Апстракција

За другу употребу, погледајте страницу Апстракција (објектно-оријентисано програмирање).

Апстракција (лат. abstractio) је мисаоно издвајање неких особина и својстава предмета од самог предмета, као и апстрактан појам издвојен од нечега конкретног за који је везан. Апстрахирати или апстраховати (нем. abstrahieren): вршити апстракцију, и не узети (узимати) нешто у обзир, не обазрети се, не обазирати се на нешто. Апстрактно: добијено апстракцијом, мисаоно; супротно од конкретно. Фактички, када је нешто апстрактно, то значи да се нешто не односи само на једну појединост, већ на неку већу целину, скуп нечега и сл. Апстрактно мишљење је врста мишљења која се одликује тиме да високо надилази перцептивни ниво и конкретне појаве и да оперише апстрактним симболима.

Порекло

Thinking in abstractions is considered by anthropologists, archaeologists, and sociologists to be one of the key traits in modern human behaviour, which is believed to have developed between 50,000 and 100,000 years ago. Its development is likely to have been closely connected with the development of human language, which (whether spoken or written) appears to both involve and facilitate abstract thinking.

Историја

Abstraction involves induction of ideas or the synthesis of particular facts into one general theory about something. It is the opposite of specification, which is the analysis or breaking-down of a general idea or abstraction into concrete facts. Abstraction can be illustrated by Francis Bacon's Novum Organum (1620), a book of modern scientific philosophy written in the late Jacobean era of England to encourage modern thinkers to collect specific facts before making any generalizations.

Bacon used and promoted induction as an abstraction tool; it complemented but was distinct from the ancient deductive-thinking approach that had dominated the intellectual world since the times of Greek philosophers like Thales, Anaximander, and Aristotle. Thales (c. 624–546 BCE) believed that everything in the universe comes from one main substance, water. He deduced or specified from a general idea, "everything is water," to the specific forms of water such as ice, snow, fog, and rivers.

Modern scientists can also use the opposite approach of abstraction, or going from particular facts collected into one general idea, such as the motion of the planets (Newton (1642–1727)). When determining that the sun is the center of our solar system (Copernicus (1473–1543)), scientists had to use thousands of measurements to finally conclude that Mars moves in an elliptical orbit about the sun (Kepler (1571–1630)), or to assemble multiple specific facts into the law of falling bodies (Galileo (1564–1642)).

Теме

Compression

An abstraction can be seen as a compression process, 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).

For example, picture 1 below illustrates the concrete relationship "Cat sits on Mat".

Chains of abstractions can be construed, 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".

For example, graph 1 below expresses the abstraction "agent sits on location". This conceptual scheme entails no specific hierarchical taxonomy (such as the one mentioned involving cats and mammals), only a progressive exclusion of detail.

Instantiation

Non-existent things in any particular place and time are often seen as abstract. By contrast, instances, or members, of such an abstract thing might exist in many different places and times.

Those abstract things are then said to be multiply instantiated, in the sense of picture 1, picture 2, etc., shown below. It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and "telephone" abstract ideas since despite their varying appearances, a particular cat or a particular telephone is an instance of the concept "cat" or the concept "telephone". Although the concepts "cat" and "telephone" are abstractions, they are not abstract in the sense of the objects in graph 1 below. 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.

Material process

Still retaining the primary meaning of 'abstrere' or 'to draw away from', the abstraction of money, for example, works by drawing away from the particular value of things allowing completely incommensurate objects to be compared (see the section on 'Physicality' below). Karl Marx's writing on the commodity abstraction recognizes a parallel process.

The state (polity) as both concept and material practice exemplifies the two sides of this process of abstraction. Conceptually, 'the current concept of the state is an abstraction from the much more concrete early-modern use as the standing or status of the prince, his visible estates'. At the same time, materially, the 'practice of statehood is now constitutively and materially more abstract than at the time when princes ruled as the embodiment of extended power'.

За више информација погледајте: Power projection и Display behavior

Ontological status

The way that 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.

Physicality

За више информација погледајте: History of accounting § Ancient history

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. However, in the secondary sense of the term 'abstraction', this physical object can carry materially abstracting processes. For example, record-keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers. According to Schmandt-Besserat 1981, these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as something of a bill of lading or an accounts book. In order to avoid breaking open the containers for the count, marks were placed on the outside of the containers. These physical marks, in other words, acted as material abstractions of a materially abstract process of accounting, using conceptual abstractions (numbers) to communicate its meaning.

У математици

Апстракција, односно апстраховање у математици је процес разматрања извесних особина објеката изостављањем других које нису релевантне. То је основа класификовања, процедуре која резултује скупом чланова са посебним особинама. Поменути скуп се означава са $\{x:F(x)\},$ чит. икс такво да је еф од икс, односно х које има особину F(х), где је F(х) својство које чланови скупа морају задовољити. На пример, {x:x је птица}, означава скуп у којем су сви елементи птице.

Аксиома апстракције

Нека је дата произвољна особина f(x), тада постоји скуп чији чланови поседују баш ту особину, тј.

$(\exists y)(\forall x)(x\in y\iff F(x)).$

Наведена аксиома апстракције је први пут експлицитно формулисана од стране Фригеа 1893. године, да би затим, од стране Расела, била доведена у контрадикцију:

Нека је дата особина F(x), поменутог аксиома, особина не-припадања самом себи. Тада је

$(\exists y)(\forall x)(x\in \iff x\notin x),$

аксиом избора, који једноставним корацима води у контрадикцију

$y\in y\wedge y\notin y.$

Да би избегао овај, тзв. Раселов парадокс, Зермело је 1908. увео аксиом сепарације:

$(\exists y)(\forall x)(x\in y\iff x\in z\wedge F(x)),$

у којем егзистенција скупа у није више претпостављена безусловно.

Види још

• Апстрактна уметност
• Апстрактна алгебра
• Зермело-Френкелова теорија скупова

Литература

• James, Paul (1996). Nation Formation: Towards a Theory of Abstract Community. London: Sage Publications. 
• James, Paul (2006). Globalism, Nationalism, Tribalism: Bringing Theory Back In - Volume 2 of Towards a Theory of Abstract Community. London: Sage Publications. 
• Jung, C.G. (1971). Psychological Types. Collected Works. 6 (1921 изд.). Princeton, NJ: Princeton University Press. ISBN 0-691-01813-8. .
• The American Heritage Dictionary of the English Language, 3rd edition. Houghton Mifflin (1992). 1992. ISBN 0-395-44895-6. 
• Sohn-Rethel, Alfred (1977) Intellectual and manual labour: A critique of epistemology, Humanities Press.
• Schmandt-Besserat, Denise (1981). „Decipherment of the Earliest Tablets”. Science. 211 (4479): 283—285. Bibcode:1981Sci...211..283S. PMID 17748027. doi:10.1126/science.211.4479.283. .
• Korisettar, Ravi (1998). Early Human Behaviour in Global Context. Routledge. 
• McBrearty, Sally; Brooks, Allison (2000). „The revolution that wasn't: a new interpretation of the origin of modern human behavior”. Journal of Human Evolution. 39 (5): 453—563. PMID 11102266. doi:10.1006/jhev.2000.0435. „Proponents of the model known as the 'human revolution' claim that modern human behaviors arose suddenly, and nearly simultaneously, throughout the Old World ca. 40–50 ka. [...] In fact, many of the components of the 'human revolution' claimed to appear at 40–50 ka are found in the African Middle Stone Age tens of thousands of years earlier. These features include blade and microlithic technology, bone tools, increased geographic range, specialized hunting, the use of aquatic resources, long distance trade, systematic processing and use of pigment, and art and decoration.” 
• Henshilwood, Christopher; Marean, Curtis (2003). „The Origin of Modern Human Behavior: Critique of the Models and Their Test Implications”. Current Anthropology. 44 (5): 627—651. PMID 14971366. S2CID 11081605. doi:10.1086/377665. 
• Hill, Kim; et al. (2009). „The Emergence of Human Uniqueness: Characters Underlying Behavioral Modernity”. Evolutionary Anthropology. 18 (5): 187—200. CiteSeerX 10.1.1.469.5702 . S2CID 56384790. doi:10.1002/evan.20224. 
• D'Errico, F; et al. (1998). „Neanderthal Acculturation in Western Europe? A Critical Review of the Evidence and Its Interpretation”. Current Anthropology. 39 (S1): S1–S44. S2CID 144799519. doi:10.1086/204689. 
• Klein, Richard (1995). „Anatomy, behavior, and modern human origins”. Journal of World Prehistory. 9 (2): 167—198. S2CID 10402296. doi:10.1007/bf02221838. 
• McBrearty, Sally; Brooks, Allison (2000). „The revolution that wasn't: a new interpretation of the origin of modern human behavior”. Journal of Human Evolution. 39 (5): 453—563. PMID 11102266. doi:10.1006/jhev.2000.0435. 
• Marean, Curtis; et al. (2007). „Early human use of marine resources and pigment in South Africa during the Middle Pleistocene”. Nature. 449 (7164): 905—908. Bibcode:2007Natur.449..905M. PMID 17943129. S2CID 4387442. doi:10.1038/nature06204. 
• Powell, Adam; et al. (2009). „Late Pleistocene Demography and the Appearance of Modern Human Behavior” (PDF). Science. 324 (5932): 1298—1301. Bibcode:2009Sci...324.1298P. PMID 19498164. S2CID 206518315. doi:10.1126/science.1170165. 
• Premo, Luke; Kuhn, Steve (2010). „Modeling Effects of Local Extinctions on Culture Change and Diversity in the Paleolithic”. PLOS ONE. 5 (12): e15582. Bibcode:2010PLoSO...515582P. PMC 3003693 . PMID 21179418. doi:10.1371/journal.pone.0015582 . 

Спољашње везе

• Internet Encyclopedia of Philosophy: Gottlob Frege
• Discussion at The Well concerning Abstraction hierarchy