Abstraction

Abstraction is a process where general rules and concepts are derived from the use and classifying
of specific examples, literal (real or concrete) signifiers, first principles, or other methods.

"An abstraction" is the outcome of this process — a concept that acts as a common noun for all
subordinate concepts and connects any related concepts as a group, field, or category.[1]

Conceptual abstractions may be made by filtering the information content of a concept or an

observable phenomenon, selecting only those aspects which 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.[1] In a type–token distinction, a type
(e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').

Abstraction in its secondary use is a material process,[2] discussed in the themes below.

Origins

Thinking in abstractions is considered by anthropologists, archaeologists, and sociologists to be

one of the key traits in modern human behaviour, which is believed[3] 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.

History

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[4] 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.[5] 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 used the approach of abstraction (going from particular facts collected into one
general idea). Newton (1642–1727) derived the motion of the planets from Copernicus' (1473–
1543) simplification, that the Sun is the center of the Solar System; Kepler (1571–1630)
compressed thousands of measurements into one expression to finally conclude that Mars moves
in an elliptical orbit about the Sun; Galileo (1564–1642) repeated one hundred specific experiments
into the law of falling bodies.

Themes

Compression

An abstraction can be seen as a compression process,[6] mapping multiple different pieces of

constituent data to a single piece of abstract data;[7] 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,[8] 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.

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. This is similar
to qualia and sumbebekos.

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'.[9]

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

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.[10][11]

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 below, the graphical relationships like the arrows joining
boxes and ellipses might denote predicates.

Referencing and referring

Abstractions sometimes have ambiguous referents. For example, "happiness" can mean
experiencing various positive emotions, but can also refer to life satisfaction and subjective well-
being. Likewise, "architecture" refers not only to the design of safe, functional buildings, but also to
elements of creation and innovation which aim at elegant solutions to construction problems, to the
use of space, and to the attempt to evoke an emotional response in the builders, owners, viewers
and users of the building.
Simplification and ordering

Abstraction uses a strategy of simplification, wherein formerly concrete details are left ambiguous,
vague, or undefined; thus effective communication about things in the abstract requires an intuitive
or common experience between the communicator and the communication recipient. This is true
for all verbal/abstract communication.

Conceptual graph for A Cat sitting on

the Mat (graph 1)

Cat on Mat (picture 1)

For example, many different things can be red. Likewise, many things sit on surfaces (as in picture 1,
to the right). The property of redness and the relation sitting-on are therefore abstractions of those
objects. Specifically, the conceptual diagram graph 1 identifies only three boxes, two ellipses, and
four arrows (and their five labels), whereas the picture 1 shows much more pictorial detail, with the
scores of implied relationships as implicit in the picture rather than with the nine explicit details in
the graph.

Graph 1 details some explicit relationships between the objects of the diagram. For example, the
arrow between the agent and CAT:Elsie depicts an example of an is-a relationship, as does the arrow
between the location and the MAT. The arrows between the gerund/present participle SITTING and
the nouns agent and location express the diagram's basic relationship; "agent is SITTING on location";
Elsie is an instance of CAT.[12]

Although the description sitting-on (graph 1) is more abstract than the graphic image of a cat sitting
on a mat (picture 1), the delineation of abstract things from concrete things is somewhat
ambiguous; this ambiguity or vagueness is characteristic of abstraction. Thus something as simple
as a newspaper might be specified to six levels, as in Douglas Hofstadter's illustration of that
ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979):[13]
 (1) a publication
(2) a newspaper
(3) The San Francisco Chronicle
(4) the May 18 edition of The San Francisco Chronicle
(5) my copy of the May 18 edition of The San Francisco Chronicle
(6) my copy of the May 18 edition of The San Francisco Chronicle
as it was when I first picked it up (as contrasted with my copy
as it was a few days later: in my fireplace, burning)

An abstraction can thus encapsulate each of these levels of detail with no loss of generality. But
perhaps a detective or philosopher/scientist/engineer might seek to learn about something, at
progressively deeper levels of detail, to solve a crime or a puzzle.

Thought processes

In philosophical terminology, abstraction is the thought process wherein ideas are distanced from
objects. But an idea can be symbolized.[14]

As used in different disciplines

In art

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.[15] 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.[16] Later still,
abstraction was manifest in more purely formal terms, such as color, freedom from objective
context, and a reduction of form to basic geometric designs.[17]
In computer science

Computer scientists use abstraction to make models that can be used and re-used without having
to re-write all the program code for each new application on every different type of computer. They
communicate their solutions with the computer by writing source code in some particular computer
language which can be translated into machine code for different types of computers to execute.
Abstraction allows program designers to separate a framework (categorical concepts related to
computing problems) from specific instances which implement details. This means that the
program code can be written so that code does not have to depend on the specific details of
supporting applications, operating system software, or hardware, but on a categorical concept of
the solution. A solution to the problem can then be integrated into the system framework with
minimal additional work. This allows programmers to take advantage of another programmer's
work, while requiring only an abstract understanding of the implementation of another's work, apart
from the problem that it solves.

In general semantics

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)."[18]

In history

Francis Fukuyama defines history as "a deliberate attempt of abstraction in which we separate out
important from unimportant events".[19]

In linguistics

Researchers in linguistics frequently apply abstraction so as to allow an analysis of the phenomena

of language at the desired level of detail. A commonly used abstraction, the phoneme, abstracts
speech sounds in such a way as to neglect details that cannot serve to differentiate meaning. Other
analogous kinds of abstractions (sometimes called "emic units") considered by linguists include
morphemes, graphemes, and lexemes.

Abstraction also arises in the relation between syntax, semantics, and pragmatics. Pragmatics
involves considerations that make reference to the user of the language; semantics considers
expressions and what they denote (the designata) abstracted from the language user; and syntax
considers only the expressions themselves, abstracted from the designata.

In mathematics

Abstraction in mathematics is the process of extracting the underlying structures, patterns or

properties of a mathematical concept or object, 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:

It reveals deep connections between different areas of mathematics.

Known results in one area can suggest conjectures in another related area.

Techniques and methods from one area can be applied to prove results in other related area.

Patterns from one mathematical object can be generalized to other similar objects in the same
class.

The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn,
and might require a degree of mathematical maturity and experience before they can be
assimilated.

In music

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 by the exploration of internal numeric relationships.[20]

In neurology

A recent meta-analysis suggests that the verbal system has a greater engagement with abstract
concepts when the perceptual system is more engaged in processing concrete concepts. This is
because abstract concepts elicit greater brain activity in the inferior frontal gyrus and middle
temporal gyrus compared to concrete concepts which elicit greater activity in the posterior
cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus.[21] Other research into the human
brain suggests that the left and right hemispheres differ in their handling of abstraction. For
example, one meta-analysis reviewing human brain lesions has shown a left hemisphere bias during
tool usage.[22]

In philosophy

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 the discussion of
abstraction is thought space.

John Locke defined abstraction in An Essay Concerning Human Understanding:

'So words are used to stand as outward marks of our internal ideas, which are taken from particular
things; but if every particular idea that we take in had its own special name, there would be no end
to names. To prevent this, the mind makes particular ideas received from particular things become
general; which it does by considering them as they are in the mind—mental appearances—separate
from all other existences, and from the circumstances of real existence, such as time, place, and so
on. This procedure is called abstraction. In it, an idea taken from a particular thing becomes a
general representative of all of the same kind, and its name becomes a general name that is
applicable to any existing thing that fits that abstract idea.' (2.11.9)

In psychology

Carl Jung's definition of abstraction broadened its scope beyond the thinking process to include
exactly four mutually exclusive, different 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 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).

In social theory

Social theorists deal with abstraction both as an ideational and as a material process. Alfred Sohn-
Rethel (1899–1990) asked: "Can there be abstraction other than by thought?"[2] He used the
example of commodity abstraction to show that abstraction occurs in practice as people create
systems of abstract exchange that extend beyond the immediate physicality of the object and yet
have real and immediate consequences. This work was extended through the 'Constitutive
Abstraction' approach of writers associated with the Journal Arena. Two books that have taken this
theme of the abstraction of social relations as an organizing process in human history are Nation
Formation: Towards a Theory of Abstract Community (1996)[23] and an associated volume published
in 2006, Globalism, Nationalism, Tribalism: Bringing Theory Back In.[24] These books argue that a
nation is an abstract community bringing together strangers who will never meet as such; thus
constituting materially real and substantial, but abstracted and mediated relations. The books
suggest that contemporary processes of globalization and mediatization have contributed to
materially abstracting relations between people, with major consequences for how humans live their
lives.

One can readily argue that abstraction is an elementary methodological tool in several disciplines of
social science. These disciplines have definite and different concepts of "man" that highlight those
aspects of man and his behaviour by idealization that are relevant for the given human science. For
example, homo sociologicus is the man as sociology abstracts and idealizes it, depicting man as a
social being. Moreover, we could talk about homo cyber sapiens[25] (the man who can extend his
biologically determined intelligence thanks to new technologies), or homo creativus[26] (who is
simply creative).

Abstraction (combined with Weberian idealization) plays a crucial role in economics - hence
abstractions such as "the market"[27] and the generalized concept of "business".[28] Breaking away
from directly experienced reality was a common trend in 19th-century sciences (especially physics),
and this was the effort which fundamentally determined the way economics tried (and still tries) to
approach the economic aspects of social life. It is abstraction we meet in the case of both Newton's
physics and the neoclassical theory, since the goal was to grasp the unchangeable and timeless
essence of phenomena. For example, Newton created the concept of the material point by following
the abstraction method so that he abstracted from the dimension and shape of any perceptible
object, preserving only inertial and translational motion. Material point is the ultimate and common
feature of all bodies. Neoclassical economists created the indefinitely abstract notion of homo
economicus by following the same procedure. Economists abstract from all individual and personal
qualities in order to get to those characteristics that embody the essence of economic activity.
Eventually, it is the substance of the economic man that they try to grasp. Any characteristic beyond
it only disturbs the functioning of this essential core.[29]

See also

Abstract art
Philosophy portal
Abstract and concrete

Abstract interpretation

Abstract labour and concrete labour

Abstract structure

Abstraction (sociology)

Charles Sanders Peirce

Concept

Conceptual model

Emergence

Engaged theory

Gottlob Frege

High- and low-level

Hypostatic abstraction

Inventor's paradox

Leaky abstraction

Lyrical abstraction

Nucleophilic abstraction

Object of the mind

Platonic realism

Reification (knowledge representation)

 Symbol Theory

Politechnika Wrocławska

References

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2. Alfred Sohn-Rethel, Intellectual and manual labour: A critique of epistemology, Humanities Press,
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283–285. Bibcode:1981Sci...211..283S (https://ui.adsabs.harvard.edu/abs/1981Sci...211..
283S) . doi:10.1126/science.211.4479.283 (https://doi.org/10.1126%2Fscience.211.447
9.283) . PMID 17748027 (https://pubmed.ncbi.nlm.nih.gov/17748027) ..

Further reading

James, Paul (1996). Nation Formation: Towards a Theory of Abstract Community (https://archive.or
g/details/nationformationt00jame) . London: Sage Publications.

James, Paul (2006). Globalism, Nationalism, Tribalism: Bringing Theory Back In - Volume 2 of
Towards a Theory of Abstract Community (https://www.academia.edu/1642214) . London: Sage
Publications.

Jung, C.G. (1971). Psychological Types. Collected Works. Vol. 6 (1921 ed.). Princeton, NJ:
Princeton University Press. ISBN 0-691-01813-8..
External links

Abstraction (https://www.inphoproject.org/idea/2013) at the Indiana Philosophy Ontology

Project

Abstraction (https://philpapers.org/s/Abstraction) at PhilPapers

Internet Encyclopedia of Philosophy: Gottlob Frege (http://www.utm.edu/research/iep/f/frege.ht

m)

Discussion at The Well concerning Abstraction hierarchy (http://originresearch.com/sd/sd1.cf

m)