# abstraction

The word abstraction ( Latin abstractus 'withdrawn', participle perfect passive from abs-trahere 'deduct', 'remove', 'separate') mostly describes the inductive thought process of the necessary omission of details and the transfer to something more general or simpler. There are also specific and unspecific uses of the term in certain individual sciences and individual theories , theses and assertions of various octases.

## philosophy

In philosophy, abstraction describes a conceptual process by which certain given, but considered to be insignificant features of an object are dispensed with. In this way, the focus should be on the essentials, i. H. to a very specific conceptual meaning of the special characteristics recorded in this way . Already here the question arises whether such an abstraction process can be described as similar in every case if it is used both inter-individually - between different people - and categorically - for different types of terms. These kinds of questions are the subject of abstraction theory . As a result of these theories, different methods of abstraction are assumed, such as the method of isolating abstraction . Here, the key for a specific object properties are exposed somewhat in the manner of a parlor game in which the phrase guessed by yes / no answers from an ever closer by a given number of features concept extent be crystallized needs.

Abstraction often denotes an operation of thinking which “subtracts” general properties from concrete objects of reality (such as this tree here, that tree there, etc.) and, for example, forms general terms from them (such as the genus tree ). For this purpose, certain individual properties of the concrete objects must be disregarded, so that the abstracted characteristics also apply to several other objects. Some philosophers (so-called universal realists) attribute such general terms to independent reality (the term tree also exists when there are no trees in the real world or there are no words in any natural language expressing the content of the tree term). According to some theorists, precisely because they are abstractions , such terms have a specific status of their own, as is inherent in informational contents: namely, these contents are not spatially and temporally localized and are only accessible to those consciousnesses who are able to perform abstractions of the corresponding type at all. The latter approaches so-called idealistic or constructivist positions with regard to abstract concepts. These are opposing positions to universal realism, which assert that general terms and the like are mere constructs and have no being independent of thought or more precise abstraction operations. (In addition, one calls those extreme positions that teach that there is only one type of being, namely mental, as thought, mostly also idealistic .) Debates on such ontological and epistemological topics have been going on for centuries and have been in the last decades once again increased in complexity. For example, different realistic theories regarding natural species (objects such as hydrogen , trees, etc.) have been worked out; there are so-called trope theories which describe universals as only, but completely, existing in individuals. The first type of theories denies that species concepts obtained through correct abstraction are mere abstractions.

In order to capture the intuitively plausible, but difficult to explain exactly, distinction between abstract and concrete objects, complicated theories were worked out, for example by Crispin Wright and Bob Hale or by Edward N. Zalta . While theorists like George Bealer try to show the necessary existence of abstract objects a priori and Hilary Putnam on an epistemological basis, Hartry Field wants to prove the opposite, especially for the philosophy of mathematics.

### Selected positions in the history of philosophy

Even the pre-Socratics were looking for one or more primary materials to explain reality by tracing back to abstract objects or principles. Heraclitus, for example, looked for the common in all that existed.

Plato bases every thing on a perfect idea of the object: this tree is a tree because it participates in the idea of ​​the tree, which itself is not localized in space and time and is also recognized not simply through abstraction, but through recollection of the idea of ​​the tree becomes. The problems associated with such a realism of ideas were partly discussed by Plato himself.

Aristotle called the features of an object that were considered insignificant as accident . In his teaching he set up three levels of abstraction. These have had a significant impact on metaphysics. If one assigns the highest level of abstraction as the highest generality to so-called being , this term becomes very comprehensive, but also so empty of content that one saws off the branch on which one is sitting or believing to be sitting, cf. → Extension and Intension , Arbor porphyriana . Aristotle discusses the Platonic doctrine of ideas much more critically. He himself works with the term eidos . This is a kind of structural principle of objects of a certain type. But this itself is localized in beings and metaphysically not separable from them (there is no redness if there are no red objects). Aristotle, however, also teaches a quartet of causes. The cause of the form is particularly relevant here. By tracing back to more fundamental , more abstract causes, objects and their so-quality are also explained. Since this return should not go on indefinitely, Aristotle uses an "unmoved mover" himself. All "movement", which means in particular every change in position and condition , has its first cause in it.

The juxtaposition of abstract and concrete comes from the late antique philosopher Boëthius .

The so-called universal dispute over whether the abstract terms “before” or “after things” existed or were formed kept the thinkers of the Middle Ages in suspense.

Johannes Duns Scotus, for example, assumed in his “abstract” epistemology that an object can only be experienced through the senses and creates an image in the mind. Through the independent, active activity of the mind, this still disordered idea is determined as the universal in the image . This means that the general contained in the picture is abstracted from the special and material conditions of the individual object. The result is a clearly delimited knowledge that conceptually grasps the object in all its facets. The knowledge is only completed when it is anchored in the memory . Only through (passive) internalization does an object become intelligible and can shine as a possibility in the visualization, that is, be called back into consciousness. The concept of an object, once acquired, can be replaced by another concept, just as ideas can be changed or newly created through combination.

Also some English philosophers of the early modern period, e.g. B. John Locke and George Berkeley (the latter drove the abstraction to the no longer obscure "something") as well as Gottfried Wilhelm Leibniz , Baruch Spinoza and René Descartes were concerned with the topic and argued among other things. a. it is about whether our concepts of essences (what constitutes water as such or what makes water) are innate or acquired.

David Hume , who advocated an empirical approach, also took part in this dispute ; Cause and effect, for example, would only be formed from the experience of a sequence from something to something, but we would never know with certainty whether the sun would rise again tomorrow. Hume was again criticized by Immanuel Kant , who developed the counter-concept of the (presupposed) “ conditions of the possibility of every experience”: the pure forms of intuition, the categories of understanding, the regulators of reason.

The philosophical movement of the so-called German idealism around the turn of the 18th to the 19th century (e.g. Georg Wilhelm Friedrich Hegel , Friedrich Wilhelm Joseph von Schelling ) determined the very presupposing concept of concretion as a counter-concept to abstraction. These theories are very complicated. The idealists understood by concretion not the process of thinking the (common) concrete or applying a (common) general term to something concrete, but rather the "dialectical abolition" of the difference between the abstract and the concrete in a higher unity which, according to their statements, is only possible should adequately grasp reality.

Martin Heidegger , who in Sein und Zeit (1927) accused the entire tradition of thought, and especially the idealists, of having skipped the “everyday”, formed another pair of opposites that should grasp the abstraction and concreteness of “everyday”: “at hand” and “available ".

In the Philosophical Dictionary (Apel / Ludz, 1958) abstraction is seen as the opposite of determination , that is, quite different from z. B. with the idealists, and a number of different abstraction methods listed: isolating or generalizing (generalizing), quantitative or qualitative, negative or positive abstraction.

The different conceptions of epistemology result in different approaches to defining abstraction. The representatives of modern philosophy of science and analytical philosophy also took part in this dispute.

The term concretization is also contrasted with abstraction.

Unanimity of views has not been achieved. Only since ancient times has there been a consensus, even among philosophers, that mathematics and logic are purely abstract sciences. Today the systems theory of computer science is also considered a purely abstract science.

Other sciences can be viewed from an abstract perspective, among other things. In art, works are called abstract that move away from the objective point of view.

## art

In the fine arts , abstraction describes, on the one hand, the more or less pronounced stylistic reduction of the things represented to essential or specific aspects. In this case one speaks of abstracting from the general to the essential . What is considered essential determines on the one hand the creativity of the artist and on the other hand the perception of the viewer.

The drawings by Steffen Flossmann depict a stag beetle in different degrees of abstraction. Abstraction can result in changes, for example in perspective, color, structure or style. Characteristic changes are often particularly noticeable, that is, things that, like the yellow area in example F, do not belong to the object or like the additional leg links in example D emphasize a characteristic.

On the other hand, the term in art denotes various currents of modernity or contemporary art , the characteristic of which is even the complete absence of a specific object reference. ( Abstract art , especially abstract painting ) Here the viewer must increasingly expand his individual ability to abstract in order to be able to understand the changes made by the artist. Works of these trends, for example, thematize the formal design principles themselves ( geometric abstraction in the creative arts), the sign language of the artist ( action painting ) or the changes in color ( informel , tachism , drip painting ). In the performing arts , too , abstraction can go so far that the original features (e.g. of a conversation or an action) can only be understood by the viewer if he recognizes the essentials. All currents of abstract art require skills of perception and interpretation.

The description of moments in art that are not subject to a mimetic reference to an object - a norm formulated historically in particular for the visual and performing arts, which can only be referred to music, architecture and literature with considerable restrictions - as an abstraction, however a possible perspective that contradicts the self-image of various currents in art history. Thus, the marginalized Suprematism Kasimir Malevich and Constructivism as irrelevant explicitly from the abstract art (such as Wassily Kandinsky ) from when illusionismusfreier creation of new concrete reality in the works of art (Suprematism) and creative design of material life (constructivism).

## mathematics

In mathematics and modern philosophy , abstracts are mostly identified with equivalence classes . Starting from a given set K of Concrete , one defines an equivalence relation ~ on K and assigns the Concrete to an abstraction (also called a ' class ').

All variants of the modern abstraction theory have in common the basic idea that a transition should be made from the concrete and their existing equivalence relation to the identity of the respective abstractions. A list of examples will make this clearer:

• bodies of the same weight have the same weight;
• sets of equal power have the same cardinal number;
• congruent numbers leave the remainder when divided by a fixed number;
• parallel straight lines have the same direction;
• Synonymous predicates express the same term.

Fields, sets, straight lines and predicates are the concrete K in this list; Weights, cardinal numbers, directions and concepts are the abstractions obtained from them; “Equal weight”, “equally powerful”, “parallel”, “synonymous” express the equivalence relation ~. In the case of numbers, this has already been formulated by David Hume in his Treatise of Human Nature , which is why one speaks of Hume's principle .

From this list, a general scheme can win: ; read: For all concretions x and y the abstract a to x is identical to the abstract a to y if and only if x is in ~ to y. Gottlob Frege described this in his Fundamentals of Arithmetic as a redistribution: The content of z. B. "parallel" migrates z. T. in the general "=", z. T. in the abstractive functor a . ${\ displaystyle \ forall x \ forall y \ (K (x) \ land K (y) \ rightarrow (a (x) = a (y) \ leftrightarrow x \ thicksim y))}$

However, this does not work as a definition of the functor a . Frege's original suggestion from the Fundamentals of Arithmetic therefore consists in simply viewing the associated equivalence class as the abstraction for a given equivalence relation. In the case of numbers, he gives the famous definition:

The number assigned to the term F is the scope of the term “equal to the term F”.

Generalized and transferred into modern notation, it can be said: . In words: The abstraction to x under a given equivalence relation ~ is the set of those y which are in the equivalence relation ~ to x. ${\ displaystyle \ forall x \ (a (x) = \ {y | y \ thicksim x \})}$

## psychology

In psychology , abstraction is the term used to describe the process that reduces information to its essential properties to such an extent that it can be processed psychologically using methods other than the original information. Examples are images , ideas , models , symbols , transformations and concepts . In everyday life, for example, every shape of a chair as a seat is perceived completely differently in every situation in terms of view , shape , etc., but linguistically reduced to its useful property for use by humans (seat object with only vaguely loosely outlined shape). Only in this way can the request “give me a chair, please” be understood, because the person requesting and the recipient have a common, abstract idea of ​​what is needed for the respective purpose.

In psychology, the ability to abstract is the prerequisite for the formation of terms and rules and thus the prerequisite for cognitive abilities such as thinking , learning , perception or memory . To make things easier, terms are often collected and defined in encyclopedias or dictionaries. The larger number of all terms is generated individually, however, they are only relevant to the situation.

Concept formation through abstraction is described as an essential individual and cultural ability. A person like Borges ' fictional character Funes, who experiences every second of his life as new and unique, would not be able to survive.

The level of abstraction of terms ( called icon in the pictorial area ) can vary. The human brain works optimally with terms at a medium level of abstraction that are neither too general, i.e. not very informative (example: "Give me the thing!"), Nor too specific, i.e. burdened with unimportant details. Advantages of these moderately abstract conceptual representations (Zeitz) are:

1. They are stable in long-term memory , so new detailed information does not immediately invalidate them.
2. They are fertile because they are neither activated by everyone nor exclusively by very special cues.
3. They can easily be adapted to the given situation.

Numerous studies have shown that people generally get by with three levels of abstraction per term: the middle basic level (e.g. "chair"), plus a more abstract generic term (e.g. "furniture") and the more specific level of individual examples (e.g. B. "my kitchen chair"). The terms of the basic level are also called basic categories and are characterized by characteristic properties:

1. Children learn them first (eg first “clock”, later “measuring device” and “wristwatch”).
2. Dealing with them often requires special movements (“sitting on them” is similar for all chairs).
3. They look roughly the same, so the whole category can be represented in the memory by a single picture (see picture books for toddlers).

With increasing experience, the assignment of the three abstraction levels changes, so a furniture seller will not remember every single chair, but will use the price ranges to differentiate.

Ability to abstract is also an important prerequisite for effective and efficient learning. In learning psychology there is therefore the term “progressive abstraction”, i. H. the ability to be able to summarize more and more information of the same kind under certain general terms and thus to network one's knowledge more and more closely.

The ability to abstract as a psychological achievement can also be disturbed : For example, people with different forms of schizophrenia , with severe neuroses or with a reduced intelligence can have problems understanding or distinguishing between terms. They often lack social interactions . In the case of an intellectual disability, for example, terms such as “ladder” and “stairs” can no longer be distinguished from one another in an abstract manner. People with abstraction deficits often describe these objects, for example, as “you can climb up there” instead of recognizing differences (here e.g. transportability or angle of incline). Typical of a lack of abstraction ability is the inability to understand a specific object, e.g. B. "Staircase in my house at Musterstrasse 3" can be recognized as functionally identical to all other "stairs".

### Abstraction in depth psychology

Carl Gustav Jung defines abstraction as a mental activity that pulls unique, incomparable or individual content away from a link, differentiates it. If one is abstracted towards the object, an attempt is made to get rid of the object as a unique whole and to withdraw interest from the object and let it flow back to the subject. According to Jung, abstraction is a withdrawal of the libido (= energy ) from the object to the subjective abstract content, which equates to an object devaluation. In other words, abstraction is an introverted libido movement. According to Jung, the opposite of abstraction is the attitude towards concretism .

## Linguistics

A linguistic abstraction is the formation of categories ( taxonomy ) that do not describe the individual objects. An abstract category is formed that integrates the properties of the individual objects, but does not name them precisely. The “furnishings” category is an abstraction of the specific terms “sofa”, “table”, “cupboard”, “lamp” etc. which are included in the “furnishings” category.

The abstraction into grammatical categories such as adverbs, adjectives, nouns, predicates, copula, is an extended intellectual performance that is not accessible to small children. In everyday life, this abstraction process takes place involuntarily and unnoticed. The incarnation was crucially related to the development of the ability to abstract ideas. However, thinkers and scientists do not always agree on what exactly is meant by abstraction.

## literature

• G. Frege: The basics of arithmetic. Wroclaw 1884.
• Chr. Metzger: Theory of Abstraction, Passages, Vienna, 2020.
• G. Siegwart: Abstraction under one equality. In: HJ Sandkühler (Ed.): Encyclopedia Philosophy. Hamburg 1999.
• Chr. Thiel: Gottlob Frege: The abstraction. In: J. Speck (ed.): Basic problems of the great philosophers. Philosophy of the Present I. Göttingen 1972, pp. 9–44.

Commons : Abstraction  - collection of images, videos and audio files
Wiktionary: Abstraction  - explanations of meanings, word origins, synonyms, translations

## supporting documents

1. ^ A b Peter Prechtl , Franz-Peter Burkard (original): Metzler Lexicon Philosophy. Terms and definitions. 3rd, exp. and actual Edition. Verlag JB Metzler, Stuttgart 2008, ISBN 978-3-476-02187-8 , p. 6.
2. ^ Fritz Mauthner : Dictionary of Philosophy. Diogenes-Verlag, Zurich 1980, ISBN 3-257-20828-7 , pp. 9-11.
3. ^ Jean-Marie Zemb : Aristotle. with personal testimonials and picture documents. (= Rowohlt's monographs. 63). 13th edition. Rowohlt Taschenbuch, Reinbek bei Hamburg 1995, ISBN 3-499-50063-9 , p. 59.
4. ^ IJM Van den Berg: L'abstraction et ses degrés chez Aristote. In: Actes du X e Congr. int.philos. 3, Brussels / Amsterdam 1951, pp. 109, 113.
5. Andrei B. Nakov, Michel Petris: Avertissement the traducteurs. In: Nikolaj Tarabukin: Le dernier tableau. Éditions Champ Libre, Paris 1972, pp. 21-23.
6. Gottlob Frege: The basics of arithmetic. Breslau 1884, § 64; Cf. Geo Siegwart: Abstraction under one equality. In: Hans Jörg Sandkühler (Ed.): Encyclopedia Philosophy. Meiner, Hamburg 1999.
7. G. Frege: Fundamentals of arithmetic. Breslau 1884, p. 79f.
8. Jorge Luis Borges: Funes el memorioso (1942, Eng . The inexorable memory ).
9. ^ CM Zeitz: Some concrete advantages of abstraction. In: PJ Feltovich et al. (Ed.): Expertise in context. MIT Press, Cambridge (Mass.) 1997.
10. M. Eysenck, M. Keane: Cognitive Psychology . Psychology Press, Hove (UK) 2000.