 internalconsciousness.^[1] (SeePopper's three worlds.)

Another popular proposal for drawing the abstract–concrete distinction contends that an object is abstract if it lackscausal 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 relevantStanford Encyclopedia of Philosophy article.^[9]

In the 2010s, there was some philosophical interest in the development of a third category of objects known as thequasi-abstract. Quasi-abstract objects have drawn particular attention in the area ofsocial ontology anddocumentality. Some argue that the over-adherence to theplatonist duality of the concrete and the abstract has led to a large category of social objects having been overlooked or rejected asnonexistent 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]

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 atPhilPapers
• Nominalism, Realism, Conceptualism, fromThe Catholic Encyclopedia
• Abstract vs. Concrete in Writing, from Writing for Results