Abstraction theory

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Abstraction theory focuses on the relationship of sensual given material to the optionally for each knowledge presupposed general concepts as well as to the importance of when conceptualization applied abstracting method . Concepts can only be formed or constituted through very specific intellectual acts . This genesis should be shown with the help of abstraction theory. This relationship applies to both mathematical subjects and general concepts.

Concrete questions

Is the abstraction process always to be seen as constant? What is "withdrawn" or "taken away" by whom? A distinction must be made between ...

  • psychologically active "extracted features" of an object, which are therefore only subjectively viewed as essential from the point of view of the knowledge interest , and the ...
  • possibly logically more or less compelling procedures for such features of an object, which objectively turn out to be insignificant in the course of a special abstraction procedure? (e.g. when determining biological genera and species )

Are there different subject areas that each require different abstraction processes? Is z. B. to distinguish the type of abstraction in nomothetic and idiographic objects? See also → differentia specifica , difference and Akzidenz .

These different research approaches go back to Kant's distinction between empirical and pure terms (KrV B 3, 74, 75). In the case of pure concepts, there are no empirical moments, such as B. Sensation . These are "taken away" (KrV B 34). The neo-Kantian , however, has a dissatisfaction with the lack of basic justifications for the individual sciences expressed. The fundamental ontology of Martin Heidegger wants to be the basis for all empirical sciences. Heidegger also expresses himself in Being and Time, for example, about symptoms of illness. In medicine, there are in fact fundamental criticism of the established in Germany since 2000 disease classification according to ICD-10 . Diseases are abstract concepts. Nevertheless, it is not surprising that the disease constructs with which z. B. Psychiatrists work in spite of elaborate classification glossaries, overlap and show indistinct boundaries. The criticism of those glossaries, including that of the DSM-IV, is primarily directed against an excessively monocausal orientation of the concept, i.e. H. against a concept that is only valid for organic diseases and therefore against a uniform scientific generalization of this group of psychiatric diseases (ICD-10 Chapter F). As a result, in the eyes of the critics, too little consideration is given to the individual case. Ludolf von Krehl calls for treating sick people, not illnesses.

The history of philosophy already shows that different degrees of abstraction were assumed depending on the subject area of ​​a term.

Double etymological meaning

The term “abstraction”, which has only been in use since the 18th century, goes back to the meaning of “abstractio” introduced by Boëthius (475-526) as a translation of the Greek ἀφαίρεσις or τά ἐξ ἀφαιρέσεως into the Latin philosophical literature. The term ἀφαίρεσις comes from the writings of Aristotle and means "taking away" [a selected part]. In the Middle Ages, however, the meaning expressed by Aristotle through the verb χωρίζειν (= separate) came into play with abstraction, with which he denoted the conception of a "separate" subject area used by the Platonists of an independent, "separate" subject matter. In addition to “generalization”, the meaning “conceptual mapping” is also used for abstraction. This follows etymologically the meaning of ancient Greek σχῆμα (shape, figure, form, pattern, outline, geometric figure), cf. → Schematism and the role of the image. Even this closer etymological consideration makes different theoretical concepts of abstraction clear.

Math objects

Aristotle used the term ἀφαίρεσις (removal) to characterize mathematical objects. His view was contrary to Plato. While Aristotle saw mathematical facts as derived from the material-sensible, Plato took the opposite view, namely that mathematics had its own essence. In the case of geometric objects, according to Aristotle, matter is only more or less “excluded”. This different, more or less strong exclusion results from the frequent use of the phrase τά ἐξ ἀφαιρέσεως (that which has been taken away from). Geometry is associated with spatial ideas and therefore still has contact with matter. However, this contact is completely excluded from mathematics. The transition from the geometric to the arithmetic object is "more abstract". - With this view u. a. Aristotle also described different degrees of abstraction .

Logical and ontological separation

Aristotle criticizes the conception of the Platonists by saying that mathematical objects are "tacitly" viewed as separate from them (λανθάνουσι δέ τοῦτο ποιοῦντες), which in fact are not "separate", but only an existence "derived" from the sensual being able to lead. But even with Aristotle, a certain ambiguity cannot be denied between “separated from the sensual by a mental act” and “existing for itself in a separate state”. But Aristotle is understandable when he says that a purely logical separation should not be confused with an ontological one , cf. → hypostatization . - Thomas Aquinas put an end to this ambiguity by realizing that in Aristotle abstraction is the act through which the mind recognizes what is knowable in the sensual. The mind thus regards what is separate, not what is separate (“non separata, sed separatim”). Aristotle accordingly allows formal abstraction, but not total abstraction as it was represented by scholasticism , see Chap. Abstraction process . - Even if Aristotle used the term abstraction specifically for mathematical objects, one single exception is noteworthy: Aristotle speaks of the “whiteness” of a person as an abstraction from the white person. This use of the term abstraction is to be understood as an analogue in the realm of the physical.

Abstraction process

Formal abstraction

Formal abstraction refers to the manner of abstraction that Aristotle used for mathematical objects, see Chap. Math objects . The abstraction is understood as a process that derives the essentials from the sensual experience.

Total abstraction

Total abstraction is also known as simple abstraction and means the form of abstraction as it was represented by the Platonists and by medieval scholasticism. The abstraction understands itself as a procedure which regards the essential as an entity separated from the sensual, cf. Cape. Mathematical subjects and chap. Logical and ontological separation .

Constitutive abstraction

Here psychological-subjective processes are made responsible for the abstraction process. The constitutive perspective emphasizes a new conceptual creation brought about by abstraction. The constitutively generalizing abstraction enables the reference to an open set of given and possibly still occurring cases, beyond the limited set of the present cases. - Sigmund Freud called the Jewish concept of God an abstract concept. The abstraction consists in the fact that it was forbidden to make an idol of God. This command included the compulsion to worship a god who cannot be seen. The abstraction consisted in a "setting back of sensual [optical] perception against an idea to be called abstract, a triumph of spirituality over sensuality, strictly speaking a renunciation of instincts with its psychologically necessary consequences" . Hannah Arendt took this idea further. The Jewish tradition of God is that this God is heard but not seen. The sense of hearing affects people directly in a passive way, while the optical senses allow people greater distance, freedom and objectivity, cf. the meaning of words like obedience , hearing and include .

Hypothetical abstraction

The hypothetical abstraction underlines both the psychological-process-like course of the formation of general terms, their constructivist character and the process of abstraction related to sensory data. It thus occupies a middle position between constitutive abstraction and the isolating abstraction described below.

Isolating abstraction

Here are logical operations in a given subject area ostensibly about the manner of a parlor game in which, by yes / no answers from a tighter term scope must be crystallized a very special concept. Trees can e.g. B. can be characterized by the features of root, trunk, branch, twig, leaf. But since meadow flowers also have roots and leaves, the characteristics “root” and “leaf” are to be regarded as immaterial for the description of the object “tree”. With this type of concept formation, the subject area is related to species and generic concepts, see also → Genus proximum et differentia specifica . It is a logically objectifiable abstraction process, free of psychological-subjective influences. Only so-called universal realists claim that sensory perception can be disregarded here .

Transcendental abstraction

The transcendental abstraction points out that when using a concept from the diversity of what is contained under it, i. H. the special features are disregarded. The abstraction represents a transcendental moment of all empirical knowledge. This moment is understood as a necessary connection (synthesis) of conceptual (formal) and sensual (material) elements. In the language of brain physiology, the sensory perceptions (e.g. acoustic and optical) are related to the respective primary cerebral sensory centers, the conceptual to the secondary and tertiary centers (→ knowledge or gnostic meaning of the sense organs). In this transition to the secondary and tertiary centers, transformations of the sensual material through assimilation processes are necessary and inevitable.

Individual evidence

  1. ↑ a b c d e Metzler Lexicon: Philosophy . Terms and definitions. Lim. by Peter Prechtl u. Franz-Peter Burkard , Verlag JB Metzler, Stuttgart 3 2008 ISBN 978-3-476-02187-8 ; page 6
  2. ↑ a b Schischkoff, Georgi (ed.): Philosophical dictionary. Alfred-Kröner, Stuttgart 14 1982, ISBN 3-520-01321-5 ; (a) Re. “Neo-Kantianism”: page 482 f .; (b) on fundamental ontology: page 207.
  3. ↑ Heidegger, Martin : Being and time . [1926] - Max Niemeyer-Verlag, Tübingen 15 1979, ISBN 3-484-70122-6 ; § 7 The phenomenological method of investigation; A The concept of the phenomenon; Page 29, line 20
  4. ↑ Adler, Rolf (Ed.): Psychosomatic Medicine. Models of medical thought and action. Founded by Thure von Uexküll. Urban & Schwarzenberg, Munich 2003, 1564 pages, chap. 24 - ICD-10 and DSM-IV - a critical opinion on the use of the international diagnostic codes. Pages 389–395, on stw. “Inadequacies in the generalizing treatment of psychiatric disease diagnoses” Pages 390, 394 f.
  5. ↑ a b c d e f Ritter, Joachim (Hrsg.): Historical dictionary of philosophy . Volume 1: AC, Schwabe & Co Basel 1971, (a) on article “Degrees of abstraction”: column 65; (b) to chap. “Double etymological meaning”: column 42; (c) to chap. "Mathematical objects": Column 42 f .; (d) to chap. “Logical and ontological separation”: Columns 43 f., Zf. 2, (e) to chap. “Formal abstraction”: ibid. (F) to chap. “Total abstraction”: ibid.
  6. ↑ Aristotle : De caelo III, 1, 299 a 15; De anima I, 1.403 b 14; III, 4, 429 b 18; III, 7, 431 b 12; III, 8, 432 a 4; Met. VII, 4 1029 b 29-33; XI, 3, 1061 a 28; XIII, 2, 1077 a 36-b 14
  7. ↑ Drosdowski, Günther: Etymologie. Dictionary of origin of the German language; The history of German words and foreign words from their origins to the present. Dudenverlag, Volume 7, Mannheim, 2 1997, ISBN 3-411-20907-0 ; P. 18.
  8. ↑ Aristotle: Phys . I, 2, 193 b 35
  9. ↑ Thomas Aquinas : De anima . III. ed. from Priotta No. 781
  10. ^ Aristotle: Metaphysics . M, 2, 1077 b 4 ff.
  11. ↑ Freud, Sigmund : The man Moses and the monotheistic religion. In: Collected Works, ed. v. Anna Freud , Vol. XVI, page 220
  12. ↑ Arendt, Hannah : From the life of the spirit . The thinking. Vol. I. (1971) R. Piper & Co., Munich 1979, ISBN 3-492-02486-6 ; Page 115 f.
  13. ↑ Mauthner, Fritz : Lexicon of Philosophy . Diogenes-Verlag, CH-8032 Zurich, 1980 ISBN 3-257-20828-6 , pages 9-11