We might look at other graphs, in a progression from "cat" to "mammal" to "animal", and see that "animal" is more abstract than "mammal"; but on the other hand "mammal" is a harder idea to express, certainly in relation to "marsupial" or "monotreme".
A physical object (a possible referent of a concept or word) is considered "concrete" (not abstract) if it is a "particular individual" that occupies a particular place and time.
Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experiences, like the color red. That definition, however, suffers from the difficulty of deciding which things are real (i.e. which things exist in reality). For example, it is difficult to agree to whether concepts like "God", "the number three", and "goodness" are real, abstract, or both.
An approach to resolving such difficulty is to use "predicates" as a general term for whether things are variously real, abstract, concrete, or of a particular property (e.g. "good"). Questions about the properties of things are then propositions about predicates, which propositions remain to be evaluated by the investigator. In the "graph 1" above, the graphical relationships like the arrows joining boxes and ellipses might denote predicates. Different levels of abstraction might be denoted by a progression of arrows joining boxes or ellipses in multiple rows, where the arrows point from one row to another, in a series of other graphs, say graph 2, etc.
Abstraction in philosophy is the process (or, to some, the alleged process) in concept-formation of recognizing some set of common features in individuals, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals. It has also recently become popular in formal logic under predicate abstraction. Another philosophical tool for discussion of abstraction is thought space.
The way in which physical objects, like rocks and trees, have "being" differs from the way that properties of abstract concepts or relations have "being". For example, the way the concrete, particular, individuals pictured in "picture 1" exist differs from the way the concepts illustrated in "graph 1" exist. That difference accounts for the ontological usefulness of the word "abstract". The word applies to properties and relations to mark the fact that, if they exist, they do not exist in space or time, but that instances of them can exist, potentially in many different places and times.
Perhaps confusingly, some philosophies refer to "tropes" (instances of properties) as "abstract particulars". E.g., the particular redness of a particular apple is an "abstract particular". Akin to qualia and sumbebekos.
If an abstract concept, such as "society" or "technology" is treated as if it were a concrete object, that is a fallacy (an error). In linguistics, it may happen that abstract concepts are used as if they were nouns that signify concrete objects:
This is called "metonymy". It can blur the distinction between abstract and concrete things.
An abstraction can be seen as a process of mapping multiple different pieces of constituent data to a single piece of abstract data based on similarities in the constituent data, for example many different physical cats map to the abstraction "CAT". This conceptual scheme emphasizes the inherent equality of both constituent and abstract data, thus avoiding problems arising from the distinction between "abstract" and "concrete". In this sense the process of abstraction entails the identification of similarities between objects and the process of associating these objects with an abstraction (which is itself an object).
Chains of abstractions can therefore be constructed moving from neural impulses arising from sensory perception to basic abstractions such as color or shape to experiential abstractions such as a specific cat to semantic abstractions such as the "idea" of a CAT to classes of objects such as "mammals" and even categories such as "object" as opposed to "action".
This conceptual scheme entails no specific hierarchical taxonomy (such as the one mentioned involving cats and mammals), only a progressive exclusion of detail.
A recent meta-analysis suggests that the verbal system has greater engagement for abstract concepts when the perceptual system is more engaged for processing of concrete concepts. This is because abstract concepts cause greater brain activity in the inferior frontal gyrus and middle temporal gyrus, compared to concrete concepts when concrete concepts cause greater activity in the posterior cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus.
Other research into the human brain suggests that the left and right hemispheres, of the brain, differ in their handling of abstraction. For example, one meta-analysis reviewing human brain lesions has shown a left hemisphere bias during tool usage.
Typically, "abstraction" is used in the arts as a synonym for abstract art in general. Strictly speaking, it refers to art unconcerned with the literal depiction of things from the visible world—it can, however, refer to an object or image which has been distilled from the real world, or indeed, another work of art. Artwork that reshapes the natural world for expressive purposes is called abstract; that which derives from, but does not imitate a recognizable subject is called nonobjective abstraction. In the 20th century the trend toward abstraction coincided with advances in science, technology, and changes in urban life, eventually reflecting an interest in psychoanalytic theory. Later still, abstraction was manifest in more purely formal terms, such as color, freed from objective context, and a reduction of form to basic geometric designs.
In music, the term "abstraction" can be used to describe improvisatory approaches to interpretation, and may sometimes indicate abandonment of tonality. Atonal music has no key signature, and is characterized the exploration of internal numeric relationships.
Carl Jung's definition of abstraction broadened its scope beyond the thinking process to include exactly four mutually exclusive, opposing complementary psychological functions: sensation, intuition, feeling, and thinking. Together they form a structural totality of the differentiating abstraction process. Abstraction operates in one of these opposing functions when it excludes the simultaneous influence of the other functions and other irrelevancies, such as emotion. Abstraction requires selective use of this structural split of abilities in the psyche. The opposite of abstraction is concretism. "Abstraction" is one of Jung's 57 definitions in Chapter XI of "Psychological Types".
There is an abstract "thinking", just as there is abstract "feeling", "sensation" and "intuition". Abstract thinking singles out the rational, logical qualities ... Abstract feeling does the same with ... its feeling-values. ... I put abstract feelings on the same level as abstract thoughts. ... Abstract sensation would be aesthetic as opposed to sensuous "sensation" and abstract intuition would be symbolic as opposed to fantastic "intuition". (Jung, [1921] (1971):par. 678).
Computer scientists use abstraction to understand and solve problems, such as organizing data to be stored in a database.
Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real-world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
The advantages of abstraction in mathematics are:
The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.