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Abstraction in its main sense is a conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal signifiers, first principles, or other methods.
Concepts are defined as abstract ideas or general notions that occur in the mind, in speech, or in thought. They are understood to be the fundamental building blocks of thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science.
Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist." A more elaborate version was given by Gottfried Leibniz (1646–1716); this is the version that Gödel studied and attempted to clarify with his ontological argument.
Mathematics includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.
Nominalism is a philosophical view which comes at least in two varieties. In one of them it is the rejection of abstract objects, in the other it is the rejection of universals.
Ontology is the philosophical study of being. More broadly, it studies concepts that directly relate to being, in particular becoming, existence, reality, as well as the basic categories of being and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology often deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, and subdivided according to similarities and differences.
Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, reality is the totality of a system, known and unknown. Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology, which is a major branch of metaphysics in the Western philosophical tradition. Ontological questions also feature in diverse branches of philosophy, including the philosophy of science, philosophy of religion, philosophy of mathematics, and philosophical logic. These include questions about whether only physical objects are real, whether reality is fundamentally immaterial, whether hypothetical unobservable entities posited by scientific theories exist, whether God exists, whether numbers and other abstract objects exist, and whether possible worlds exist.
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and finding out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.
A data model is an abstract model that organizes elements of data and standardizes how they relate to one another and to the properties of real-world entities. For instance, a data model may specify that the data element representing a car be composed of a number of other elements which, in turn, represent the color and size of the car and define its owner.
Abstract and concrete are classifications that denote whether the object that a term describes has physical referents. Abstract objects have no physical referents, whereas concrete objects do. They are most commonly used in philosophy and semantics. Abstract objects are sometimes called abstracta and concrete objects are sometimes called concreta. An abstract object is an object that does not exist at any particular time or place, but rather exists as a type of thing—i.e., an idea, or abstraction. The term abstract object is said to have been coined by Willard Van Orman Quine. The study of abstract objects is called abstract object theory.
An entity–relationship model describes interrelated things of interest in a specific domain of knowledge. A basic ER model is composed of entity types and specifies relationships that can exist between entities.
A conceptual system is a system that is composed of non-physical objects, i.e. ideas or concepts. In this context a system is taken to mean "an interrelated, interworking set of objects".
In metaphysics, realism about a given object is the view that this object exists in reality independently of our conceptual scheme. In philosophical terms, these objects are ontologically independent of someone's conceptual scheme, perceptions, linguistic practices, beliefs, etc.
A conceptual model is a representation of a system, made of the composition of concepts which are used to help people know, understand, or simulate a subject the model represents. It is also a set of concepts. Some models are physical objects; for example, a toy model which may be assembled, and may be made to work like the object it represents.
In analytic philosophy, universality is the idea that universal facts exist and can be progressively discovered, as opposed to relativism. In certain theologies, universalism is the quality ascribed to an entity whose existence is consistent throughout the universe, whose being is independent of and unconstrained by the events and conditions that compose the universe, such as entropy and physical locality.
3D computer graphics, or three-dimensional computer graphics, are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images. The resulting images may be stored for viewing later or displayed in real time.
Mathematical beauty is the aesthetic pleasure typically derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians often express this pleasure by describing mathematics as beautiful. They might also describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the integer 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any integer is defined by their respective place in this structure of the number line. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
The arts refers to the theory and physical expression of creativity found in human cultures and societies. Major constituents of the arts include visual arts, literature, and performing arts.
In information science a conceptualization is an abstract simplified view of some selected part of the world, containing the objects, concepts, and other entities that are presumed of interest for some particular purpose and the relationships between them. An explicit specification of a conceptualization is an ontology, and it may occur that a conceptualization can be realized by several distinct ontologies. An ontological commitment in describing ontological comparisons is taken to refer to that subset of elements of an ontology shared with all the others. "An ontology is language-dependent", its objects and interrelations described within the language it uses, while a conceptualization is always the same, more general, its concepts existing "independently of the language used to describe it". The relation between these terms is shown in the figure to the right.
References
- ↑ Betancourt, Michael (February 2007). "A Taxonomy of Abstract Form Using Studies of Synesthesia and Hallucinations". Leonardo. 40 (1): 59–65. doi:10.1162/leon.2007.40.1.59 . Retrieved 27 October 2013.