In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, common examples illustrate the difference: numbers, sets, and ideas are typically classified as abstract objects, whereas plants, dogs, and planets are considered concrete objects.
Philosophers have proposed several criteria to define this distinction:
Ontology is the philosophical study of being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of reality and every entity within it. To articulate the basic structure of being, ontology examines the commonalities among all things and investigates their classification into basic types, such as the categories of particulars and universals. Particulars are unique, non-repeatable entities, such as the person Socrates, whereas universals are general, repeatable entities, like the color green. Another distinction exists between concrete objects existing in space and time, such as a tree, and abstract objects existing outside space and time, like the number 7. Systems of categories aim to provide a comprehensive inventory of reality by employing categories such as substance, property, relation, state of affairs, and event.
Ontologists disagree regarding which entities exist at the most basic level. Platonic realism asserts that universals have objective existence, while conceptualism maintains that universals exist only in the mind, and nominalism denies their existence altogether. Similar disputes pertain to mathematical objects, unobservable objects assumed by scientific theories, and moral facts. Materialism posits that fundamentally only matter exists, whereas dualism asserts that mind and matter are independent principles. According to some ontologists, objective answers to ontological questions do not exist, with perspectives shaped by differing linguistic practices.
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, relationship, or mathematical formula. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise different concepts and experiences. All communication is achieved through the use of symbols: for example, a red octagon is a common symbol for "STOP"; on maps, blue lines often represent rivers; and a red rose often symbolizes love and compassion. Numerals are symbols for numbers; letters of an alphabet may be symbols for certain phonemes; and personal names are symbols representing individuals. The academic study of symbols is called semiotics.
In the arts, symbolism is the use of a concrete element to represent a more abstract idea. In cartography, an organized collection of symbols forms a legend for a map.
Existence is the state of having being or reality in contrast to nonexistence and nonbeing. Existence is often contrasted with essence: the essence of an entity is its essential features or qualities, which can be understood even if one does not know whether the entity exists.
Ontology is the philosophical discipline studying the nature and types of existence. Singular existence is the existence of individual entities while general existence refers to the existence of concepts or universals. Entities present in space and time have concrete existence in contrast to abstract entities, like numbers and sets. Other distinctions are between possible, contingent, and necessary existence and between physical and mental existence. The common view is that an entity either exists or not with nothing in between, but some philosophers say that there are degrees of existence, meaning that some entities exist to a higher degree than others.
A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs.Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach, cognitive science.
In contemporary philosophy, three understandings of a concept prevail:
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations. A model may help to characterize a system by studying the effects of different components, which may be used to make predictions about behavior or solve specific problems.
In works of art, literature, and narrative, a symbol is a concrete element like an object, character, image, situation, or action that suggests or hints at abstract, deeper, or non-literal meanings or ideas. The use of symbols artistically is symbolism. In literature, such as novels, plays, and poems, symbolism goes beyond just the literal written words on a page, since writing itself is also inherently a system of symbols.
Artistic symbols may be intentionally built into a work by its creator, which in the case of narratives can make symbolism a deliberate narrative device. However, it also may be decided upon by the audience or by a consensus of scholars through their interpretation of the work. Various synonyms exist for this type of symbol, based on specific genre, artistic medium, or domain: visual symbol, literary symbol, poetic symbol, etc.
Abstraction is the process of generalizing rules and concepts from specific examples, literal (real or concrete) signifiers, first principles, or other methods. The result of the process, an abstraction, is a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a group, field, or category.
Abstractions and levels of abstraction play an important role in the theory of general semantics originated by Alfred Korzybski. Anatol Rapoport wrote "Abstracting is a mechanism by which an infinite variety of experiences can be mapped on short noises (words)." An abstraction can be constructed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects that are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, excluding but not eliminating the other phenomenal and cognitive characteristics of that particular ball. In a type–token distinction, a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').