Editing Abstraction (section)

==Themes==

===Compression===
<!--Is this section common knowledge or original research? -->
An abstraction can be seen as a [[data compression|compression]] process,<ref>{{Citation |first=Gregory |last=Chaitin |author-link=Gregory Chaitin | url=http://www.umcs.maine.edu/~chaitin/sciamer3.pdf | archive-url=https://web.archive.org/web/20150509165230/http://www.umcs.maine.edu/~chaitin/sciamer3.pdf | archive-date=2015-05-09 |title=The Limits Of Reason |journal=Scientific American |volume=294 |issue=3 |pages=74–81 |year=2006|pmid=16502614 |doi=10.1038/scientificamerican0306-74 |bibcode=2006SciAm.294c..74C }}</ref> mapping multiple different pieces of [[wikt:constituent|constituent]] data to a single piece of abstract data;<ref>[[Murray Gell-Mann]] (1995) "[http://onlinelibrary.wiley.com/doi/10.1002/cplx.6130010105/pdf What is complexity? Remarks on simplicity and complexity by the Nobel Prize-winning author of The Quark and the Jaguar]" ''Complexity'' states the 'algorithmic information complexity' (AIC) of some string of bits is the shortest length computer program which can print out that string of bits.</ref> 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 (philosophy)|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 [[#Physicality|itself an object]]).
:For example, ''[[#Simplification and ordering|picture 1 below]]'' illustrates the concrete relationship "Cat sits on Mat".
Chains of abstractions can be [[construe]]d,<ref name = Ross>Ross, L. (1987). The Problem of Construal in Social Inference and Social Psychology. In N. Grunberg, R.E. Nisbett, J. Singer (eds), ''A Distinctive Approach to psychological research: the influence of Stanley Schacter''. Hillsdale, NJ: Earlbaum.</ref> 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 "[[#Physicality|object]]" as opposed to "action".
:For example, ''[[#Simplification and ordering|graph 1 below]]'' expresses the abstraction "agent sits on location". This conceptual scheme entails no specific [[hierarchical]] [[Taxonomy (biology)|taxonomy]] (such as the one mentioned involving cats and mammals), only a progressive [[#Simplification and ordering|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 [[#Simplification and ordering|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'' [[#Simplification and ordering|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 [[philosophy|philosophies]] refer to ''[[trope (philosophy)|tropes]]'' (instances of properties) as ''[[abstract particular]]s''—e.g., the particular [[red]]ness of a particular [[apple]] is an ''abstract particular''. This is similar to [[qualia]] and [[sumbebekos]].

===Material process===
{{further|Power projection|Display behavior}}
Still retaining the primary meaning of '{{lang|la|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).

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'.<ref>{{Cite book | last= James | first= Paul |author-link= Paul James (academic) | title= Globalism, Nationalism, Tribalism: Bringing Theory Back In – Volume 2 of Towards a Theory of Abstract Community |url= https://www.academia.edu/1642214 | year= 2006 | publisher= Sage Publications | location= London }}, pp. 318–19.</ref>
===Ontological status===
The way that physical objects, like rocks and trees, have [[category of being|being]] differs from the way that properties of abstract concepts or relations have being, for example the way the [[concrete (philosophy)|concrete]], [[particular]], [[individual]]s pictured in ''[[#Simplification and ordering|picture 1]]'' exist differs from the way the concepts illustrated in ''[[#Simplification and ordering|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===
{{Further|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 {{harvnb|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.<ref>Eventually ([http://www.laits.utexas.edu/ghazal/Chap1/dsb/chapter1.html Schmandt-Besserat estimates it took 4000 years] {{webarchive |url=https://web.archive.org/web/20120130084757/http://www.laits.utexas.edu/ghazal/Chap1/dsb/chapter1.html |date=January 30, 2012 }}) the marks on the outside of the containers were all that were needed to convey the count. The clay containers evolved into clay tablets with marks for the count.
</ref><ref>{{cite book|first=Eleanor|last=Robson|author-link=Eleanor Robson|year=2008|title=Mathematics in Ancient Iraq|publisher=Princeton University Press |isbn=978-0-691-09182-2}}. p. 5: these calculi were in use in Iraq for primitive accounting systems as early as 3200–3000 BCE, with commodity-specific counting representation systems. Balanced accounting was in use by 3000–2350 BCE, and a [[sexagesimal number system]] was in use 2350–2000 BCE.</ref>

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 ''[[predicate (grammar)|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 [[proposition]]s about predicates, which propositions remain to be evaluated by the investigator. In the ''graph 1'' [[#Simplification and ordering|below]], the graphical relationships like the arrows joining boxes and ellipses might denote predicates.

===Referencing and referring===
Abstractions sometimes have ambiguous [[referent]]s. 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 [[emotion|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 .<!--See discussion pages 3 to 12 in Eugene Raskin, ''Architecturally Speaking, 2nd edition'', a Delta book, Dell (1966), trade paperback, 129 pages-->

===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 [[intuition (knowledge)|intuitive]] or common experience between the communicator and the communication recipient. This is true for all verbal/abstract communication.
[[File:Conceptual graph for A Cat sitting on the Mat Hi-res.png|alt=|thumb|[[Conceptual graph]] for A Cat sitting on the Mat ''(graph 1)'']]
[[File:JerryFelix.JPG|thumb|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 ''[[red]]ness'' and the [[Relation of Ideas|relation]] ''[[sitting|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 [[noun]]s ''agent'' and ''location'' express the [[diagram]]'s basic relationship; ''"agent is SITTING on location"''; ''Elsie'' is an instance of ''CAT''.<ref>[[John F. Sowa|Sowa, John F.]] (1984). ''Conceptual Structures: Information Processing in Mind and Machine''. Reading, MA: Addison-Wesley. {{ISBN|978-0-201-14472-7}}.</ref>

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):<ref>{{cite book|author-link = Douglas Hofstadter|first = Douglas|last = Hofstadter|date = 1979|title = [[Gödel, Escher, Bach]]|publisher= Basic Books|isbn = 978-0-465-02656-2}}</ref>
{{blockquote|
:(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 [[philosophy|philosophical terminology]], ''abstraction'' is the [[thinking|thought process]] wherein [[idea]]s are distanced from [[object (philosophy)|objects]]. But an idea can be [[symbol]]ized.<ref>"A symbol is any device whereby we are enabled to make an abstraction." p. xi and chapter 20 of [[Suzanne K. Langer]] (1953), ''Feeling and Form: A Theory of Art Developed from Philosophy in a New Key'', New York: Charles Scribner's Sons.</ref>