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. 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 '' 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). 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'.
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 , 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. 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. Architecture also refers to the __abstract__ arrangement, design of computer code to implement complex software systems .
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. for A Cat sitting on the Mat
(graph 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. 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): 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. ==As used in different disciplines==