In the context of abstract algebra, for example, a mathematical object is an algebraic structure such as a group, ring, or vector space.

For example, an abstract stack data structure could be defined by three operations:, that inserts some data item onto the structure,, that extracts an item from it ( with the constraint that each pop always returns the most recently pushed item that has not been popped yet ), and, that allows data on top of the structure to be examined without removal.

An abstraction can be seen as a process of 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 ".

For example, the abstract general idea or concept that is designated by the word " red " is that characteristic which is common to apples, cherries, and blood.

The prototypical example of this abstract notion is the self-referential structure at the core of Gödel's incompleteness theorems.

For example, the skills, rules, and knowledge taxonomy of human behavior has been used by designers to develop systems that are compatible with multiple " ways of knowing ": abstract analytic reasoning, experience-based ' gut feelings ', and ' craft ' sensorimotor skills.

For Avicenna ( Ibn Sina ), for example, the a tabula rasa is a pure potentiality that is actualized through education, and knowledge is attained through " empirical familiarity with objects in this world from which one abstracts universal concepts " developed through a " syllogistic method of reasoning in which observations lead to propositional statements which when compounded lead to further abstract concepts.

For example, Old Norse poets might replace sverð, the regular word for “ sword ”, with a more abstract compound such as “ wound-hoe ” ( Egill Skallagrímsson: Höfuðlausn 8 ), or a genitive phrase such as randa íss “ ice of shields ” ( Einarr Skúlason: ‘ Øxarflokkr ’ 9 ).

Chrysippus ' point is more abstract than Antipater's, and Galen quotes the passage as an example of an opinion contrary to his own.

* In the PANGLOSS example, about 50. 000 nodes were intended to be subsumed under the smaller, manually-built upper ( abstract ) region of the ontology.

For example, numbers can be held to be particular yet abstract objects.

For example, they have been used to study abstract reasoning of children, acculturation of immigrants, intelligence, the differing mental processes in mental illness, cultural themes, etc.

These commentators speak thus: For example, a particular tree, with a branch or two missing, possibly alive, possibly dead, and with the initials of two lovers carved into its bark, is distinct from the abstract form of Tree-ness.

The German word Zeitgeist is one such example: one who speaks or understands the language may " know " what it means, but any translation of the word apparently fails to accurately capture its full meaning ( this is a problem with many abstract words, especially those derived in agglutinative languages ).

For example, one might hold that numbers are particular yet abstract objects.

A more abstract example of an uncountable set is the set of all countable ordinal numbers, denoted by Ω or ω < sub > 1 </ sub >.

Chomsky has speculated that UG might be extremely simple and abstract, for example only a mechanism for combining symbols in a particular way, which he calls Merge.

An example of this would be an abstract factory class that provides interfaces to create a number of products ( e. g. and ).

For example, rather than explaining how the abstract for an article might be visually formatted, DocBook simply says that a particular section is an abstract.

As defined in linguistics, a sentence is an abstract entity — a string of words divorced from non-linguistic context — as opposed to an utterance, which is a concrete example of a speech act in a specific context.

For example, the abstract concept of number springs from the experience of counting discrete objects.

This abstract problem is relevant in many contexts: in VLSI circuit design, for example, one wants to minimize energy used by decreasing the amount of electric signals required between the different components during a distributed computation.

The following example shows how to use Bison and flex to write a simple calculator program ( only addition and multiplication ) and a program for creating an abstract syntax tree.

God knows what the African nations, who hold 25 per cent of the voting stock in the U.N. were thinking -- they may, for example, have been thinking of the U.S. abstention when the vote on Algerian freedom was before the Assembly -- but I think I have a fairly accurate notion of what the Negroes in the gallery were thinking.

According to bundle theory, an object consists of its properties and nothing more: thus neither can there be an object without properties nor can one even conceive of such an object ; for example, bundle theory claims that thinking of an apple compels one also to think of its color, its shape, the fact that it is a kind of fruit, its cells, its taste, or at least one other of its properties.

For example, he expresses a subjectivistic idea when he says to Rosencrantz: " there is nothing either good or bad, but thinking makes it so ".

An example of this line of thinking can be found in Russell's Introduction to Mathematical Philosophy.

Many people routinely engage in black-and-white thinking, an example of which is someone who labels other people as all good or all bad.

Drawing on Classical sources and upon their own internal interactions — for example, the hostility between the English and Irish was a powerful influence on early European thinking about the differences between people — Europeans began to sort themselves and others into groups based on physical appearance, and to attribute to individuals belonging to these groups behaviors and capacities which were claimed to be deeply ingrained.

" Jennifer Porter and Darcee McLaren wrote that McCoy is an " unintentional " example of how " irrational prejudices and fixations, wishful thinking and emotional reasoning, denial and repression, and unresolved neurotic disturbances " compromise " scientific rationality " in Star Trek.

A notable example is the now defunct belief in the Ptolemy planetary model that held sway until changes in scientific and religious thinking were brought about by Galileo and proponents of his views.

This is an example of the theoretical thinking shifting the emphasis from faith and theoretical principles such as sovereignty to the socio-economic logic, as Karl Marx did.

Any human movement which involves no conscious choice and thinking could not be an example of praxis or doing.

Heidegger, however, has on occasion appeared to take an opposing view, stating for example that " those in the crossing must in the end know what is mistaken by all urging for intelligibility: that every thinking of being, all philosophy, can never be confirmed by ' facts ,' i. e., by beings.

Merge is part of Universal Grammar whether it is specific to language or whether, as Chomsky suggests, it is also used for example in mathematical thinking.

For example, influences on thinking that originate from outside of an individual's consciousness were reflected in the ancient ideas of temptation, divine inspiration, and the predominant role of the gods in affecting motives and actions.

Aristotle, for example, stated that phantasia ( imagination: that which can hold images or phantasmata ) and phronein ( a type of thinking that can judge and understand in some sense ) also exist in some animals.

* The Cymbalista Synagogue is an example of modern architecture and new thinking in synagogue design-designed by Mario Botta, it accommodates Orthodox, Conservative, and Reform congregations in one structure and promotes dialogue and interaction

Since the 16th century, some grammarians, such as Louis Meigret or Dominique Bouhours, have claimed that the strict rules governing French word order ensure that the language conforms more closely to a natural order of thinking than Latin, for example.

For example, the superposition principle of quantum physics can be explained using the dialectical method of thinking — likewise the example below from dialectical biology.

For example they may not be able to pick up a phone when asked to do so, but can perform the action without thinking when the phone rings .< Ref name = Sathian >

Juan Gabriel Valdés, Chile's foreign minister in the 1990s, described the Chile Project as " a striking example of an organized transfer of ideology from the United States to a country within its direct sphere of influence ... the education of these Chileans derived from a specific project designed in the 1950s to influence the development of Chilean economic thinking.

For example the presence of an anomalous medieval pottery sherd in what was thought to be an Iron Age ditch feature could radically alter onsite thinking on the correct strategy for digging a site and save a lot of information being lost due to incorrect assumptions about the nature of the deposits which will be destroyed by the excavation process and in turn, limit the sites potential for revealing information for post-excavation specialists.

In higher-level tournaments, such as the Kisei tournament, the player's time is often composed entirely of byo-yomi periods ( for example, in an eight-hour game, the player may have 480 periods of one minute each ), rather than having a main block of thinking time.